Voting Rules that are Unbiased but not Transitive-Symmetric

Abstract

We explore the relation between two natural symmetry properties of voting rules. The first is transitive-symmetry – the property of invariance to a transitive permutation group – while the second is the "unbiased" property of every voter having the same influence for all i.i.d. probability measures. We show that these properties are distinct by two constructions – one probabilistic, one explicit – of rules that are unbiased but not transitive-symmetric.