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IV.: An Illustration - 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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We shall illustrate the difference between private and public choice with a simple example. A person is in a collective-choice setting that presents two options in t0, one of which will be chosen by the decision rule that combines individual expressions of preference between the two options. Each one of the options is expected to generate results that will be realized in t1, at which time a second pairwise selection between two later options will be faced. The “choice” emergent from the decision rule in t1 will, in turn, generate results that will be realized in t2. We shall truncate the sequence arbitrarily at t2 for the sake of simplicity.
The individual evaluates the expected payoffs from the perspective at t0. Figure 5.1 depicts the example in a tree diagram, with specific numerical values for expected payoffs, all of which are evaluated from t0. The initial options are A and B; which of these will command the expression of preference by our reference person, whose payoffs are as depicted? The “choice” will depend on what the individual predicts the subsequent collective “choice” at t1 will be. If the setting were purely private, with identical payoffs, the person would know that control over the options at t1 would remain internal. Hence, a reasonably high probability would be placed on the choice of a1 at t1, so as to allow the ultimate achievement of the highest present-valued payoff of 1,000. Despite the recognition that the person at t1 will be different from the chooser at t0, the latter’s subjective sense of continuity will make such a probability assessment rational. If the setting were one of private choice, therefore, A would be selected over B in t0.
The postulated setting is one in which the individual is one among many, however, and the decision is to be made for the collectivity as a unit, with the results applicable to all persons in the community. We are concerned with how the individual will express a preference between A and B in the voting booth at t0.
Our reference person may well vote for B rather than A in t0, reversing the revealed preference that might be exhibited in the private-choice setting. He may take this action because of his inability to place a high probability on the prospect that the collectivity, as a unit and via the operation of the existing decision rule, will, when faced with the options a1 and a2 at t1, select the a1 option, the result indicated to be the most desirable to the person in question. There is here no continuity of consciousness, no sense of quasi-permanent psychological unity. Even if the voter-chooser at t0 reckons that there will be no change in individual preference orderings, either in his own or in those of others, between the two time periods, a lower probability must be placed on the prospect that the decision rule will generate the most desirable result in t1. This lower probability stems from the fact that the individual has no way of knowing why others, who may be partners in the coalition that might express preferences for A in t0, order the options predicted to be faced at t1. Persons in such a prospective coalition may well order the alternatives in Figure 5.1 in precisely opposed fashion to the person whose payoffs are depicted.
To make our example even more specific, consider a risk-neutral voter in the large-number setting who has no knowledge of the preferences of others. Under simple majority voting rules, this voter will assign a .5 prospect to each alternative at each stage in the pairwise choice sequence. In the numerical example of Figure 5.1, the individual will then vote for B over A, despite the fact that the present value of the sequence Aa1 is higher than that of any other. If B is chosen, the individual enjoys the payoff of 600 units at t1. By contrast, if A is selected by the decision rule, there is only a .5 prospect that t1 having been reached, the rule will generate a1 at the critical second node.
A more general way of stating the central proposition of the analysis is to say that the individual participant in collective choice will find it difficult to make instrumental use of the collectivity in the furtherance of genuinely long-term objectives. “Investmentlike” collective alternatives will tend to be placed lower than “consumptionlike” alternatives in individual orderings. This basic reason for the limited time perspective exhibited in collective or public choice is quite different from other, more familiar reasons having to do with electoral term limits and the nonmarketability of individualized shares in “public good.”