Front Page Titles (by Subject) IV.: The Incidence of Unrestricted Majoritarianism - The Collected Works of James M. Buchanan, Vol. 10 (The Reason of Rules: Constitutional Political Economy)
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IV.: The Incidence of Unrestricted Majoritarianism - Geoffrey Brennan, The Collected Works of James M. Buchanan, Vol. 10 (The Reason of Rules: Constitutional Political Economy) 
The Collected Works of James M. Buchanan, Vol. 10 (The Reason of Rules: Constitutional Political Economy) Foreword by Robert D. Tollison (Indianapolis: Liberty Fund, 1999).
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The Incidence of Unrestricted Majoritarianism
In this and the ensuing sections, we shall attempt to derive the pattern of distributional outcomes that can be expected to emerge under majority rule, subject to a variety of institutional restrictions.3 Our object in doing this is to take political institutions more or less as we know them and ask, first, whether there is any theoretical presumption that political processes tend to generate greater “distributive justice” than, say, a predominantly market-oriented regime; and second, what restrictions on the operation of political institutions seem likely to be conducive to the pursuit of “distributive justice.” Throughout, we shall deal with an extremely simple, highly abstract model of majority rule.
Specifically, we shall consider a simple three-person community, composed of persons A, B, and C.4 All three vote, and all are assumed to cast their votes in accordance with their interests.5 There is no altruism; all aim to maximize their own real incomes.6 We define the length of a period to be the length of time between elections, so there is by definition one election each period. Finally, in order to focus solely on the distributional consequences of majority rule, we assume that the only thing government does is make transfers; that is, we abstract from any provision of public goods that the government may undertake.7 Because we wish to focus on the distributions that emerge, we shall depict all outcomes as a triplet of the form [a, b, c], where a is the total income of A, b the total income of B, and c the total income of C.
Consider, on this basis, the conceptual benchmark represented by the distribution under an entirely “free” market order. No transfers, either public or private, occur. This distribution will reflect individuals’ differing productive capacities, preparedness to take risks, propensities to accumulate, and differing histories. Therefore, we would not expect this outcome to reflect distributional equality, in general. We denote this “free-market outcome” by the vector M = [ma, mb, mc], where mi is the ith individual’s market income. Without loss of generality, let A be the richest and C the poorest, so that ma > mb > mc. The total of the m’s is national income more or less as conventionally measured.
Let us now introduce the prospect of governmental transfer, assuming that majority rule is the only operative constraint. As a point of departure, consider the case in which all transfers are “lump sum,” that is, total income can be redistributed at will without loss. Aggregate money income (and the aggregate wealth stock) are totally unaffected by the transfer process. On this basis, suppose initially that B and C form a decisive coalition. Then, clearly, they will rationally take all of A’s income (and wealth). To do otherwise would be to forgo income that the majority could costlessly appropriate and would prefer to have. The outcome will then be of the form L = [0, lb, lc], where lb + lc = YM. Note that no such outcome is stable. Outcome L can be defeated at the next election by a coalition between, say, A and B involving an outcome of the form J = [ja, jb, 0], where jb > lb, and ja + jb = YM; or alternatively by a coalition between A and C involving an outcome of the form K = [ka, 0, kc], where kc > lc and ka + kc = YM. Some such coalition in which two of the three parties are made better off must always exist. The situation here is the familiar one in public-choice theory (and in game theory) in which every possible outcome can be defeated under majority rule by some other. No outcome is inherently stable. Rather, we would expect continuous “cycling” as the composition of the decisive majority coalition changed. Nevertheless, whatever the precise identity of the majority coalition, all outcomes here will exhibit the same characteristic feature: the income of the minority member will always be driven to zero. Transfers will always be pushed to the confiscatory level.
We should note that parties to a prevailing majority coalition have an incentive to form binding agreements to maintain the coalition, for by entering such an agreement each majority member avoids a fifty-fifty chance of receiving a zero income in the next period. Of course, it would not be rational to refuse unilaterally to break the coalition. One could then lose only if one’s current partner decided to break the agreement. Despite the continuous pressure for a coalition to break down, however, the possibility that a particular minority will be exploited systematically over a long sequence of electoral periods cannot be ruled out.
Three general points should be noted about this simple model. First, given the assumption that all transfers are lump sum, it is clear that the “benchmark” pretax, pretransfer income distribution is of no significance at all. Each individual has an expected average income over any sequence of electoral periods of 1/3YM. No one is intrinsically “richer” than anyone else. Differential labor productivities or differential propensities to save or take risks exercise no influence at all on the distributional outcome, not even as some relevant point of departure. No one can properly be said to “own” anything, except what he can extract from the political process itself. And what the individual does extract is his only for the duration of the current electoral period. Here, the simple pie-carving analogy is perfectly proper. There is a fixed pie, and it is up for grabs.
Second, because the precise composition of the decisive majority at each point is unpredictable, each individual naturally has the same expected income over any future electoral sequence, namely 1/3YM. In itself, this equalization of expected incomes can be interpreted as a major step toward distributive justice, as normally construed. The equality of expected income, however, has to be evaluated in light of the fact that there will be, at any point in the electoral sequence, one party that has zero income. Moreover, there is the possibility that particular coalitions may turn out to be stable over many elections, in which event the same party will face totally confiscatory transfer policy for substantial periods. Given this fact, the failure of standard criteria of distributive justice to address distributions of fluctuating parameters seems a major inadequacy. The impact of majoritarian political process on distributive justice in this simple model remains rather unclear.
Third, the assumption of lump-sum transfers is highly unrealistic. The level of income generated under the majoritarian system will necessarily be reduced by the revolving ownership rights. Consider, for example, the incentives for A, currently a party to the majority coalition, to accumulate capital assets when he recognizes that there is at least a one-in-three chance that he will be the exploited minority in the next election and have his assets confiscated. Incentives to acquire skills that add to labor income, to take risks, or to pursue entrepreneurial opportunities are substantially muted by the fact that the individual expects to reap only a fraction of the attendant benefits. Furthermore, securing membership in the majority coalition is a privately profitable activity. If, as seems likely, the time and energy individuals devote to becoming part of the decisive coalition have positive value when used in alternative ways, the expenditure of such time and energy is a net loss to the community. Such losses fall under the rubric of “rent-seeking” losses and are being increasingly recognized as major sources of inefficiency in contexts where institutional structures create opportunities for private gain that do not involve increased production.8
All this implies that transfers can be “lump sum” only in a very narrow sense. It may, in any period, be profitable for the prevailing majority to confiscate all the minority’s income and assets, but in making plans for future electoral periods, all agents can be expected to bear in mind the prospect that they themselves will be minority members and that their assets will be confiscated. Therefore, there will be much less available for confiscation than there otherwise would be. In particular, the sum of posttax-transfer incomes will be significantly less than YM at all points in the electoral sequence.
In light of this fact, all may well be better off in the expected sense if restrictions are placed on taxes and transfers in order to limit redistribution from the minority to the majority at any point. Moreover, such restrictions would have a presumptively desirable distributional consequence in that the distribution would be less inequitable at each point in the electoral sequence. We shall therefore turn, in Section V, to a brief examination of various possible restrictions that might be imposed on the tax-transfer process.
[3. ]For a very general examination of some of the redistributional implications of majority rule, see James M. Buchanan, “The Political Economy of Franchise in the Welfare State,” in Capitalism and Freedom: Problems and Prospects, ed. Richard T. Selden (Charlottesville: University Press of Virginia, 1975), pp. 52-77.
[4. ]These “persons” can be conceived as standing for completely homogeneous groups of equal size.
[5. ]This assumption is by no means unexceptionable, as we have argued elsewhere. See Geoffrey Brennan and James Buchanan, “The Logic of the Levers” (Center for Study of Public Choice, Fairfax, Va., 1983, mimeographed). It does, however, follow conventional public-choice practice and is highly convenient here.
[6. ]In Chapter 4, we attempted to justify this assumption as an analytically appropriate tool.
[7. ]This assumption is a “fudge.” A market order requires institutions to protect property rights and enforce contracts, and such institutions require access to resources in order to function. Taxes will then not be zero in the absence of transfers. However, it is useful to assume that there are no taxes in the zero-transfer case.
[8. ]For extended treatments of this phenomenon, see James M. Buchanan, Robert D. Tollison, and Gordon Tullock (eds.), Toward a Theory of the Rent-Seeking Society (College Station: Texas A&M University Press, 1980).