A Remark on Similarity Conditions

Peter Wagstaff

British Journal of Political Science, 1975, vol. 5, issue 3, 391-392

Abstract: Kramer has shown how singularly restrictive are all ‘similarity’ conditions which guarantee transitivity of majority rule by limiting the family of admissible preference orderings (so-called exclusion restrictions). For suppose, plausibly, that social alternatives are points in an open convex policy space S ⊂ Rn, n ≥ 2, and that voters' preferences, {Rl)1=1…‥ l, are representable by continuously differentiable semi-strictly quasi-concave utility functions ul,. Suppose further that at a single point x ε S, any three voters' utility functions have gradients ∇ul(x), ∇uf(X), ∇uk(x), no one of which can be expressed as a positive linear combination of the other two, and no two of which are linearly dependent. Then all exclusion conditions must fail on S.

Date: 1975
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