Robustness Among Multiwinner Voting Rules

TL;DR

This paper examines the robustness of multiwinner voting rules to small preference order changes, analyzing the impact on election outcomes, computational complexity, and experimental stability measures.

Contribution

It provides a detailed analysis of how minor preference swaps affect election results and introduces algorithms for computing minimal changes, highlighting differences among voting rules.

Findings

Small preference swaps can change at most one committee member or the entire committee.

Computing minimal swaps for outcome change is NP-hard but admits FPT algorithms.

Experimental results show the average swaps needed to alter results vary across rules.

Abstract

We investigate how robust the results of committee elections are to small changes in the input preference orders, depending on the voting rules used. We find that for typical rules the effect of making a single swap of adjacent candidates in a single preference order is either that (1) at most one committee member might be replaced, or (2) it is possible that the whole committee will be replaced. We also show that the problem of computing the smallest number of swaps that lead to changing the election outcome is typically NP-hard, but there are natural FPT algorithms. Finally, for a number of rules we assess experimentally the average number of random swaps necessary to change the election result.