Manipulation of Voting Schemes: A General Result

Abstract

NUMBER 4 MANIPULATION OF VOTING SCHEMES: A GENERAL RESULT BY ALLAN GIBBARD 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.

Consistency and construction in stated WTP for health risk reductions: A novel scope-sensitivity test

“…Carson et al (1999) build upon Hoehn and Randall (1987) to make a case in favour of using a single dichotomous choice (DC) question to elicit WTP responses 7 . This case is based upon the incentive compatibility properties of such single responses as set out by the work of Gibbard (1973) and Satterthwaite (1975) establishing the potential incentive compatibility of one-shot referenda. Carson et al (1999) argue that the use of incentive compatible DC elicitation techniques is a vital element in the estimation of theoretically consistent preferences.…”

Further results on dictatorial domains

“…Theorem 1 (Gibbard (1977), Satterthwaite (1975)) A scf f : P n → A is strategy-proof and satisfies unanimity if and only if it is dictatorial.…”

“…The seminal result of Gibbard (1977) and Satterthwaite (1975) states that a surjective and strategy-proof social choice function (scf) with a range of at least three alternatives, defined over the complete domain, is dictatorial. Aswal et al (2003) show that the assumption of a complete domain is far from being necessary for this result.…”

Computational Decision Support Regret-Based Models for Optimization and Preference Elicitation

“…In our restaurant example, under the plurality rule, voter 4 might be better off voting for d rather than d : since he prefers d to the winner d , by voting for d he would improve the plurality score for d to 2, tying it with d (and depending on the tie-breaking protocol, give d a chance to win). The celebrated Gibbard-Satterthwaite theorem (Gibbard, 1973;Satterthwaite, 1975) demonstrates the theoretical impossibility of avoiding such manipulation in general. However, when one considers more market-oriented mechanisms for making group decisions-that is, mechanisms that allow the transfer of payments between participants-strategyproof mechanisms-that is, mechanisms in which all parties are incentivized to reveal their preferences truthfully-can be constructed for certain domains.…”