Econometrica Vol. 47 No. 3 1979
Consistent Majority Rules over Compact Sets of Alternatives
Abstract
[Consider a society with n individuals who must choose an alternative from a given non-empty set X. For an integer d ≤ n, a d-majority equilibrium is an alternative x* ∈ X such that no alternative in X is preferred to x* by at least d individuals. It is proved that when X is a compact and convex set of dimension m, a necessary and sufficient condition that, for every profile of individuals' convex and continuous preferences, there exists a d-majority equilibrium, is that d be greater than (m/(m + 1))n. Using this result for the case when X consists of a finite number, T, of alternatives, it is shown that a necessary and sufficient condition that for every individuals' preference orderings there exists a d-majority equilibrium is that d exceeds ((T - 1)/T)n.]
- DOI
- 10.2307/1910410
- Volume
- 47
- Issue
- 3
- Pages
- 627
- Sources
- bibtex:phds-export.bib crossref openalex