Vote Swapping in Representative Democracy

Abstract

We investigate group manipulation by vote exchange in two-tiers elections, where voters are first distributed into districts, each with one delegate. Delegates' preferences result from aggregating voters' preferences district-wise by means of some aggregation rule. Final outcomes are sets of alternatives obtained by applying a social choice function to delegate profiles. An aggregation rule together with a social choice function define a constitution. Voters' preferences over alternatives are extended to partial orders over sets by means of either the Kelly or the Fishburn extension rule. A constitution is Kelly (resp. Fishburn) swapping-proof if no group of voters can get by exchanging their preferences a jointly preferred outcome according to the Kelly (resp. Fishburn) extension. We establish sufficient conditions for swapping-proofness. We characterize Kelly and Fishburn swapping-proofness for Condorcet constitutions, where both the aggregation rule and the social choice function are based on simple majority voting. JEL Class D71, C70.