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• W3126093370 abstract "Many political and social choice processes, particularly those based on some form of voting rule, can be usefully represented as simple games. A simple game differs from the usual variety of n-person game in that certain combinations or coalitions of voters are all-powerful , and are able to enforce their will irrespective of the desires or actions of the players who are not members of the coalition, while all of the remaining coalitions are essentially powerless to affect the outcome. A familiar example is a majority game, in which any coalition containing a majority of players can secure any outcome its members are able to agree upon, while no minority coalition can influence the outcome if the opposing majority is agreed upon a course of action. Other examples of simple games, some very complicated, are cited in [8] and [9, Chapter 10]. While simple games clearly represent a rather special form of the more general n-person game, they may nevertheless be quite complex in structure and difficult to analyse. Moreover, the existence of a co-operative solution, such as the core, is by no means assured in games of this type. Many simple games are known for which no core exists; the famous voters' paradox is a particularly elementary three-player example of such a game. Indeed, much of the social choice and voting theory literature, though not cast in an explicitly game-theoretic framework, can be interpreted as showing how difficult it is to ensure the existence of a co-operative equilibrium in multi-person situations based on any reasonable kind of voting process or social choice mechanism. A particular equilibrium condition for majority rule known as single peakedness has played an important role in the voting theory literature. This condition was shown by Duncan Black to be sufficient to ensure existence of a majority winner, which is essentially equivalent to the existence of a core in a majority game. In fact, the condition is even more powerful than this, for it can also be shown to be sufficient for the existence of a core in any simple game (Theorem 2 of the present paper). Roughly speaking, singlepeakedness is equivalent to requiring that the relevant set of alternatives or possible outcomes be one-dimensional, and that voter preferences over this set be representable by strictly quasi-concave utility functions. While the condition is clearly restrictive, it is none the less a useful one, for in mBny economic problems it often arises as a natural consequence of the convexity of individual preferences. The usual examples of voting on resource-allocation or other public sector problems [3], [6, Chapter 6] are of this type. There have, however, also arisen examples of voting problems which, though essentially one-dimensional in character, are nevertheless such that the single-peakedness condition" @default.
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• W3126093370 date "1972-01-01" @default.
• W3126093370 modified "2023-09-25" @default.
• W3126093370 title "Existence of a 'Local' Cooperative Equilibrium in a Class of Voting Games" @default.
• W3126093370 hasPublicationYear "1972" @default.
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