Topic
Approval voting
About: Approval voting is a research topic. Over the lifetime, 1199 publications have been published within this topic receiving 33266 citations.
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Papers
TL;DR: In this paper, it was shown that any non-dictatorial voting scheme with at least three possible outcomes is subject to individual manipulation, i.e., an individual can manipulate a voting scheme if, by misrepresenting his preferences, he secures an outcome he prefers to the "honest" outcome.
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
3,464 citations
TL;DR: Kemeny's rule as discussed by the authors is the unique social welfare function that satisfies a variant of independence of irrelevant alternatives together with several other standard properties, and is the most likely ranking of the alternatives.
Abstract: Condcrcet's criterion states that an alternative that defeats every other by a simple majority is the socially optimal choice. Condorcet argued that if the object of voting is to determine the “best” decision for society but voters sometimes make mistakes in their judgments, then the majority alternative (if it exists) is statistically most likely to be the best choice. Strictly speaking, this claim is not true; in some situations Bordas rule gives a sharper estimate of the best alternative. Nevertheless, Condorcet did propose a novel and statistically correct rule for finding the most likely ranking of the alternatives. This procedure, which is sometimes known as “Kemeny's rule,” is the unique social welfare function that satisfies a variant of independence of irrelevant alternatives together with several other standard properties.
702 citations
TL;DR: In this article, it was shown that given suitably systematic, however slight, deviations from an impartial culture situation, the probability of a cycle converges either to zero (more typically) or to one (less typically) as the number of individuals increases.
Abstract: This item was published as 'Appendix 3: An Implication of the k-option Condorcet jury mechanism for the probability of cycles' in List and Goodin (2001) http://eprints.lse.ac.uk/705/. Standard results suggest that the probability of cycles should increase as the number of options increases and also as the number of individuals increases. These results are, however, premised on a so-called "impartial culture" assumption: any logically possible preference ordering is assumed to be as likely to be held by an individual as any other. The present chapter shows, in the three-option case, that given suitably systematic, however slight, deviations from an impartial culture situation, the probability of a cycle converges either to zero (more typically) or to one (less typically) as the number of individuals increases.
614 citations
TL;DR: In this article, a Condorcet social choice function elects the candidate that beats every other candidate under simple majority when such a candidate exists, and several extensions of the simple majority principle have been proposed.
Abstract: A Condorcet social choice function elects the candidate that beats every other candidate under simple majority when such a candidate exists. Various extensions of Condorcet’s simple majority principle that deal with situations that have no simple majority winner have been proposed.Nine Condorcet social choice functions are analyzed and compared on the basis of how well they satisfy a number of conditions for social choice functions. The conditions include several generalizations of Condorcet’s Principle. Remarks on the relative merits of the nine basic functions are included.
610 citations
TL;DR: In this article, it was shown that Borda's rule is compatible with Condorcet's principle of choosing the majority alternative whenever one exists, and that consistency of the outcome under aggregation of subgroups is also compatible with the Pareto property.
Abstract: Condorcet's principle of choosing the majority alternative whenever one exists is violated not only by Borda's rule but also by any scoring method; nevertheless, the essential property of scoring functions -- "consistency" of the outcome under aggregation of subgroups -- is shown to be compatible with Condorcet's principle. Moreover, these two properties, suitably interpreted, together with neutrality and the Pareto property, determine a unique rule known as Kemeny's rule.
526 citations
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Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 9 |
| 2024 | 17 |
| 2023 | 39 |
| 2022 | 32 |
| 2021 | 27 |
| 2020 | 25 |