Stability of Decision Systems under Majority Rule

Abstract

As the well-known “Paradox of Voting” indicates, a decision system under majority rule does not necessarily have an equilibrium; that is, it might be that for every alternative there is a majority preferring another. Many writers, particularly political scientists, thus inferred the weakness of majority-rule systems (see, for example, Brams (1976), Riker and Ordeshook (1973)). A social system with no equilibrium might be thrust into continuous cyclic change. Moreover, the individual members who believe in democracy would be permanently dissatisfied, since they are always convinced (and correctly so), that there is a majority in favor of a social reality different from the existing one. Many attempts have been made to find sufficient conditions for the existence of equilibrium in systems under majority rule, for example, Arrow (1963), Davis and Hinich (1972), Dommet and Farquharson (1961), Nakamura (1975), and Plott (1967). The prevalent impression arising from reading these works is that only strong conditions on the decision system lead to the existence of equilibrium. (This impression is expressed topologically in Rubinstein (1979).) The starting point of all these papers is the definition of equilibrium and the identification of social stability with the existence of equilibrium. The existence of a majority preferring b to a deprives a of stability. The individuals are assumed not to take into account what happens after the system switches to b. In this paper I will attempt to see if the general picture is less pessimistic when we assume that the individuals are aware of possible future developments. The behavior pattern examined is that determined by the following reasoning: “True, I prefer b to a, but if b is adopted, then a situation arises where the majority prefers c. Since c is worse than a from my point of view, I will not take any chances and will not vote for b in place of a.” A social possibility will be considered to be stable if no majority exists for change when all the individuals adopt this more farseeing behavior 150 0022-0531/80/05015(r10$02.00/0

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Cite this paper

@inproceedings{Rubinstein2003StabilityOD, title={Stability of Decision Systems under Majority Rule}, author={Ariel Rubinstein}, year={2003} }