Arthur T. Denzau, Amoz Kats; Expected Plurality Voting Equilibrium and Social Choice Functions, The Review of Economic Studies, Volume 44, Issue 2, 1 June

In a final section to our article in this Review, we pointed out problems that might arise in a democratic setting from attempts to provide publicly private goods that are easily exchangeable. In particular, we considered the case in which the political collectivity in question was a small part of a larger, open economy so that the publicly distributed good could be resold to individuals outside the collectivity. We then attempted to deduce the restrictions on the distribution of benefit shares and tax shares that were necessary for an equilibrium to involve public provision of the good at a finite level. In simplest terms, we argued that if, for example, the town of Blacksburg attempted to provide bread publicly and a majority of its citizen-voters faced tax prices less than the price at which they could export the good to the rest of the economy, then this majority coalition would support unbounded increases in the level of public provision of bread. The pursuit of these by the majority coalition would imply, of course, bankruptcy for the minority coalition. These types of problems, we argued, made it unlikely that easily exchangeable private goods would be publicly provided.' Robert Staaf and E. G. West (hereafter, S-W) have taken issue with this section of our paper on several grounds. First, they argue that even if the collectivity is a small part of an open economy, individuals would not vote for an unbounded amount of the private good to be publicly provided since this would exhaust individual and total community They seem to argue that a voter would not support a level of public provision if his implied tax bill exhausted his initial income. This clearly is not true for those voters with tax shares less than their benefit shares. These individuals would be perfectly willing to borrow to finance their tax bills since they earn significant arbitrage profits at the exchange stage. In essence, S-W assume that individuals cannot borrow even when they can so easily arbitrage between the domestic and outside market at a profit. Ruling out borrowing in this context is arbitrary and, of course, it is no surprise that it leads to a bounded solution. As a result, we find this criticism of our conclusion unconvincing. Staaf and West also assert that in an open-economy setting, public provision of a private good leads, through a sequence of voting, to convergence to income equality. In this case, they are not simply tinkering with our assumptions to generate different results; rather, they are making a serious logical error. They argue that since the outcome resulting from public provision of a private good with exchange within a period is equivalent to a certain income increase or decrease, the individual's income in the next period can be treated as if it actually were higher or lower by that amount. Alternatively put, they treat the individual's wealth at the exchange stage during one period as the relevant income or wealth variable for the beginning of the next period. This is simply incorrect. The value of an individual's wealth at the exchange stage, denoted w1, consists of his initial income or *University of Arizona and Virginia Polytechnic Institute and State University, respectively. We would like to thank Carolyn Weaver, Robert Tollison, and Geoffrey Brennan for their helpful comments. The research for this paper was supported by the National Science Foundation under Grant SOC76-22438. 'We went on to argue that public provision is more likely to involve those types of private commodities, such as services, for which price discrimination is feasible. Thus, the issue is not whether there will be public provision of private goods or not but rather what types of private goods are more likely to be provided publicly.

In the burgeoning literature on collective decision making, attention generally has been focused on the public provision of goods in equal quantities to all recipients. As a result, there has been little positive analysis of the effects of differential distribution of the benefits of public activities. This state of affairs contrasts with the more developed literature on the effects of differential distribution of the costs of public activities. By analogy to the tax share concept in the study of cost sharing, this paper examines the effects of differential benefit shares, or of changing benefit shares, on voting behavior at the individual and aggregate level in a majority voting model. Just as the early literature on cost sharing often assumed equal sharing by all and thus the same tax share for all, the assumption of equal quantities for all can be interpreted as equal benefit shares. This equal quantities assumption requires a distinction between production units (the units relevant for production and cost functions) and consumption units (the units relevant for individual preference relations).' This distinction immediately raises the issue of the distribution of public benefits, i.e., the transformation of production units into consuimption units. A benefit share measures the rate at which a production unit is transformed into an individual's consumption units.2 For example, in the case of a pure public good, without exclusion, the benefit shares would all equal unity. The problem this paper is concerned with can now be stated in its simplest form by the following example. Suppose that the state has made private trading in bread illegal. In lieu of market exchange, the government distributes the bread at a zero price, with the cost of the bread met through taxation. The total amount of the bread provided (units in production) is set by a majority vote, while the distribution of bread (units in consumption) is based on a fixed share arrangement. For example, if the total distribution is 100 loaves per week and Joe's benefit share is .02, then he receives 2 loaves per week. If the distribution scheme is changed-the fixed benefit shares are changed-how does this affect the total amount of bread (in production units) that voters will most prefer? On what factors does each voter's demand depend and how do these individual demands aggregate into market level results? Section IA examines the individual choice problem: how does an individual's most preferred public sector size change as his benefit share changes? Buchanan (1968, p. 54) conjectures that an individual with * Assistant professors, department of economics, and research associates, Center for Study of Public Choice, Virginia Polytechnic Institute and State University. We are indebted to the Ford Foundation for financial support of this research. We acknowledge the helpful comments of James Buchanan, Robert Parks and Theodore Bergstrom on earlier drafts of the paper. We are also deeply indebted to our late colleague Winston Bush who helped us launch our joint research. Earlier drafts of this paper were presented at the Southern Economic Association Meetings in Atlanta 1974, and in seminars at the University of Arizona and the University of Illinois. I This distinction is made in Buchanan (1966), further developed in Buchanan (1968, pp. 52-56), and is a major issue in the discussion between Albert Breton and Buchanan (1967). 2 Recent empirical work has explicitly utilized this distinction by assuming equal sharing in the consumption units. For examples of the use of the equal sharing assumption in the recent empirical literature, see Thomas Borcherding and Robert Deacon, Theodore Bergstrom and Robert Goodman, or Robert Spann.