Voting and Lottery Drafts as Efficient Public Goods Mechanisms

This paper characterizes interim efficient mechanisms for public good production and cost allocation in a two-type environment with risk-neutral, quasi-linear preferences and fixed-size projects, where the distribution of the private good, as well as the public goods decision, affects social welfare. An efficient public good decision can always be accomplished by a majority voting scheme, where the number of "YES" votes required depends on the welfare weights in a simple way. The results are shown to have a natural geometry and an intuitive interpretation. We also extend these results to allow for restrictions on feasible transfer rules, ranging from the traditional unlimited transfers to the extreme case of no transfers. For a range of welfare weights, an optimal scheme is a two-stage procedure which combines a voting stage with a second stage where an even-chance lottery is used to determine who pays. We call this the "lottery draft mechanism" Since such a cost-sharing scheme does not require transfers, it follows that in many cases transfers are not necessary to achieve the optimal allocation. For other ranges of welfare weights the second stage is more complicated, but the voting stage remains the same. If transfers are completely infeasible, randomized voting rules may be optimal. The paper also provides a geometric characterization of the effects of voluntary participation constraints.

[1]  E. H. Clarke.  Multipart pricing of public goods , 1971 .

[2]  H. Rosenthal,et al.  Digitized by the Internet Archive in 2011 With^ Funding from Testing Game-theoretic Models of Free Riding: New Evidence on Probability Bias and Learning , 2022 .

[3]  Roger B. Myerson,et al.  Optimal Auction Design , 1981, Math. Oper. Res..

[4]  E. H. Clarke.  Incentives in public decision-making , 1980 .

[5]  Robert M. Townsend,et al.  Resource Allocation under Asymmetric Information , 1981 .

[6]  John Orbell,et al.  The Minimal Contributing Set as a Solution to Public Goods Problems , 1983, American Political Science Review.

[7]  Theodore Groves,et al.  Incentives in Teams , 1973 .

[8]  C. d'Aspremont,et al.  Incentives and incomplete information , 1979 .

[9]  H. Rosenthal,et al.  Participation and the provision of discrete public goods: a strategic analysis , 1984 .

[10]  Claude d'Aspremont,et al.  Bayesian incentive compatible beliefs , 1982 .

[11]  E. Maskin,et al.  Optimal Auctions with Risk Averse Buyers , 1984 .

[12]  Kim C. Border.  IMPLEMENTATION OF REDUCED FORM AUCTIONS: A GEOMETRIC APPROACH , 1991 .

[13]  Jacques Cr.  Incentives and the Existence of Pareto-Optimal Revelation Mechanisms , 1990 .

[14]  Thomas R. Palfrey,et al.  Testing for effects of cheap talk in a public goods game with private information , 1991 .

[15]  Andrew Postlewaite,et al.  Asymmetric Information Bargaining Problems with Many Agents , 1990 .

[16]  E. Maskin,et al.  Advances in Economic Theory: The theory of incentives: an overview , 1982 .

[17]  A. Rapoport.  Provision of Public Goods and the MCS Experimental Paradigm , 1985, American Political Science Review.

[18]  W. Güth,et al.  The private supply of a public good , 1986 .

[19]  M. Satterthwaite,et al.  Efficient Mechanisms for Bilateral Trading , 1983 .

[20]  Matthew O. Jackson,et al.  Implementing a public project and distributing its cost , 1992 .

[21]  Steven A. Matthews.  On the Implementability of Reduced Form Auctions , 1984 .

[22]  H. Rosenthal,et al.  Private incentives in social dilemmas: The effects of incomplete information and altruism , 1988 .

[23]  R. Myerson,et al.  Efficient and Durable Decision Rules with Incomplete Information , 1983 .

[24]  T. Groves,et al.  Optimal Allocation of Public Goods: A Solution to the 'Free Rider Problem' , 1977 .

[25]  L. Hurwicz.  Outcome Functions Yielding Walrasian and Lindahl Allocations at Nash Equilibrium Points , 1979 .

[26]  T. Groves,et al.  Some limitations of demand revelaing processes , 1977 .

[27]  Louis-André Gérard-Varet,et al.  Utilitarian fundamentalism and limited information , 1993 .