Generic Instability of Majority Rule

Norman Schofield ()

The Review of Economic Studies, 1983, vol. 50, issue 4, 695-705

Abstract: Majority rule voting with smooth preferences on a smooth policy space W is examined. It is shown that there is an integer w(n), which is 2 when the size of the society n is odd and 3 when n is even such that when the dimension of W is at least w(n) then, for almost preference profiles on W, the core of the voting game is empty when the dimension of W exceeds w(n) then for almost all preference profiles on W, there exist dense preference cycles in W. Moreover in dimension w(n) + 1 the policy space can be partitioned into a finite number of path connected components, such that any two points in one of the components can be connected by a majority voting trajectory. In dimension greater than w(n) + 1 there exists only one such component.

Date: 1983
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