Sincere voting

Abstract: It has been conjectured that no system of voting can preclude strategic voting-the securing by a voter of an outcome he prefers through misrepresentation of his preferences. In this paper, for all significant systems of voting in which chance plays no role, the conjecture is verified. To prove the conjecture, a more general theorem in game theory is proved: a gameform is a game without utilities attached to outcomes; only a trivial game form, it is shown, can guarantee that whatever the utilities of the players may be, each player will have a dominant pure strategy. I SHALL PROVE in this paper that any non-dictatorial voting scheme with at least three possible outcomes is subject to individual manipulation. By a "voting scheme," I mean any scheme which makes a community's choice depend entirely on individuals' professed preferences among the alternatives. An individual "manipulates" the voting scheme if, by misrepresenting his preferences, he secures an outcome he prefers to the "honest" outcome-the choice the community would make if he expressed his true preferences. The result on voting schemes follows from a theorem I shall prove which covers schemes of a more general kind. Let a gameform be any scheme which makes an outcome depend on individual actions of some specified sort, which I shall call strategies. A voting scheme, then, is a game form in which a strategy is a profession of preferences, but many game forms are not voting schemes. Call a strategy dominant for someone if, whatever anyone else does, it achieves his goals at least as well as would any alternative strategy. Only trivial game forms, I shall show, ensure that each individual, no matter what his preferences are, will have available a dominant strategy. Hence in particular, no non-trivial voting scheme guarantees that honest expression of preferences is a dominant strategy. These results are spelled out and proved in Section 3. The theorems in this paper should come as no surprise. It is well-known that many voting schemes in common use are subject to individual manipulation. Consider a "rank-order" voting scheme: each voter reports his preferences among the alternatives by ranking them on a ballot; first place on a ballot gives an alternative four votes, second place three, third place two, and fourth place one. The alternative with the greatest total number of votes wins. Here is a case in which an individual can manipulate the scheme. There are three voters and four alternatives; voter a ranks the alternatives in order xyzw on his ballot; voter b in order wxyz; and voter c's true preference ordering is wxyz. If c votes honestly, then, the winner is his second choice, x, with ten points. If c pretends that x is his last choice by giving his preference ordering as wyzx, then x gets only eight points, and c's first choice, w, wins with nine points. Thus c does best to misrepresent his

Abstract: List of tables and figures Series editor's preface Preface PART I. INTRODUCTION: 1. Introduction 2. Duverger's propositions PART II. STRATEGIC VOTING: 3. On electoral systems 4. Strategic voting in single-member single-ballot systems 5. Strategic voting in multimember districts 6. Strategic voting in single-member dual-ballot systems 7. Some concluding comments on strategic voting, PART III. STRATEGIC ENTRY: 8. Strategic voting, party labels and entry 9. Rational entry and the conservation of disproportionality: evidence from Japan PART IV. ELECTORAL COORDINATION AT THe SYSTEM LEVEL: 10. Putting the constituencies together 11. Electoral institutions, cleavage structures and the number of parties PART V. COORDINATION FAILURES AND THE DEMOCRATIC PERFORMANCE: 12. Coordination failures and representation 13. Coordination failures and dominant parties 14. Coordination failures and realignments PART VI. CONCLUSION 15. Conclusion Appendices References Subject index Author index.

Abstract: The Condorcet Jury Theorem states that majorities are more likely than any single individual to select the "better" of two alternatives when there exists uncertainty about which of the two alternatives is in fact preferred Most extant proofs of this theorem implicitly make the behavioral assumption that individuals vote "sincerely" in the collective decision making, a seemingly innocuous assumption, given that individuals are taken to possess a common preference for selecting the better alternative However, in the model analyzed here we find that sincere behavior by all individuals is not rational even when individuals have such a common preference In particular, sincere voting does not constitute a Nash equilibrium A satisfactory rational choice foundation for the claim that majorities invariably "do better" than individuals, therefore, has yet to be derived