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Appendix - James M. Buchanan, The Calculus of Consent: Logical Foundations of Constitutional Democracy 
The Collected Works of James M. Buchanan, Vol. 3. The Calculus of Consent: Logical Foundations of Constitutional Democracy, with a Foreword by Robert D. Tollison (Indianapolis: Liberty Fund, 1999).
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Foreword, coauthor note, and indexes © 1999 Liberty Fund, Inc. The Calculus of Consent, by James Buchanan and Gordon Tullock © 1962, 1990 by the University of Michigan.
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Marginal Notes on Reading Political Philosophy
Neither of the authors of this book is a full-fledged political scientist by disciplinary specialization and training. Moreover, even within the ranks of the acknowledged professionals, political theory and political philosophy constitute subdisciplines of substantial independence. It would, therefore, be presumptuous in the extreme for us to claim here that we have mastered even the accepted “classics” of political philosophy sufficiently to measure our own preliminary investigations and analysis against some wider criteria than our own subjective standards.
We are well aware, however, that the problems of social organization discussed in this book are among the most important that learned philosophers have debated throughout recorded history. Our work could, quite properly, be charged with serious omission if we should fail to include what must be, at best, relatively uninformed commentary on the classical treatment of some of these problems. Therefore, it appears useful in this Appendix to offer some marginal comments that have been prompted by a reading of some of the selected works in political philosophy. We hope that these notes will be helpful in relating our analysis to what has gone before and in pointing up the differences which, in our view, make the analysis contained in the main text of this book essentially unique.
Politics, Morals, and the Methodology of Political Science
“What ought to be” is the primary normative question. “What is” remains the basic positive one. The distinction has separated the moral philosopher on the one hand from the scientist on the other, but the dichotomy so achieved is too simple in relation to the problems that arise in political theory and philosophy. At the beginning of the text of this book, we stated that political philosophy has been concerned with what the State ought to be while political theory has been concerned with what the State is. Note that, even in such a purely introductory and nonrigorous statement, it was necessary to move beyond the simple form of the normative-positive dichotomy. A subject for the “ought” and “is,” the State, was introduced; and this apparently slight change gives rise to a whole set of particularly difficult problems.
The State, or the polity, may be conceived as a set of rules or institutions through which individual human beings act collectively rather than individually or privately. That is to say, we may best describe what is normally called “the State” in terms that specify such rules and institutions. As we have previously emphasized, all attempts to make the State into more than this are regarded as falling entirely outside our frame of reference in this book. It seems unnecessary for us to compare our constructions with those of scholars who, at base, have adopted organic conceptions of collective life. A given set of rules describes a social organization, a political order. In discussing this order a useful, indeed an essential, line may be drawn between positive and normative theory. A positive science of politics should analyze the operation of an existing, or a postulated, set of rules for collective decision-making quite independently of the efficacy of this set in furthering or in promoting certain “social goals.” A normative theory of politics should, by contrast, array the alternative sets of rules in accordance with their predicted efficiency in producing certain ends or goals which should be, if possible, made quite explicit. Normative theory must be erected upon and must draw its strength from the propositions of positive science, but it is only when this extension of normative theory is made that “reform” in existing institutions can be expected to emerge from specialized scholarship. Indeed the only purpose of science is its ultimate assistance in the development of normative propositions. We seek to learn how the world works in order to make it work “better,” to “improve” things: this is as true for physical science as it is for social science.
Political science, normative or positive, is a science of human action; or, to adopt modern terminology, it is a behavioral science. The social order which is its subject matter consists, finally, in a network of human actions, human relationships. Moreover, individual behavior is not wholly predictable or predetermined, even when some allowance is made for stochastic variation. Individual human beings can make errors, and they can deliberately choose differently from the ways which, in fact, they do choose. Saying this, of course, commits us to a definite, but still debatable, philosophical position. However, the validity or the invalidity of presuming individual freedom of will is only indirectly relevant to the main point to be made here. This is that once individual behavior is introduced as a variable in the study of the social order under analysis, a second whole area of normative theorizing is opened. Moreover, as the whole history of political philosophy so amply demonstrates, it becomes very difficult to separate norms for the organizational structure—for the rules within which individual actions take place—from norms for regulating individual behavior itself.
The introduction of an analogy with the science of political economy may be useful in clarifying the distinction that is of central importance here. Here, as in politics, the study involves a social organization, the social order that relates the separate economic activities of individuals to each other. Here, also, a set of positive propositions may be derived, and, on the basis of these, normative propositions aimed at “improving” the working of the economy may be developed. However, students and scholars alike have continued to confuse this essentially appropriate normative theorizing with a second sort which relates to “improving” individual achievement in the operation of any specific economic setting. Many ill-informed scholars and students, especially those who work on the fringes of the discipline, conceive the study of economics to be aimed primarily at establishing norms for the earning of higher incomes by individuals and higher profits by business firms. The normative statements of economics are conceived to take the form of demonstrating to the individual what he should do (how he should behave) in order to further his own position in the economy vis-à-vis that of his fellows. Properly understood, this is not at all the subject matter of political economy: the latter is concerned with the norms for individual behavior only insofar as these norms determine individual action which, in turn, becomes data to the analysis of social organization.67
Having generated considerable confusion in economics, where by comparison the distinction is relatively straightforward, it is not surprising that the fully analogous but far more subtle distinction has been blurred in political theory. To compare the study of business administration with that of political obligation may appear ridiculous at first glance, but a moment’s reflection will reveal that methodologically the two are precisely analogous in their relation to economics on the one hand and to politics on the other. The science of politics, normative and positive, should be confined to the study of the political order. The positive aspects of this science should include the derivation of propositions that are conceptually refutable. The normative aspects should involve the construction of proposals aimed at securing “improvement” in the social organization (in the political order of affairs)—“improvement” being measured against some postulated set of goals derived, finally, from a fundamental ethical position. As with the science of economics, the behavior of the human actors in the process should be incorporated as data in the underlying positive analysis. There should be a sharp distinction made between the norms for ordering this individual behavior and those for improving or reforming the social order itself.
This basic distinction has never been made sufficiently clear. As a result the history of political theory-philosophy has been one of “politics and morals.” Few modern theorists who discuss the underlying conceptual basis of polity have been able to free themselves of the compulsion to discuss political obligation. The obligation or the duty of the individual citizen to obey the law, to abide by the will of the majority, to act collectively in the “public” rather than in the “private” interest: these have occupied center stage in much of modern political philosophy.68 These are, of course, vital and significant issues, but it should be recognized that they raise questions of personal morality. As problems, they do not belong properly in political theory. Political obligations, as accepted by the average citizen and as revealed in his political behavior, become (or should become) data to the political theorist. The task of the theorist here does not include the derivation of normative propositions relating to these duties of citizenship or these responsibilities of rulers. Along with the economist and other social scientists, the political theorist should take his human actors as he finds them.
It should once more be emphasized that this proposed separation of politics from morals does not suggest that the political theorist remain purely positivist. There remain normative aspects of political theory, quite apart from morals. These aspects relate to proposed “improvements” in the political order, in the institutions of politics, and not to improvements in individual behavior. Problems of social organization need not be moral problems.69 The separation called for is not, however, so straightforward as the above paragraphs might have initially suggested. The methodological breakthrough is complicated by the fact that questions or issues of political obligation (of personal morality) arise in two distinct places. First, there is the question concerned with individual obedience to or acquiescence to the sovereign will, independent of the manner in which this will is itself determined. Secondly, there are those questions concerned with the moral precepts to be employed in determining this will (in the making of the law): that is, the obligation, duty, or responsibility of the prince, the bureaucrat, the cabinet minister, the legislator, or even the ordinary elector, to act in a certain way in his capacity as decision-maker, law-giver, for the collectivity. Both of these obligations—that of citizen and that of ruler—involve moral issues, and both require the introduction of norms for individual behavior. It is relatively easy to see that if the State is conceived at base to be nothing other than a continuing embodiment of the sovereign will, and, further, if it is assumed that this will is the only meaning of law, any “improvement” or “reform” can only come through some change in the behavior of individuals. Under this conception of political order it becomes impossible to separate politics from morals.
The point to be made can be most clearly illustrated with reference to the genuinely absolutist ruler. Under such a regime, making the State what it “ought to be” in terms of any postulated ethical standard reduces quite simply and quickly to making the prince “behave” differently from the way that he does, in fact, behave. In this model it is not possible to separate the moral choices of the prince from the institutional setting within which these choices are made and implemented. There would be little point in making any attempt at separation in any case since, by hypothesis, the institutional setting itself can only be modified by the action of the prince himself.
The divorce of politics, as a science, from political obligation, as a moral problem, can only be accomplished if the institutions through which collective decisions are made are themselves subject to variation (to change) only as a result of a second or “higher order” kind of collective decision-making process. Only if the “constitutional” decision, as we have called it, can be separated from operational collective decisions (that is, from those decisions that are taken within predefined constitutional rules) can political science emerge independently from the rather murky discussions of political obligation. The achievement of this independence seems to have been one of the essential logical purposes or aims of the contractarian approach to political philosophy, despite its obvious shortcomings and despite the confusion that has served to obscure this aspect in modern discussion of contract theory.
As the political order is shifted away from absolutism and toward democracy, the distinction called for here can be more clearly made. A genuine “science of politics” can be developed that is almost wholly independent of moral philosophy. This “social” science can include both positive and normative elements, but the variables with which it deals are social institutions, rules of the political game, not human motives. Insofar as this science becomes normative, ethical questions must remain, but these do not pertain to precepts for ordering individual behavior in acceding to or participating in collective decision-making. Within “political science,” so limited, the scholar who proposes to answer the question “What ought the State to be?” must first make an explicit ethical choice. The information that he provides to the external observer then becomes as follows: “Given these ends for society, the set of rules describing the political order that would come closest to achieving these ends is as follows....” In this process the political scientist may specify the goals of social organization as broadly or as narrowly as he chooses. He may restrict himself to presenting his own personalized view of the “good” political society, always constructed from the behavior of real human beings rather than that of idealized “good” men. Or, by contrast, the political scientist may try, as best he can, to develop the normative implications of a set of ethical standards that he thinks should command widespread acceptance among all members of the social group. The point to be made is that, in either case, he must take men as they are, not as he would like them to be.
The normative aspects of the theory developed in this book are more restricted than either of those mentioned. We have tried to develop a “theory” of the political constitution. This theory is based on an analysis of specific rules for collective choice-making, given certain well-defined assumptions about human behavior in political action. On the basis of this analysis, we have then tried to answer the question: What set of rules should the fully rational individual, motivated primarily by his own self-interest, seek to achieve if he recognizes that the approval of such rules must embody mutual agreement among his fellows? Stated somewhat differently: What is the structure of the political constitution that will maximize “efficiency,” in the broadest sense, for all individuals in the group, independently considered? As we have suggested earlier, the approach taken requires a minimum of ethical premises. We assume only that individuals are the relevant philosophical entities to be considered and that all individuals are to be considered equally capable of choosing. We have been concerned primarily with demonstrating the calculus through which constitutional decisions might be made, not with the precise configurations of the political institutions that might result from the calculus.
We have assumed that the individual whose calculus we have analyzed (the “representative” or the “average” individual) is motivated by self-interest, that his fellows in the constitutional decision are similarly motivated, and that, within the chosen set of rules for collective choice, individual participants are likewise directed. As we have suggested, this assumption about human motivation is perhaps the most controversial part of our analysis. It seems useful to repeat, in this methodological context, that, by making this assumption, we are not proposing the pursuit of self-interest as a norm for individual behavior in political process or for political obligation. The self-interest assumption, for our construction, serves an empirical function. As such, it may or may not be “realistic”: this can only be determined by a comparison of some of the positive analytical implications with observable real-world facts.
From this rather elliptic discussion of the relation of political science to moral philosophy and the place of our own construction in this respect, we may now try to suggest some of those “classics” which seem congenial. It is perhaps clear that most of the so-called idealist theory-philosophy of political order is quite foreign to our approach. Writers in this tradition concern themselves more or less directly with questions of political duty or obligation. By our suggested classification these works belong in moral philosophy, and we should look to these, not for help in devising reforms in political institutions, but for guidelines of an individual ethic. It should not be surprising, therefore, that the most “sympathetic” or “congenial” works are to be found among the “realists” in the history of political doctrine. Initially we look to Glaucon in Plato’s Republic, to Thomas Hobbes, and to Benedict Spinoza. Of these, and others within this tradition, only Spinoza’s work seems to have much in common with our own, and only his seems deserving of special comment.
In his Tractatus Politicus, published posthumously in 1677,70 Spinoza approaches the whole study of political organization in a way that seems surprisingly modern by our standards. First of all, men are assumed to be motivated solely by considerations of interest. This is an underlying assumption of the models through which Spinoza examines alternative organizational arrangements. He states, quite specifically, that human behavior is taken as an empirical fact and that he makes no attempt to attach either praise or condemnation to the behavior that he observes. Spinoza examines the various political institutions in terms of their efficacy in producing results which he holds to be desirable. To him, political institutions are variables subject to change and perfection, and he conceives the primary task of the political scientist to be that of analyzing the workings of alternative organizational structures and of making such recommendations for change as seem indicated. His work on the political order anticipates, in many respects, that of David Hume and that of Adam Smith on the economic order. Spinoza deliberately sets out to construct political institutions in such a fashion that individuals acting in pursuit of their own interests will be led, by the institutional structure within which such action takes place, to further the interests of their fellow members in the political group.
The constitutional and the operational levels of collective decision-making are clearly separated in Spinoza’s work. For the latter, at least in his aristocracy model (his discussion of democracy was not completed), simple majority rule is acknowledged as appropriate for reaching decisions in legislative assemblies. For changes in the constitution, in the basic laws, “common consent” or relative unanimity is suggested. Spinoza’s work, in many respects therefore, may be taken as the most appropriately chosen classical precursor to that of this book. It should be stated, however, that Spinoza’s influence on our own ideas has been limited to his general and indirect effects on the Western intellectual tradition. In a specific sense, we have carefully reviewed Spinoza only after the completion of an initial draft of the main body of this book.
Although Spinoza is often described as a follower of Hobbes, we do not find Hobbes’ work at all similar to Spinoza’s in relation to our own construction. As we have suggested above, it seems essential that some separation of the constitutional and the operational level of decision be made before politics, as a social science, can be satisfactorily divorced from moral philosophy. If sovereignty is conceived as being necessarily undivided and indivisible, this essential separation cannot be made readily. The contractual apparatus, to Hobbes, becomes an excuse or a justification for political obedience of the individual and little more. Hobbes’ construction is aimed at establishing a basis for political obligation, whereas Spinoza’s construction becomes a genuine theory of political order that, more than most others, is largely divorced from all issues of obligation.
At this point, as elsewhere in this Appendix, it is necessary to refer to the work of David Hume. As we shall suggest in the following section, Hume did discuss issues of political obligation, and he made notable advances over the contractarian theorists in this respect. Hume recognized quite clearly, however, that the question of the obligation of the individual to obey the law was conceptually distinct from those questions that arise when alternative political orders are considered. He specifically divorces “political science” from “moral philosophy”: indeed the title of one of his essays is “That Politics May Be Reduced to a Science.”71 In this essay he states that the purpose or aim of the checks and controls provided by the political constitution should be that of making it “the interest, even of bad men, to act for the public good.”
Rational Choice of Restrictive Rules
As we have suggested, most of the important political philosophers have been concerned with the question of political obligation. In their discussions of this subject we may find points of departure that are helpful to an explanation of our work. John Locke and all of the writers who were responsible for developing the conception of “natural rights” made much of the distinction between the constitutional decision, which determines the rules for collective action, and the operational decision, which determines the shape of collective action within previously chosen rules. The individual, possessing certain inherent or natural rights, enters into a contractual relationship with his fellows, a relationship that is expressed in a constitution. The subsequent obligation of the individual to abide by the decisions made by the collectivity, so long as these are reached constitutionally, lies in his obligation to fulfill the contract once made. This basis of political obligation runs into immediate difficulty as soon as constitutional rules are made to apply to individuals other than those who might have been party to the original contract.
It is in this respect that the conceptions of David Hume appear most helpful, and they seem to have much in common with our own. Our basic analysis of the individual calculus that is involved in choosing among alternative organizational rules, in selecting a political constitution, has demonstrated that it will often be to the rational self-interest of the individual to select a particular rule that can be predicted to produce results on occasion that run counter to the self-interest of the individual calculated within a shorter time span. By shifting the choice backward from the stage of the specific collective decision to the stage of the constitutional decision, we have been able to incorporate the acquiescence of the individual to adverse collective action into a calculus that retains an economic dimension and that can still be analyzed in nonmoral terms. In this respect our immediate precursor is Hume, who quite successfully was able to ground political obligation, neither on moral principle nor on contract, but on self-interest. Hume did this by resorting to the idea that the self-interest of each individual in the community dictates the observance of conventional rules of conduct. These rules, which may or may not have been formalized in contract, are necessary for the orderly conduct of social affairs. This argument, which does not base political obligation on contractual obligation, allows the primary difficulty of the contract theorists to be neatly surmounted. Not only is it to the initial interest of parties to agree on conventional rules if such rules do not exist, but it is also to the continuing interest of individuals to abide by the conventional rules in existence. Hume recognized, of course, that, were it possible, the individual’s own interest would best be served by the adhering to the conventional rules of all other persons but himself while remaining free to violate these rules. However, precisely because such rules are socially derived, they must apply generally. Hence each individual must recognize that, were he to be free to violate convention, others must be similarly free; and, as compared to this chaotic state of affairs, he will rationally choose to accept restrictions on his own behavior.72
Individualism as an Analytical Method and as a System of Social Order
Many political philosophers, and especially those who have been concerned with the history of political doctrine, have not recognized the dual sense in which “individualism” may be employed as a descriptive noun identifying a theoretical-philosophical system. In the interest of clarity in discussion it seems useful to distinguish individualism as a method of analysis and individualism as a norm for organizing society. The fact that, in the development of political theory, those who have adopted the individualistic methodology have tended for the most part to adopt individualistic norms for social organization has served only to compound this particular confusion.
Individualism as an analytical method suggests simply that all theorizing, all analysis, is resolved finally into considerations faced by the individual person as decision-maker. Regardless of the role of the individual in the actual social-choice structure—whether he be ruler or ruled—analysis reduces to an examination of his choice problem and of his means or opportunities for solving this problem. To this approach is opposed that which starts from the presumption that some unit larger than the single person, some group of persons that includes two or more members, is the entity whose choice problems are to be examined. In this approach the individual member becomes an integral and inseparable part of the larger entity, and an independent-choice calculus for the separate parts is presumed meaningless. The individualistic method of analyzing political and social action is contrasted with the organic method, and these methodological differences need not, indeed should not, necessarily carry particular implications concerning the normative rules for organizing society.73
One of the primary purposes of the contract theorists of political order seems to have been that of reducing the logic of collective organization to a logic of individual calculus, or, stated somewhat differently, of deriving a logic, an “idea of reason,” as it was called by Kant, for collective organization from the individual-choice situation. These theorists asked the question: Can the existing organization of the State be “explained” as an outgrowth of a rational calculation made by individual human beings? In large part, the success or failure of the contract theorists should be assessed in these terms against their attempts to answer this question.
The individualist approach or method tends to obliterate any logical distinction or difference between the “public” and the “private” sectors of human activity. Collective action, along with private action, is motivated by individually conceived ends, and all action proceeds only after a mental calculus is performed by some individual or individuals. As decision-making or choosing bodies, individual human beings remain fundamentally invariant over the range of both private and public activity. All attempts of the political philosophers to distinguish sharply between “public right” and “private right” seem foreign to this approach.
Our theory of constitutional choice is avowedly individualistic in this analytical-methodological sense. Therefore, we react sympathetically to the works of those political theorists who have most clearly discussed the logic of collective organization in terms of an individual calculus and who have specifically rejected the conceptual demarcation between public and private sectors of human activity in the analysis of this choice problem. Johannes Althusius, who wrote very early in the seventeenth century, must be noted especially in this respect, for he seems to have been the first scholar who attempted to derive a logical basis for collective organization from contractual principles that were held to be applicable to all forms of human association. Later writers of the seventeenth and the eighteenth centuries, within the general contractarian tradition, followed Althusius on this point, although the emphasis on the common logical basis for public and private association tends to become less pronounced in their works than it is in Althusius’.74
We find a similar emphasis in the writings of Christian Wolff in 1750. Wolff’s work is also noteworthy because of his clear conception of the collective organization as a set of rules or institutions that are subject to analysis, to modification, and to reform. His method, like that of Spinoza, was that of examining alternative political institutions on which members of the community of rational individuals might agree jointly.75
The individualist methodology found another staunch defender more than a century later in A. Fouillée,76 and his work is important for our purposes because he recognized, more clearly than most other writers, the distinction discussed in this section: that between individualism as a method of analysis and individualism as a norm for social organization. He recognized that there exists no logical inconsistency between individualism as a method of deriving principles of social organization and collectivism as a descriptive characteristic of this organization. As we have suggested, an individualistic approach is contrasted methodologically with an organic one. Either approach may be employed conceptually as a means of presenting either individualistic or collectivistic ideas for social reform. Given certain underlying assumptions about human-behavior patterns, along with a specific ethical position, a collectivist political-economic order may be rationalized from a calculus of individual choice. Fouillée understood this, and he argued correctly that there was nothing internally contradictory in Fichte’s position which tended to be both individualist (contractarian) and socialist (collectivist). In our terminology Fichte’s position could be described as methodologically individualistic, up to a point, and normatively collectivistic. Among political thinkers Burke comes perhaps closest to representing the reverse position. As regards alternative systems of social order, Burke was anticollectivist. On the other hand, methodologically he was clearly anti-individualist, and he vigorously rejected all attempts to explain collective activity on the basis of rational individual choice.
It is perhaps not surprising that proponents of methodological individualism are to be found among French political theorists as a part of the reaction against the excesses committed in the name of Rousseau’s conception of the “general will.” Somewhat later than Fouillée we find the work of Leon Duguit. He rejected categorically the conception of “national sovereignty” as the foundation for a system of public law, and he attempted to construct an alternative system on the basis of the public-service State. Duguit saw the State, not as an organ of command exerting power over its subjects, but instead as a means through which public services may be provided to individuals. These services were said to be required because of the fact of social interdependence. To this point Duguit’s approach is similar to our own, which, at base, defines the political relationship in terms of co-operation. Duguit failed, however, to recognize that different individuals and different groups may desire different “public services” from the collectivity. To him, “public utilities” assume an objective character which, presumably, reasonable men can discover without great difficulty. He did not consider, therefore, the problem of the proper extension of public services. As a result his conception of the “public-service” State can easily be employed to provide a theoretical foundation for the growth of what is sometimes called the “welfare State.”77
Realism and Relevance in Contract
The contract theory of the State can be interpreted as representing both an attempt to divorce political theory from moral philosophy and as an attempt to derive a logic of collective action from an analysis of individual choice. Since our own efforts embody both of these elements, it follows that our work falls within the broadly defined limits of the contractarian tradition. It seems useful, therefore, to discuss some of the criticisms that have been advanced to this conception and to try to relate these to our analysis.
Both the contractarians and their critics have been too much concerned with the origins of government. The contractarians have discussed the original formation of government out of the voluntary consent of rational, previously “free” men. Their critics seem to have considered the contractarians demolished when they showed that such an original contract was, for all intents and purposes, a purely intellectual construction with little or no basis in reality. The relevance of the contract theory must lie, however, not in its explanation of the origin of government, but in its potential aid in perfecting existing institutions of government. Moreover, viewed in this light, some version of contractarian theory must be accepted in discussion about matters politic.
The origin of civil government and the major influences in its development may be almost wholly nonrational in the sense that explanation on a contractual basis is possible. Societies form governments and change governments for a variety of reasons, many of which remain mysterious and far below the level of objective, scientific analysis. Political institutions, like languages, get changed, almost beyond recognition, by the gradual and largely unconscious modification imposed on them by the movement through time. In this sense political society can be said to develop and to grow organically; and, if the purpose of investigation is solely that of explaining such growth, there is perhaps little purpose in inventing anything like the contractual apparatus.
It is clear, however, that the uncontrolled and the uncontrollable process of historical development is rarely called on to explain all changes in political society. If all change, from some origin to the present and beyond, is presumed to take place independently of conscious direction, political science, as a positive-normative discipline, loses its purpose. If, in fact, political institutions are not considered to be subject to rationally chosen modification and change, it is surely wasted effort to try to explain uncontrollable change. On the other hand, if it is accepted that political society is “perfectible,” that political institutions are subject to designed “improvement,” the analysis of alternative possible changes and the selection of criteria through which actual or potential changes may be judged become highly important tasks. At this level the explanations of the origin of civil government and the reasons for the major nonrational developments of this government are almost wholly irrelevant. Discussion must be concentrated on the “margins” of variation in political institutions, not on the “totality” of such institutions, and the relevant question becomes one of criteria through which the several possible marginal adjustments may be arrayed.
The contract theory, in this context, may be interpreted as providing one such criterion. Adopting the criterion implicit in the contract theory, the analysis of political institutions asks: On what changes in the existing set of rules defining the political order can all citizens agree? This embodiment of the unanimity rule for all basic, structural reforms in political institutions, in the constitution, reflects the individualistic ethic in its broadest sense. Other criteria for judging changes in the political constitution may, of course, be advanced. These may range from the purely personal criterion of the scholar who asks: What changes in the existing set of political rules do I think should be made?—to the more complex criterion introduced by the scholar who asks: What changes in the existing set of political rules would be “best” for the “greatest number” of individuals in the group, as I interpret their interests? Note, however, that such criteria as these, and any others that might be employed, must introduce a stronger ethical postulate than the individualistic criterion that the contract theory embodies.
In this interpretation the contract theory of the State in political theory occupies a position that is analogous to the Pareto rule for assessing changes in the more technical discipline of modern welfare economics. It may be useful to recall the discussion of Chapter 12 in the text. To define a position as Pareto-efficient or Pareto optimal does not suggest that all changes that have moved the group to that position were themselves Pareto optimal. On the other hand, to define a position as nonoptimal does suggest that there exists a means of moving to an optimal position in a Pareto-optimal manner. Applying this fully analogous reasoning to the contractarian terminology, we may say that the definition of an existing set of political rules (the constitution) as reflecting consensus implies only that there exist no particular changes on which all citizens can agree. Analogous to the Pareto-optimality surface, which contains an infinity of points, the fact that an existing set of political institutions reflects consensus, so defined, does not in any way imply that this set, and this set only, is the only “optimal” or “efficient” government. There must exist also an infinite number (conceptually) of other institutional arrangements which would similarly embody consensus. By contrast, the definition of an existing set of institutions as nonoptimal in the sense that it does not reflect consensus means strictly that changes are possible on which all members of the group may agree.
This interpretation of the contract theory, which divorces the existence of consensus from the means through which the existing situation has been produced, allows Hume’s criticism of the contractarians to be fully accepted without seriously weakening the usefulness of the construction itself in its provision of a meaningful criterion against which changes in political constitutions may be judged. Having advanced this “marginalist” interpretation of the contract theory, we do not suggest that an explicit statement of this interpretation is to be found in the writings of the contractarians. To our knowledge they did not make the essential distinction between the “total” and the “marginal” explanation of political constitutions. Strictly interpreted, therefore, their “theory” of government cannot be accepted. However, when an attempt is made to advance an alternative “theory,” one which will provide a useful criterion for evaluating constitutional change that is, in fact, controllable, some modified “marginalist” version of the contract approach seems essential. It is in this latter sense that the constructions of this book may be classified as falling within the contractarian tradition.
The Economic Approach to a Theory of Politics
As we have suggested in Chapter 5, the relatively recent work of William J. Baumol78 represents almost the only attempt to develop a theory of collective activity from the economic calculus of the individual citizen. Baumol’s work, in one sense, developed the political implications of modern welfare economics, grounding the logic of State activity squarely and quite properly on the existence of external effects resulting from the private behavior of individuals. We believe that our work extends that of Baumol in two essential respects. First, as we have noted, the generalized-externality argument is applied to the constitutional problem, the choosing of decision-making rules. Secondly, the essentially economic approach embodied in the concentration on alternatives open for choice is more fully analyzed. The existence of external effects from private behavior has been shown to be neither a necessary nor a sufficient condition for collective action. A theory of collective action has been developed only after a careful consideration of the costs and the benefits expected to result from alternative organizational structures (alternative sets of rules).
In the literature of political theory-philosophy, a partial reading of which prompts this Appendix, it is not surprising that no narrowly conceived precursors to our work in this particular sense are to be found. The doctrinal developments in economics, on which our constructions are based, at least to some degree, have taken place during the period in which economics has existed independently of politics as a discipline. We do find, however, one rather neglected work in political theory that may be appropriately classified as being closely related to our own. It is again not surprising to discover that this work was written by one of the important figures of the Enlightenment and that it was completed during the last decade of the eighteenth century, although it was not published until a half century later. We refer to Wilhelm von Humboldt’s Ideen zu einem Versuch die Gränzen der Wirksamkeit des Staats zu bestimmen.79 Humboldt argued that the only legitimate sphere of collective action was that which included the provision of security to the individual against external attack and against the encroachment of his rights by his fellow men. The role of the State was that of removing or reducing the external costs of private action. As might be expected, Humboldt conceived the externality problem too narrowly. He rejected all efforts of collective action toward promoting the positive welfare of individuals. In so doing, he failed to recognize that, in an opportunity cost sense, the failure to take co-operative action when such is actually more “efficient” is precisely equivalent to the taking of positive private action that is detrimental to over-all “efficiency.”
It is in his careful discussion of the logic of State action in those cases of demonstrable externality, however, that Humboldt reveals clearly what was, at base, an economic approach. He recognized that the mere existence of spillover or external effects resulting from private action did not justify State action: the decision must rest on a comparison of the costs, in terms of the greater limitation on individual freedom, and the benefits, in terms of the greater security provided by some collective limitations placed on private behavior.80 He recognized that the function of theory in such cases cannot be that of laying down general rules; rather, this function must be that of “pointing out these moments of deliberation,”81 that is to say, to outline the mental processes or calculus through which such decisions must be reached.
Humboldt seems almost alone in his very clear discussion of the voluntary arrangements that would tend to emerge to remove the external effects of private action—arrangements that we have discussed at some length in Chapter 5. He argued that, where possible, such arrangements are to be preferred to State action because of the unanimity that is implicit in all voluntary arrangements.82 At the outset of his work Humboldt criticized other thinkers for their excessive concentration on the question concerning who should govern and their insufficient attention to the question concerning the proper sphere of government. He recognized clearly that these questions were closely related and that the first question was rather empty until and unless the second one was resolved. This criticism seems to hold with almost equal force against most of the modern works in political theory.
The Classical Conception of Collective Choice
To our knowledge no political philosopher has approached the question of choosing among alternative decision-making rules in a manner that is similar to that which we have attempted to develop in this book. A partial explanation for this may lie in the very fact that those scholars who have been interested in political theory have been philosophers. As such, they have tended to think of collective decisions in terms of “will.” If individuals differ in their desires for collective action, the decision-making rule must in some way determine whose “will” is to prevail. Individual or group interests, viewed in this way, tend to be treated as being mutually exclusive. Clearly the “will” of the majority and that of the minority cannot at the same time be prevalent. This whole approach to political process ignores or overlooks the possibility of quantifying individual or group interests. “Will” and “power” are terms that do not lend themselves readily to quantification.
By contrast to this “classical” approach, our approach is essentially economic, in that political decision-making is viewed, in the limit, as analogous to the determination of the terms of trade in an exchange. When individuals engage in trade, interests differ. Each individual desires to secure the most favorable terms of trade. However, no one draws from this the conclusion that the separate interests are mutually exclusive and that one must prevail over the other. Shall the “will” of the seller or the buyer prevail in a particular exchange? To the economist such a question is empty because “will” is meaningless unless specified more carefully. If it is defined as some maximum advantage from trade, the answer to the question must normally be that neither the “will” of the buyer or the seller prevails, although trade is observed to take place. On the other hand, if the term is defined as some improvement over an initial, before-trade position, the answer must be that both the “will” of the buyer and that of the seller prevail as a result of free exchange.
The point to be made here is that the very “vocabulary of politics” tends to focus attention too quickly on the particular problems presented under the existence of sharply defined and mutually exclusive alternatives. Choices at the ultimate constitutional level are interpreted as being of the “either-or” type. This is not to deny that such mutually exclusive choices do arise, and that when they do, decisions must be made. However, central to an economic approach to choice problems is the possibility of variation at the margin. If such variation is possible, choices become “either-or” only for small incremental changes; and, considering a total complex, some of all alternatives may be chosen. Interest in, or a desire for, a particular alternative becomes a function of its cost or price relative to the other alternatives available for choice. It is this functionally variable aspect that seems to have been almost wholly absent from the “classical” analysis of political decision-making. Practical politics has been traditionally recognized as consisting of the art of the possible—of the art of compromise. However, to our knowledge few political philosophers have recognized that once the necessity of compromise is acknowledged, alternatives are no longer considered as mutually exclusive, and the discussion that proceeds as if they were becomes largely irrelevant.
Although the theory presented in this book (as Appendix 1 indicates) had some foreshadowings in political science proper, its true intellectual roots lie in other areas. Economics and probability theory are its major sources, but it also owes a good deal to a series of investigations in a poorly defined field which I shall call the “strict theory of politics.” It is with this latter field that the bulk of this Appendix will concern itself, largely because any more general discussion of the history of ideas in economics and in probability is beyond both my competence and my interests. Nevertheless, some remarks about the development of probability theory and economics will be of assistance in setting the theory in its proper place among the disciplines.
The theory of permutations and combinations, which eventually developed into statistics, game theory, and modern decision theory, started out with the analysis of games of chance. A game of chance in its pure form involves a device of some sort which produces various results with varying probabilities. The initial work in what we now call statistics was an exploration of the relative frequency with which various results may be expected to appear. It might be regarded as an attempt to determine the proper way to place bets. Among gambling games, however, there are a number in which the gains or losses of some given player depend not only on the performance of a device but also on the actions of another player. In such games, although simple probability calculations are normally of some assistance to a shrewd player, they cannot give a complete set of instructions on proper play.
In these “games of strategy,” to use a modern term, if one party chooses a strategy, then this strategy will form part of the data which the other party should consider in choosing his own strategy. This is obviously true if each party announces his strategy, but it is also true if each party tries to conceal his strategy. In the latter case each will try to guess the other’s strategy, while choosing a strategy for himself which will not be anticipated by his opponent. In each case an individual’s choice of strategy depends on his opponent’s choice or on his estimate of his opponent’s choice. Examining the games with which they were familiar, the mathematicians discovered that any effort to specify the “correct” rules for a player wishing to win as much as possible led to an infinite regress. If the proper strategy for player A was strategy 1, then player B should take that fact into account and choose strategy 2, but if B chose strategy 2, then 1 was not the proper strategy for A, who should choose 3, etc. These early investigators, therefore, concluded that this type of problem was insoluble and confined their investigations to pure games of chance.
Since the investigations of these mathematicians developed eventually into the wonders of modern statistics, we can hardly criticize their decision, but other investigators had unknowingly found the clue to the solution of most strategic games. The presence of the infinite regress in games (in the old sense of the word, i.e., amusement games) is a contrived result. It comes from the fact that the games are human inventions and that the inventors aim at making games fair, interesting, and unpredictable. A well-designed game does lead to the infinite regress which disturbed the mathematicians, but there is no reason to believe that the real world has been carefully designed to be fair.83 In the real world the process of adjustment to the strategies of the other players may well lead to a perfectly definite result. Returning to the example in the last paragraph, it may well be that after player B has chosen strategy 4 and A has responded by choosing 5, neither can better himself by shifting to another strategy. Strategy 4 may be the best response to 5, and 5 the best reply to 4. In this event the parties have reached a situation which is called a “saddle point” in modern game theory.
A set of cases where the individual “players’ “ attempts to adjust to the strategies chosen by other “players” lead to a determinate result was early discovered in the economic field, thus establishing the science of economics. The early economists discovered that if a large enough number of people were engaged in buying and selling something and each attempted to adjust his strategy to the strategy (guessed or observed) of the others, then this would lead to a perfectly definite result.84 This result (the situation which would arise when each player had successfully adjusted his strategy to that of all the others, and no player still wished to make changes) was labeled by economists “equilibrium,” a term which is really operationally identical to the game theorists’ “saddle point.” If we were inventing a terminology de novo, I would opt for “saddle point” rather than “equilibrium” as the name for this condition. “Equilibrium” is widely used in the biological and physical sciences, but with a rather different meaning. This leads to a good deal of unnecessary confusion. It was not normally assumed that equilibrium would ever be achieved—there were always too many endogenous changes for that—but a continuous tendency to approach a continually changing equilibrium point was demonstrated.
This made human behavior in certain areas reasonably predictable. It further turned out to be possible to investigate what type of equilibrium would result from various “rules of the game,” and from this examination to decide which sets of such “rules” were most likely to lead to desired results. From this developed political economy, the science of improving social institutions. Economics progressed rapidly, and today it is by far the most highly developed of the social sciences. At the same time, the mathematicians were developing simple permutations and combinations into the wonder of modern statistics. Neither group appeared to recognize the existence of the relationship between the two fields that I have sketched above.
Eventually Von Neumann discovered a solution for two-person games of strategy. Specifically, he discovered two special cases in which the efforts of two players to adjust their strategies to each other would not lead to an infinite regress. The first of these two special cases—strict dominance, in which one of the players has among his possible strategies one which is superior to any other, regardless of what the other player does—is of no great importance for our present purposes. Clearly, this leads quickly and easily to a determinate result.
The second special case—the saddle point—is much more interesting. Assuming that there is no strict dominance, a game has a saddle point if the mutual efforts of the two players to adjust their strategy to each other would lead to a determinate result. This, of course, assumes that each player knows his opponent’s strategy, and Von Neumann, therefore, introduced a special and very interesting version of the economists’ “perfect knowledge” assumption. Von Neumann advises each player to act on the assumption that his opponent will make no mistakes; specifically, if player A is able to decide that strategy 2 is the proper one for him, he should realize that player B will also figure this out and choose his strategy on the assumption that A’s strategy is 2. Thus, strategy 2 can only be a good strategy for A if it is to his advantage, even assuming that B knows that A is using 2. It can be seen that all of this is simply a way of assuming perfect knowledge without using the magic words. In fact, the assumptions are much stronger than those used in economics since knowledge of another’s intentions is normally not included in the area where information is “perfect” in the economic model.
The reader will have noted that my explanation of game theory differs somewhat from that normally given. This is principally the result of my desire to emphasize the similarities between it and economics. In spite of the different approach, it seems likely that anyone familiar with game theory will realize that my description is operationally identical to the conventional one. One difference between game theory and economics, however, deserves emphasis. Game theory studies the behavior of individuals in a “game” with given rules. Economics does the same, but the end or purpose of the investigation in economics is to choose between alternative sets of rules.85 We study what the outcome of the “game” will be, but with the objective of making improvements in the rules.
Game theory normally accepts the “rules” as given. Under its assumptions the game with a saddle point does come to a perfectly determinate conclusion, and there is no infinite regress. This result, of course, comes from the structure of the game, and there is no implication that all games have a saddle point. If there is a saddle point, mutual adjustment of strategies will lead to a determinate equilibrium. Von Neumann, however, went further and demonstrated that a game which had no saddle point could be converted into a larger game in which the strategies of each party were decisions as to the type of randomized procedure which should be adopted to choose between the various strategies in the original game. This larger game has a definite saddle point in all cases, although it may be most difficult to calculate. These mixed strategies are most interesting ideas, although currently they can be computed for few real situations.
The application of this apparatus to the real world, begun by Von Neumann and Morgenstern and since greatly expanded by numerous others, has been one of the more important intellectual roots of our present work. With economics, it provided the bulk of our intellectual tools. Fortunately we were able to avoid the problems raised by mixed strategies, and, equally fortunately, the most recent developments in economics were almost perfectly suited to our needs. In particular, the recent developments in the theory of choice have been basic to our work. Specifically, we are indebted to modern game theory and modern economics for a theoretical apparatus and for three major guidelines for our investigation. (1) Modern utility theory, which has largely been developed by economists but which has also benefited greatly from the work of the game theorists, led us to concentrate on the calculus of the individual decision-maker. (2) From game theory in particular, but also from our economic background, we were led into a search for “solutions” to well-defined “political games.” (3) Political economy and the search for criteria in modern statistics led us into a search for the “optimal” set of “political rules of the game,” as conceived by the utility-maximizing individual.
The Search for a Majority Rule
In addition to these major fields of study, the much less well-known and undeveloped field which I have called “the strict theory of politics” has also influenced our work. In view of the rather limited number of people who are familiar with this field, it is necessary to discuss it in some detail. The strict theory of politics can be divided into three areas. The first of these, which has been named the “theory of committees and elections” by Duncan Black, will be the subject of this section. This will be followed by a section on the “theory of parties and candidates” and a final brief section on the “theory of constitutions.” My knowledge in the first area, like the title I have given it, comes almost entirely from the work of Duncan Black.86 I shall also follow his organizational example in separating the history of the subject prior to the mid-twentieth century from the modern period exemplified by Black and Arrow.
Black’s book contains, as Part II, an excellent discussion of the early history of the subject. I will, therefore, merely indicate the general outline of the work done before Black revived the subject and refer the reader to Black’s most excellent account for further details. The story begins with three French mathematicians and physicists writing in the period of the French Revolution. Borda opened the study and made important contributions. He was followed by Condorcet, who produced a study of the utmost importance which, unfortunately, was so badly presented that no one prior to Black appears to have understood it. Laplace added a few details to the structure as it stood. It should be noted that all of these men were much interested in the development of probability theory, and Condorcet presented his theory erroneously (this is the error which has led to his being so long misunderstood) as a branch of the mathematics of probability.
No one seems to have paid much attention to this work, and the only later development which Black was able to locate occurred in 1907 when E. J. Nanson produced a memoir on elections which clearly showed a familiarity with the work of Borda and Condorcet. His addition to the received theory was slight; the same can be said of the contributions of George H. Hallet and Francis Galton.
In the long interval between the development of the ideas of the three Frenchmen and their reappearance in the work of Nanson, another man had turned his mind to the problem. The Reverend C. L. Dodgson (Lewis Carroll), in addition to his work in formal logic and the Alice series, produced three pamphlets on voting methods. This subject is treated by Black in a particularly masterly manner, and I must refer the reader interested in the details to his account.87 Only two matters should be referred to here. In the first place, Black has succeeded in proving that Carroll’s work was entirely original; he had not taken his ideas from Borda or Condorcet. Secondly, it is clear that we have only fragments of Lewis Carroll’s work in the field. He was writing a book which was never printed, but the pamphlets themselves show unmistakable evidence of being only part of a much larger body of knowledge.
But so far I have talked about who and when, and totally ignored the what. What, then, were these people investigating? From the fact that their work attracted so little notice and that it tended to be forgotten and then reinvented,88 one might assume that it was not very important. In fact, I think that the tendency for the subject to be swept under a variety of rugs can be attributed to the importance of the challenge which it presented to traditional democratic doctrine. These investigators had found a problem which lay at the heart of traditional theory and which resisted all attempts to solve it. In a period in which democracy was almost a religion it is no wonder that most investigators turned aside.
Traditional democratic theory depends on majority voting. There are all sorts of problems about who shall vote (quorums, representation, etc.), but it is generally agreed that a majority of some group of people will eventually decide the issue. The problem which puzzled Condorcet, Carroll, Laplace, and Black was that involved in finding a system of voting which would lead to a majority which could reasonably be regarded as the genuine will of a majority of the group. To people who have not looked into the problem, this seems a foolish inquiry; it seems obvious that a majority is a majority and that is that. In reality the problem is a most difficult one.
In investigating the problem, all of the workers in this field used basically the same method. In the first place, they examined the problem of deciding an issue or group of issues in a single election. The investigation of logrolling, which interconnects different issues and different votes, was completely ignored by them. Presumably, they felt that this was more complicated than a single issue and hoped to develop a theory of logrolling after they understood the “simpler” problem. As we have shown in this book, logrolling eliminates the basic problem, so this whole line of investigation can now be regarded as simply an examination of the special case where there is no logrolling.
The second similarity in the methods of these investigators is that they all used the same mathematical device. They assume a number of voters confronted with a number of alternatives (candidates or bills), and they assume that each voter knows which of these alternatives he prefers. The more recent workers have used a matrix form of presentation in which each voter is represented by a vertical column and his order of preference by the place a given alternative occupies on that column.
Thus, voter v1 prefers A to B and B to C. From matrices of this sort it is possible to work out the results of various voting procedures, and research has largely consisted of assuming various preference orders and then testing out specific voting procedures on the assumed matrix. The problem which has puzzled the workers in this field has been the difficulty of discovering a procedure which does not lead to paradoxes.
If a group of people are confronted with the problem of making a choice between a number of different ways of dealing with a given problem, it may be that a majority of them have one of the possible ways as their most preferred alternative. If this is so, no problem arises;89 there clearly is a majority. More commonly, however, none of the possible courses of action is the first preference of a majority of the voters, a fact which is reflected in the popular view that democracy requires a willingness to compromise. If there are only two alternatives, of course, one will have a majority, and if there are only three, it is not unlikely that one will be preferred over all the others by a majority of the voters; but as the number of possible alternatives increases, the possibility that one will be preferred by a majority over all the others rapidly declines.
This being so, a number of procedures have been worked out for dealing with the problem of reaching a decision in cases where there is no alternative that is the first preference of a majority. These procedures may be divided into two general classes: those that reach a decision by some sort of manipulation of the votes but without a true majority; and those which restrict the choices confronting the voter in such a way that he is finally confronted with a choice between two, which naturally results in one or the other getting a majority. Two examples of the first type are: the system used to elect members of Parliament in England, where the candidate who receives the most votes is declared elected regardless of whether he has a true majority (this system is commonly called plurality voting); and, as our second example, each voter may mark his first, second, third, etc., preferences among the candidates. His first preference is then given, say, 5 voting points, his second 4, etc. The points are added and the candidate who has the most is declared elected.
The disadvantage of these systems is that they may elect people whom the majority of the voters dislike. To take an extreme example, suppose five men are running for some office. Candidate A is favored by 21 per cent of the voters; B, C, and D are each favored by 20 per cent of the voters; and E is favored by 19 per cent. A would be declared elected under the plurality system, although it might well be the case that 79 per cent of the voters would prefer B to A.90 Clearly, this is an odd result, and it is extremely hard to argue that this is the rule of the majority. The second method mentioned above is also subject to this difficulty. It, too, is likely to elect a man who is regarded as worse than some other candidate by a majority of the voters. In fact, all of the systems which fall in this general classification are subject to this criticism and hence cannot really be called majority rule.
Among those systems which rely on restricting choice in order to force a majority vote, we can again examine two examples. The first will be a system not infrequently used in private-club elections in which all candidates are listed, a vote is taken, and the lowest is discarded. The process is repeated until only two remain, and one of these will then gain a majority over the other.91 As in our previous examples, the result may be most unsatisfactory. It is quite possible for a candidate to be eliminated in the early stages who is preferred by a majority over the eventual victor. Again, is this majority rule?
All but one of the methods of forcing a majority by restricting choices are subject to this objection. The unique method which escapes this problem and which is used in almost all parliamentary bodies is to require that all votes be taken on a two-choice basis. Since only two choices are presented to the voters, one must get a majority of the votes cast. The rules of order are an elaborate and superficially highly logical system for forcing any possible collection of proposals into a series of specific motions which can be voted on in simple yes-no terms. In theory, all possible alternatives can be voted on in a series of pairs, each against each of the others, and the one which beats all of the others can reasonably be considered to have majority support. Unfortunately this process, which is the theoretical basis of all modern parliamentary procedure, leads directly into the worst of the voting paradoxes, the cyclical majority.
Suppose we have 101 voters who propose to choose among three measures, A, B, and C. Suppose further that the preferences of the voters among these measures are as follows:
Now we put the matter to a vote, taking each issue against each of the others. In the choice between A and B, A wins; in the choice between A and C, C wins; but, unfortunately, in the choice between B and C, B wins. There is no choice which can be considered the will of the majority. Nor is this a special and unlikely arrangement of preferences. No general function has yet been calculated to show what portion of possible preference patterns would lead to this result, but it seems likely that where there is any sizable number of possible issues and voters this is very common—quite probably this is the normal case.92
In actual parliamentary practice we never find examples of this sort of thing occurring. The most likely explanation for this would appear to be quite simple: most decision-making bodies which follow Robert’s Rules in taking decisions make a number of decisions, and consequently logrolling is possible. If logrolling is the norm (and it will be no secret to the reader that we think it is), then the problem of the cyclical majority vanishes. There are two other possible explanations for the absence of evidence of cyclical majorities in functioning parliamentary bodies, but they are both complicated and unlikely so I shall not attempt to discuss them here. However, one thing should be said: asserting that either of them was the correct explanation would, by logical implication, involve a very serious attack on the whole idea of democracy.
Thus the problem stood when Black took it up. Although he made some improvements in the analysis so far described, and produced the first comprehensive presentation of the matter, his principal contribution was his discovery of the “single-peaked preference curve.”93 It may be that the possible choices can be arranged on a single line in such a way that any individual will always prefer a choice which is closer to his own to any that is farther away. It seems likely that a good many of the issues in active political life are of that sort, particularly those that are involved in the familiar “left-right” continuum. Black demonstrated that in this situation no paradox develops. Voting on the issues in pairs, the normal parliamentary manner, simply leads to the alternative preferred by the median voter. Again, it is not obvious that this is “the will of the majority,” but at least it is nonparadoxical.
Black thus demonstrated that many issues are decided on in a manner which can legitimately be called “majority” rule, but there still remained those issues which were not “single-peaked” and which, therefore, led to the paradoxes which we have discussed. It was at this point that Kenneth Arrow published the only work in this field which has had any significant effect on the scholarly community.94 In spite of the difficulties of reading it arising from a quasi-mathematical style, Arrow’s book is widely known. Since I shall be somewhat critical of the book, I should start by saying that this relative fame is, in my opinion, quite justified. In detail, I think Arrow’s position is open to criticism, but he was the first to indicate, however vaguely, the real significance of the discoveries that we have been discussing.
All of the previous writers in this field have concerned themselves largely with attempts to develop procedures which would avoid the problems which we have been discussing. Arrow had the courage to say that they could not be avoided. Although his presentation was difficult and elliptical, the disproof of the “will of the majority” theory of democracy was implicit in his work. The impact of his book can readily be understood, and the rather forbidding format of his work, although it scared off potential readers, probably also gave it an appearance of rigor and logic which was very convincing. Altogether, the book was the sort which should have a wide impact, and it has had considerable effect.
Having said this, I wish now to turn to some criticisms of the book, at least as it now is interpreted. It should be noted that these criticisms do not go to the heart of Arrow’s achievement. They are basically disagreements with certain interpretations of his basic argument rather than with the argument itself. Arrow sets up a number of criteria which he feels any decision-making system should fulfill, and then presents a demonstration that voting does not meet them.
To start our discussion with an examination of some of his criteria, Arrow has been severely criticized for requiring “rationality” in the voting outcomes.95 His critics point out that any decision-making process is a device or instrumentality. It has no mind, and therefore we should not expect rationality. As a methodological individualist, I agree with Arrow’s critics, but, in the context of the time in which his book was published, the rationality or irrationality of the process was of some importance. It was published in 1951 at the end of a century in which democratic governments had steadily increased the proportion of decisions which were made by governmental means. At that time a large part of the intellectual community felt that the solution for many problems was that of turning operational control over to a democratic government.
If, however, governments are to serve this function of solving practically all problems and operating a very large part of the total economic apparatus, clearly they must function in a rational way. It is hard to argue that a given function should be transferred to the government if governmental decision processes are closely analogous to flipping coins. Thus, a person who believes in widespread government activities must at least be disappointed by irrationality in governmental decision-making processes. From the standpoint of the authors of this book, some irrational behavior on the part of the government is inevitable under any feasible decision-making rule. This fact should be taken into account in deciding whether or not to entrust a given activity to the government. Due to the predominance of processes in which votes are traded, where the particular type of irrationality described by Arrow is impossible,96 the basic irrationality of governmental decision-making becomes less important, but the impact of Arrow’s work on people whose views of the proper role of the government were more idealistic is readily understandable.
Arrow also says (p. 59): “Similarly, the market mechanism does not create a rational social choice.” As Buchanan has shown,97 this involves a misunderstanding of the nature of the market process. It does not produce a “social choice” of any sort, as such. Rationality or irrationality is here completely irrelevant. This is of considerable importance for our present work since democratic voting (in the view of the authors of this book) also does not produce a “social choice,” as such. Hence, here also “rationality” is not to be considered an absolute requirement.
The second criterion postulated by Arrow is independence of irrelevant alternatives. In England it is frequently the case that the Liberal party has no chance of electing an M.P. from a given constituency; nevertheless, the decision by the Liberal party on whether or not to run a candidate may be decisive as between a Conservative or a Labour victory. Thus, the outcome is dependent upon the presence or absence of an “irrelevant”98 candidate. In fact, this problem is simply the one we have discussed earlier: that a voting process may select a candidate who is considered less attractive than some other by a majority of the voters. Arrow chose to criticize the logical coherence of the result in keeping with his general approach. From our standpoint, the problem raised by these voting procedures is that they lead to results which are less desired by the majority than some other results.
Now it happens to be true that all voting procedures except the process prescribed by the rules of order, that is, taking all the feasible alternatives against each other in pairs, are subject to this problem.99 This being so, the criterion rules out all but one method of voting. Since the one remaining method is subject to the problem of the cyclical majority, it is clear that no method is available which will work without flaws. Nevertheless, if we simply try to find the best method, not the perfect one, it seems likely that our most promising field lies among the systems which are not independent of “irrelevant” alternatives.
The last of Arrow’s criteria which I wish to discuss is that the outcome should “not be imposed.” Arrow obviously included this criterion in order to rule out any method which would decide policy without regard for individual preferences. Unfortunately, the wording he chose rules out all possible voting rules except unanimity if there is logrolling. I do not think this was deliberate on his part, but in any event it is true. If decisions are made by some voting rule of less than unanimity and if they result from logrolling, then “there will be some pair of alternatives, X and Y, such that the community can never express a preference for Y over X no matter what the tastes of all individuals are.” By Arrow’s definition, therefore, the result is imposed.
An example will make the matter clear. Suppose we return to the road model, but this time we assume that the 100 farmers live in northern Michigan. We shall assume that road-repair work is impossible in the winter, but, on the other hand, people are too busy in the summer-crop season to engage in “politicking.” The normal procedure, therefore, is to vote on all road repairs in the winter but have the actual work done in the following summer. By early spring all the road-repair bills have been enacted, but none has yet been implemented. If the bargaining in the winter has proceeded to full equilibrium, then every individual farmer faces the prospect of spending more of his income in purchasing road repairs than he would freely choose. Suppose, at this point, it was proposed that 1 per cent less repairing be done on each road during the summer. On our assumptions this alternative would be unanimously approved if presented, but such an alternative could never be selected under simple majority rule.100
Thus, reaching decisions by a series of less-than-unanimous votes interconnected by logrolling violates the nonimposition criteria. Since we have pointed out at great length that the outcome will be nonoptimal, this does not disturb us greatly. It should be recognized that an imposed decision, in Arrow’s terminology, may be the best available outcome. To sum up, all means of reaching decisions by voting will, in at least some cases, reach rather unsatisfactory results. This fact should be taken into account in deciding whether some given activity should be carried on under conditions requiring decisions by voting, but it is not an insuperable obstacle to democratic government.
Turning now to Arrow’s proof of the general (im)possibility theorem, it should be noted that it is general possibility which is involved. Arrow is interested in the question of whether some given method of voting will, in every conceivable case, produce a satisfactory result. He proves that there is no voting rule which will meet this test in choosing between three or more alternatives. He does not, however, disprove the existence of a voting rule which functioned unexceptionably for 99,999,999,999,999,999,999,999,999,999 cases out of each 100,000,000,000,000,000,000,000,000,000. I suspect that complex combinations of the sort invented by Nanson101 can be built up to reduce the anomalies to any desired proportion. As in all other cases of successive approximations, the onerousness of the procedure would increase as a power of the accuracy.
The proof itself is extremely simple, although Arrow’s presentation of it is not. He assumes (p. 58, 30-1-2) the preference pattern which leads to a cyclical majority, and then demonstrates that it leads to a “contradiction.” (X is preferred to Y and Y is preferred to Z, but Z is preferred to X.) The form which he has chosen—discussion of the rationality of a nonthinking institution—is unfortunate, but it is still true that putting alternatives against each other in pairs does not lead to a final result if there is a cyclical majority. Of course, putting alternatives against each other in pairs is not the only method of voting. Arrow’s whole “proof” (pp. 51-59) makes no sense if it is applied to voting methods other than pairwise comparisons. In fact, Arrow’s insistence on “independence of irrelevant alternatives” eliminates all methods of voting except that used in his “proof.” He never proves this nor does he even mention that it plays this part in his reasoning, but since it is, in fact, true, he can be forgiven for this omission. In any event much can be forgiven the man who took the nettle in his hand. Arrow was the first to dare to challenge the traditional theory of democracy by saying that no voting rule leading to rule by “the will of the majority” was possible.
The Behavior of Politicians
The “theory of candidates and parties” treats politicians like entrepreneurs and parties like corporations or partnerships. It is based on the view that politicians want to get elected or re-elected, and that parties are simply voluntary coalitions of politicians organized for the purpose of winning elections. A corporation serves the individual economic ends of those who organize it, yet can be treated as a functional individual for some purposes. Similarly, a party serves the individual political interests of those who organize it, but can be considered as a unified body for some purposes. Altogether, this branch of investigation strongly resembles the “theory of the firm” in economics. In economics, of course, this was a relatively late development, coming long after political economy. Why it came early in politics, I do not know. It may merely reflect the fact that “strict political theory” has largely been developed in the fifteen years since the end of World War II, a very short period.
In any event this branch of political theory has been mainly developed by individuals whose basic training is in economics. The reasons for this are fairly clear. Although the subject matter is that normally studied by the political scientists, the methods are entirely economic. Almost any citizen of a democracy will know something about the subject matter of political science, but knowledge of the methodological technique of economics is not so universal. The average economist knows economic method and some political science, while the average political scientist has little facility with the mathematical techniques of the economist. Since the new field requires both a knowledge of economic method and political reality, it may be predicted that economists would come closer to possessing the desired combination of knowledge.
One can find certain foreshadowings of the “theory of candidates and elections” in the work of a number of modern economists. Hotelling102 and Schumpeter,103 in particular, made contributions. Basically, however, the theory has been developed by two people, Anthony Downs and myself. Since Downs’ book104 is fairly well known, even if not so widely read as might be hoped, while my contribution consists of a chapter in a book which has been circulated only in preliminary form,105 I may perhaps be forgiven if I emphasize my own contribution.
The formal theory in this field has been largely based on Duncan Black’s single-peaked preference curve. Although both Downs and I do discuss other possible structures, our basic picture of political preference can be equated to the left-right political continuum of the conventional political scientist. If we consider an individual candidate running for office, then both the desires of the voters for various governmental policies and the structure of the voting rules should be taken into account in determining his position on various issues. In working on this subject, I ignored the complex voting rules which have been developed by the theorists of committees and elections and confined myself to a few schemes. In one, the candidate must get 50 per cent of the votes to win, and it can readily be demonstrated that this will lead the opposing candidates to adopt closely similar positions on the issues. It also has a tendency to limit the number of active candidates in any one election to two.
Another possible scheme, much used in Europe, permits a number of candidates, say five, to be elected from each constituency. In this case, a candidate can insure his own victory by obtaining 20 per cent of the votes, and may win with less. Here, there is no tendency for the candidates to take similar positions; on the contrary, they will be spread over the full spectrum of voter opinion. These demonstrations carry over to party organizations too. The frequent lament that American and British parties are much alike, instead of representing different ideologies or, sometimes, classes, is thus a criticism of the voting rules rather than of our politicians. Further, although the European parties are ideologically different, government requires a coalition of such minority parties, and these coalitions are about as similar in their policies as are the two parties of the English-speaking world.
That the structure of the political alliances which we call parties is probably largely a reflection of the voting rules has been dimly realized in England since about the last quarter of the nineteenth century. Periodically, English scholars will argue that their system of single-member constituencies, with victory in the constituency going to whoever gets a plurality, leads to a two-party system. Undoubtedly it does have such a tendency, but the fact that since the last reform bill England has always had three parties, and that it has not infrequently been necessary to turn to coalitions between two of them to get a majority in Parliament, indicates that the tendency is merely a tendency. Still, it does seem likely that we would be able to deduce an “equilibrium” party structure from any constitutional voting scheme. Actually doing so with the rather complicated systems in use in most democracies must await further research. It would appear a particularly good field for an investigator looking for something important to do.
So much for my work, which covers a broad field rather lightly. Downs instead has covered a narrow field intensively. Basically he considers the British political system as it existed from 1945 to the date of publication of his book. From this system he removed the Liberal party, the House of Lords, and the University members, which will be generally accepted as only a minor simplification of the real world. He also made two structural changes of minor importance: elections occur at regular intervals instead of at the desire of the prime minister, and the Cabinet is elected directly by popular vote rather than indirectly through Parliament. Given the present organization of the parties in Great Britain, the latter is surely a permissible simplification, although it is startling at first glance.
Having produced this simplified model of what is already the simplest governmental system now in use in any democracy, Downs proceeds to analyze its functioning. Even at this highly simplified level,106 he finds it necessary to introduce a set of functions referring to information held by individuals and the cost of obtaining more. This series of functions is also of considerable utility in economics, but the problem of inadequate information is less pressing there. One of Downs’ more surprising conclusions is that a rational man will devote little effort to becoming well informed before voting. Since the mass of the voters clearly follow his advice, and since the traditional students of the problem continually call for more informed voting, it would appear that his approach is more realistic than those offered by the traditionalists.
This is a general characteristic of the Downs model—his conclusions are highly realistic. From a rather limited number of basic premises, most of which would not be seriously questioned, he produces by strictly logical reasoning a set of conclusions. These conclusions seem to fit the real world rather well, thus serving as a validation of the whole process. Among these conclusions are a number which we might call negative characteristics of democracy. These are matters, such as the relative lack of information of the voter, which have been widely noted but which have been regarded by traditional students as defects in the process. In the traditional view such defects result from failures on the part of the voters or politicians to “do their duty.” As a result, throughout the history of political theory there has been much preaching aimed at “improving” the voter. Downs’ demonstration that the voter was, in fact, behaving sensibly not only suggests why all of this preaching has been unsuccessful but also indicates that the preachers have been wrong.
There seems to be no point in further summarization of Downs’ main conclusions. He himself has included a summary after each chapter of his book and a final summary chapter listing all of his more important conclusions, and the curious reader can thus quickly gain the main points of his argument. If the summary leads the student on to read the whole book, so much the better. Discussion of possible further research in the field, however, does seem desirable.
In the first place, Downs’ supersimplified model of party government, taken by itself, can no doubt be further investigated. It has the very great advantage of being the easiest possible research tool. Further, many conclusions drawn from this very simple model will also be applicable to all party systems. Nevertheless, investigation of more complex systems would seem called for. Both Downs and myself have done some work on multiparty systems such as the French, but this is merely a beginning. Introduction of more complicated models should eventually lead to a good understanding of party dynamics in almost all of the democracies.
The internal politics of parties is, strictly speaking, not part of Downs’ basic model, but, in fact, he does discuss the situation of a minority within a party which is dissatisfied with the party policies. His conclusions fit the present crisis in the British Labour party very well, although they are far from a complete explanation. This field, however, is a particularly large one, and the connection between the individual active party member and the party itself should be a major area for further research. Again, it seems likely that investigation of systems more complex than that developed by Downs will be the eventual objective, but the pioneers would probably be wise to confine themselves to his supersimple model.
We, the People
The “theory of constitutions” concerns itself with a discussion of the effects of various possible democratic constitutions. These constitutions, in the book to which this essay is an appendix, are evaluated entirely in terms of their effects on individual citizens. Now that the subject has been opened up, it does not seem unlikely that others will attempt to use the same system—but without our consistent individualism. Whether this will be possible or not cannot be foretold, but at the moment the system is entirely based on individual preferences. This individualistic position raises no particular problems in connection with the “theory of committees and elections” and only apparent problems with the “theory of candidates and parties.”
In this book we have said little about parties107 and elected decision-makers. Although there have been some exceptions, we have normally assumed that decisions are made by direct popular vote. Where we have discussed elected legislatures, we have assumed that the legislator simply votes according to the majority preference in his district. This is obviously a simplification of the real world, and it might seem inconsistent with the role of the politician in the theory of candidates and parties. In fact, there is no inconsistency. The details have not yet been fully worked out, but the two branches of the “strict theory of politics” merely amount to looking at the same phenomena from two different viewpoints. The theory of candidates and parties investigates the methods of winning elections with the preferences of the voters and the constitution taken as constant. The theory of constitutions, as we have used it, investigates the constitutional method of maximizing the extent to which the voter achieves his goals with the behavior of politicians as a constant.
The pattern of behavior on the part of politicians deduced by Downs and myself is taken into account in the theory of constitutions. Again, there are problems in detail, but a politician aiming at maximizing his support in the next election will follow a course of action which fits neatly into the theory of constitutions. The situation is similar to the relationship between general economics and the theory of the firm. General economics proves that a certain social organization will maximize the degree to which individual desires are met. The theory of the firm investigates how individual businessmen or corporations achieve their ends. The two theories integrate neatly because both are based on the same basic assumptions about human behavior. These assumptions are also those of the theories of candidates and parties, and of constitutions; hence we may expect all of these theories to fit together.
The basic forerunners of the theory of constitutions in the strict theory of politics have been found in the work discussed in the second and third sections of this Appendix. However, there have been some investigators who have done preliminary work directly in this area. Buchanan demonstrated that the State must be considered as merely a device, not an end in itself.108 A State, qua State, does not have either preferences or aversions and can feel no pleasure or pain.109 Samuelson went on to point out that every citizen would agree to the establishment of the State because it provides a method of providing services needed by all.110 He also pointed out that this universal agreement would extend to an agreement to coerce individuals who attempted to obtain the advantages of membership in the State without paying the cost.
Another investigation relevant to the theory of constitutions was carried on by Karl A. Wittfogel.111 Although his principal field of investigation lay outside the area in which democracy has developed, the contrast between the “hydraulic” State and the “multicentered” State with which our own history deals greatly increases our understanding of our own institutions. From our standpoint, the main lesson to be learned is that the State should not have a monopoly of force. The oriental states were “too strong for society,” and we should do everything in our power to avoid a similar situation. The State should have enough power to “keep the peace” but not enough to provide temptation to ambitious men. The State should never be given enough power to prevent genuinely popular uprisings against it.
The work of Rutledge Vining had a major effect on both of us, largely through his emphasis on the necessity of separating consideration of what “rules of the game” were most satisfactory from the consideration of the strategy to be followed under a given set of “rules.”
A further area in which quite a bit of research has been done and which can, in a sense, be taken as supporting the position we have taken in this book is the statistical study of voting behavior. With the great modern development of statistical methods, it was inevitable that investigators would eventually turn to voting records as a source of information about politics. A great deal of work has now been done in this field, and a vast literature now exists consisting of statistical investigations of the influence of various factors on voting. We have not made any thorough attempt to survey this literature, but from what reading we have done it would appear that this work largely supports our basic position and contradicts the traditional view.
In addition to these investigations which influenced our work, we have found two clear-cut cases of previous work directly in the “theory of constitutions.” The first of these, by Wicksell,112 involves a fairly sophisticated discussion of an important constitutional problem together with recommendations for specific constitutional changes. The particular problem he discussed is now “one with Nineveh and Tyre,” but his approach is still of considerable interest. The second example is an article by J. Roland Pennock,113 a most elegant example of what can be done in this field. It had no influence on our work, but only because we had overlooked it when it first appeared and just found it recently.
Both Wicksell and Pennock overlooked the problem of the costs of decision in choosing the optimal constitutional rule. We are not in a position to criticize them on this point since we both made the same mistakes in our own earlier work. In Buchanan’s “Positive Economics, Welfare Economics, and Political Economy” and my “Some Problems of Majority Voting”114 the costs of decision-making are ignored, although these two articles clearly fall within the “theory of constitutions.”
In summary, although good work has been done in the field, the “strict theory of politics” is still an underdeveloped area. One of the purposes of this book is to attract resources, in the form of research work, into the field. There are few more promising areas for original work.
[67. ]The study of individual and business-firm behavior with a view toward establishing norms for improving strategic economic positions within a given organization of affairs is appropriately the task of “business administration.” The point here is that this whole field of scholarship must be kept rigorously separate from that of political economy.
[68. ]Cf. Isaiah Berlin, Two Concepts of Liberty (Oxford: Clarendon Press, 1958), p. 6.
[69. ]Cf. Ludwig Von Mises, Human Action (London: William Hodge, 1949), p. 2.
[70. ]Benedict Spinoza, A Treatise on Politics, trans. by William Maccall (London: Holyoake, 1854).
[71. ]Essays, Moral and Political: Selections, included in Hume’s Moral and Political Philosophy (New York: Hafner Publishing Co., 1948), pp. 295-306.
[72. ]Henry D. Aiken seems to overlook this basic point in his otherwise excellent introduction to selections from Hume’s writings. See Henry D. Aiken’s introduction to Hume’s Moral and Political Philosophy, p. xliv.
[73. ]For a discussion of “methodological individualism,” see Ludwig Von Mises, Human Action, pp. 41-44.
[74. ]Althusius’ basic work is Politica methodice digesta (1603-1610), ed. by C. J. Friedrich (Cambridge: Harvard University Press, 1932). I have also had the opportunity to consult in typescript a translation-in-substance of this work undertaken by Stanley Parry, C.S.C.
[75. ]Wolff’s ideas are discussed by J. W. Gough in his book, The Social Contract (2d ed.; Oxford: Clarendon Press, 1957), pp. 158-60. The original source is Christian Wolff, Institutiones Juris Naturae et Gentium (Halle, 1750).
[76. ]Fouillée’s work is discussed by Gough in The Social Contract, pp. 221-24. The particular work that seems directly relevant is A. Fouillée, La Science Sociale Contemporaine (1880).
[77. ]See Leon Duguit, Law in the Modern State, trans. by Frida and Harold Laski (London: Allen and Unwin, 1921). Note especially the interpretation that Laski placed on Duguit’s work in the Introduction.
[78. ]William J. Baumol, Welfare Economics and the Theory of the State (Cambridge: Harvard University Press, 1951).
[79. ]Wilhelm von Humboldt (Breslau: Eduard Trewendt, 1851). English translation: The Sphere and Duties of Government, trans. by Joseph Coulthard (London: John Chapman, 1854).
[80. ]The Sphere and Duties of Government, p. 125.
[81. ]Ibid., p. 126.
[82. ]Ibid., p. 128.
[83. ]Sometimes, of course, games are not well designed. Checkers, for example, involves a very much more limited number of possible combinations than chess. In recent years expert players have learned these combinations so thoroughly that the principal determinant of victory is who has the first move. Thus, checkers tournaments among experts now consist of a large number of games, most of which are won by the first player, and the decision over the entire series depends on the possible occurrence of mistakes in the play of one or the other player. For ordinary players, the regress, if not infinite, is still so long that the existence of genuine “correct” strategies has no effect on the game.
[84. ]One of the differences between the problem bothering the mathematician and the problem solved by the economist involves the number of independent actors in each “game.” While I think that this is less important than the difference between contrived “fair” games and natural situations, it does have some importance. The fewer the independent actors, the more likely that their mutual attempts to adjust their strategies to those of the other players will lead to an infinite regress. The attempt of the probability theorists to solve a two-person game was, therefore, an effort to solve the most difficult case. This should increase the respect we have for Von Neumann’s eventual solution.
[85. ]As many economists will already have guessed, I am indebted to Professor Rutledge Vining for this point.
[86. ]Duncan Black, The Theory of Committees and Elections (Cambridge: Cambridge University Press, 1958). The bulk of the theoretical material in this book was originally published in a series of articles in 1948 and 1949.
[87. ]Ibid., pp. 189-238. The pamphlets are also reprinted there.
[88. ]Black also reinvented the subject.
[89. ]Lewis Carroll raised questions even about this case using an analysis which, in effect, contrasted an intense minority and an indifferent majority. (Ibid., pp. 216-17.)
[90. ]This would certainly be so if the preference curves were single-peaked (see explanation below) on an array from A to E. As an example, simple plurality voting might have brought the Communists to power in France.
[91. ]In an effort to be brief, I do not give examples of all of the types of problems which I discuss. The reader who doubts my statements about the possible outcome of some system of voting should consult Black, where one can find proofs and examples.
[92. ]See Black’s work (pp. 50-51, 125-40, 173-74, and chap. XVI) for a proof which demonstrates that there could almost never be a majority for complex issues.
[93. ]I ignore chapters XII-XV and XVII in what follows, not because they are unimportant, but because they are not strictly relevant to our subject here.
[94. ]Kenneth Arrow, Social Choice and Individual Values (New York: John Wiley and Sons, 1951).
[95. ]Particularly by my coauthor, James Buchanan, in “Social Choice, Democracy, and Free Markets,” Journal of Political Economy, LXII (1954), 114-23. Reprinted in Fiscal Theory and Political Economy: Selected Essays (Chapel Hill: University of North Carolina Press, 1960). Duncan Black also has taken the position that rationality is a characteristic of rational beings, not of institutional arrangements. Arrow himself regards this criterion as weaker than his others. (Social Choice and Individual Values, p. 60, footnote.)
[96. ]If votes are traded, then the order of preference of the individual voter becomes less important than the strength of his preferences. The cyclical majority, vital to Arrow’s proof, results from the likelihood of certain orderings of preferences, together with the apparently obvious assumption that voters vote according to their preferences on each issue. Logrolling, which results in many voters voting against their own preferences on many issues, simply is not covered by Arrow’s book.
[97. ]“Social Choice, Democracy, and Free Markets.”
[98. ]The word “irrelevant” does not seem to me too good a descriptive term, but I cannot think of a better one. Arrow apparently got the term from E. V. Huntington, “A Paradox in the Scoring of Competing Teams,” Science (23 September 1938), 287-88.
[99. ]For some reason Arrow does not prove this proposition which is indispensable to his general proof. In fact, he does not even mention it. The criterion of independence of irrelevant criteria is introduced and explained on pp. 26-28, but its vital importance in eliminating all forms of voting except those prescribed by Robert’s Rules is never mentioned. Possibly he felt that it was obvious.
[100. ]This motion would be dominated by proposals to reduce repairs on 49 of the farmers’ roads by 2 per cent. Further, if it were known in advance that this sort of thing would happen, then it would be taken into account by the people in constructing their logrolling bargains. They would offer 1 per cent more than they expected to pay and demand 1 per cent more than they expected to receive.
[101. ]See Black, The Theory of Committees and Elections, p. 187. See also Condorcet’s system discussed by Black on pp. 174-75.
[102. ]Harold Hotelling, “Stability and Competition,” The Economic Journal, XXXIX (1929), 41-57.
[103. ]Joseph A. Schumpeter, Capitalism, Socialism, and Democracy (New York: Harper and Bros., 1942).
[104. ]Anthony Downs, An Economic Theory of Democracy (New York: Harper and Bros., 1957). Downs studied under Arrow, and Arrow’s influence on his work was significant.
[105. ]Gordon Tullock, A General Theory of Politics (University of Virginia, 1958), privately circulated.
[106. ]In order to avoid misunderstanding, I should point out that, although Downs has obviously obtained his basic model by the process I describe, it has wide implications and is not merely a theory of the operation of the British government.
[107. ]When we first considered undertaking this book, the possibility of thoroughly discussing parties was briefly considered. Generally speaking, the addition of formal parties does not change the conclusions we have drawn but adds a complicating factor to the reasoning. Further, in the United States, party discipline is very weak, and use of a monolithic-party model would have been completely inappropriate. Use of a weak-party model would have complicated the reasoning beyond endurance without changing the final conclusions much. Since the book showed signs of being too long anyway, we decided to put this matter off for future consideration.
[108. ]James Buchanan, “The Pure Theory of Government Finance: A Suggested Approach,” Journal of Political Economy, LVII (1949), 496-505.
[109. ]In nondemocratic states the preference schedule of an individual may be what the State device is intended to maximize; but the king is not the State, regardless of what Louis XIV said, and the State itself has no “welfare function.”
[110. ]Paul A. Samuelson, “The Pure Theory of Public Expenditure,” Review of Economics and Statistics, XXXVI (1954), 387-89.
[111. ]Karl A. Wittfogel, Oriental Despotism (New Haven: Yale University Press, 1957).
[112. ]Knut Wicksell, Finanztheoretische Untersuchungen (Jena: Gustav Fischer, 1896).
[113. ]J. Roland Pennock, “Federal and Unitary Government—Disharmony and Frustration,” Behavioral Science, IV (April 1959), 147-57.
[114. ]This article reappears in a somewhat modified form as Chapter 10 of this book.