Salvador Barberà

Voting by Committees

Problems of social choice frequently take the following form. There are n voters and a set K = (1,2,...,k) of objects. The voters must choose a subset of K. We define a class of voting schemes called voting by committees. The main result of the paper is a characterization of voting by committees, which is the class of all voting schemes that satisfy voter sovereignty and non-manipulability on the domain of separable preferences. This result is analogous to the literature on the Groves and Clarke scheme in that it characterizes all of the non-manipulable voting schemes on an important domain.

Handbook of utility theory

Preface. 14. Alternatives to Expected Utility: Foundations R. Sugden. 15. Alternatives to Expected Utility: Formal Theories U. Schmidt. 16. State-Dependent Utility and Decision Theory J.H. Dreze, A. Rustichini. 17. Ranking Sets of Objects S. Barbera, W. Bossert, P.K. Pattanaik. 18. Expected Utility in Non-Cooperative Game Theory P.J. Hammond. 19. Utility Theories in Cooperative Games M. Kaneko, M.H. Wooders. 20. Utility in Social Choice W. Bossert, J.A. Weymark. 21. Interpersonally Comparable Utility M. Fleurbaey, P.J. Hammond. Subject Index. Name Index.

Strategy-Proof Exchange

We consider the allocation of goods in exchange economies with a finite number of agents who may have private information about their preferences. In such a setting, standard allocation rules such as Walrasian equilibria or rational expectations equilibria are not compatible with individual incentives. We characterize the set of allocations rules which are incentive compatible, or in other words, the set of strategy-proof social choice functions. The social choice functions which are strategy-proof are those which can be obtained from trading according to pre-specified proportions. The number of proportions which can be accommodated is proportional to the number of agents. Such rules are necessarily inefficient, even in the limit as the economy grows.

Strategy-Proof Voting Schemes With Continuous Preferences

We prove that all nondictatorial voting schemes whose range has more than two alternatives will be manipulable, when their domain is restricted to the set of all continuous preferences over alternatives. Our result neither implies nor is implied by the original Gibbard-Satterthwaite theorem, except if the number of alternatives is finite, when they coincide. A new, direct line of reasoning is used in the proof. It is presented in an introductory section, which may be useful in classroom situations.

Top Dominance and the Possibility of Strategy-Proof Stable Solutions to Matching Problems

SummaryThis paper explores the possibility of designing strategy-proof mechanisms yielding satisfactory solutions to the marriage and to the college admissions problem. Our first result is negative. We prove that no strategy-proof mechanism can always choose marriages that are individually rational and Pareto efficient. This strengthens a result by Roth (1982) showing that strategy-proof mechanisms cannot always select stable marriages. The result also applies, a fortiori, to college admissions. Since finding difficulties with strategy-proofness is quite an expected result, we then address a second question which is classical within the incentives literature. Are there restrictions on the preferences of agents under which strategy-proof and stable mechanisms do exist? We identify a nontrivial restriction on the domain of preferences, to be called top dominance, under which there exist strategy-proof and stable mechanisms for both types of matching problems. The mechanisms turn out to be exactly those that derive from the most classical algorithms in the literature; namely, the womens optimal, the mens optimal and the students optimal. Finally, top dominance is shown to be essentially necessary, as well as sufficient, for the existence of strategy-proof stable matching mechanisms.

A Characterization of Strategy-Proof Social Choice Functions for Economies with Pure Public Goods

We characterize strategy-proof social choice functions when individuals have strictly quasi-concave, continuous and satiated utility functions on convex subsets of IRm, representing preferences for the provision of m pure public goods. When specialized to the case m=1, these assumptions amount to requiring that preferences are single peaked, and for such a domain there exists a wide class of strategy-proof social choice functions. These were studied by Moulin (1980) under strong additional assumptions. Our first results characterize the complete class, after an appropriate extension of the single-peakedness condition. The new characterization retains the flavour of Moulins elegant representation theorem. For the general m-dimensional case, previous results have shown that there is no efficient, strategy-proof, nondictatorial social choice function, even within the domain restrictions under consideration (Border and Jordan 1983; Zhou 1991). In fact, Zhous powerful result indicates that nondictatorial strategy-proof s.c.f.s will have a range of dimension one. This allows us to conclude with a complete characterization of all strategy-proof s.c.f.s on IRm, because restrictions of preferences from our admissible class to one dimensional subsets satisfy the slightly generalized notion of single-peakedness that is used in our characterization for the case m=1. We feel that a complete knowledge of the class of strategy-proof mechanisms, in this as well as in other contexts, is an important step in the analysis of the trade-offs between strategy-proofness and other performance criteria, like efficiency.

On the Weights of Nations: Assigning Voting Weights in a Heterogeneous Union

Consider a voting procedure where countries, states, or districts comprising a union each elect representatives who then participate in later votes at the union level on their behalf. The countries, provinces, and states may vary in their populations and composition. If we wish to maximize the total expected utility of all agents in the union, how to weight the votes of the representatives of the different countries, states or districts at the union level? We provide a simple characterization of the efficient voting rule in terms of the weights assigned to different districts and the voting threshold (how large a qualified majority is needed to induce change versus the status quo). Next, in the context of a model of the correlation structure of agents preferences, we analyze how voting weights relate to the population size of a country. We then analyze the voting weights in Council of the European Union under the Nice Treaty and the recently proposed constitution, and contrast them under different versions of our model.

Voting for voters: a model of electoral evolution

We model the decision problems faced by the members of societies whose new members are determined by vote. We adopt a number of simplifying assumptions: the founders and the candidates are fixed; the society operates for k periods and holds elections at the beginning of each period; one vote is sufficient for admission, and voters can support as many candidates as they wish; voters assess the value of the streams of agents with whom they share the society, while they belong to it. In spite of these simplifications, we show that interesting strategic behavior is implied by the dynamic structure of the problem: the vote for friends may be postponed, and it may be advantageous to vote for enemies. We discuss the existence of different types of equilibria in pure strategies and point out interesting equilibria in mixed strategies.

Extending an order on a Set to the power set: Some remarks on Kannai and Peleg's approach

Abstract Kannai and Peleg have shown that given an ordering over a set, it is impossible to induce an ordering over the power set satisfying certain plausible axioms. We prove an impossibility and also a possibility result in this context with closely related sets of axioms, and argue that the dividing line between impossibility and possibility here is rather thin. Also, we distinguish three possible intuitive interpretations for the formal framework of Kannai and Peleg, and argue that the acceptability of specific formal axioms may crucialy depend on the particular interpretation that one chooses to adopt.

Pivotal voters : A new proof of arrow's theorem

Abstract This paper presents a new proof of Arrows ‘General Possibility Theorem’, focusing on the way how ‘social’ preferences change in response to changes in the preferences of individuals, under given social welfare functions.