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.