Manipulation of indirect elections by vote swapping

Hayrullah Dindar -  Ph.D., Economics, İstanbul Bilgi University, İstanbul, Turkey

Hayrullah Dindar

We investigate a specific type of group manipulation in two-tiers elections, where groups of voters manipulate by exchanging votes. Two-tiers elections are modeled as a two-stage choice procedure where in the first stage voters are distributed into districts, each being assigned one delegate. Delegates’ preferences result from aggregating voters’ preferences district-wise by means of some aggregation rule. Final outcomes are subsets of alternatives obtained at the second stage by applying some social choice function to delegate profiles. Combining an aggregation rule and a social choice function defines a constitution. Voters’ preferences are linear orders over alternatives, which 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. Special attention is paid to Condorcet (resp., positional) constitutions, where both the aggregation rule and the social choice function are based on simple majority voting (resp., a score vector). We characterize Kelly and Fishburn swapping-proof Condorcet constitutions, and show that no positional constitution is Kelly or Fishburn swapping proof. Finally; if the constitution is single-valued, we show that robustness to manipulation via vote-swapping together with other desirable properties leads to dictatoriality.