Designing Stable Elections: A Survey

TL;DR

This survey reviews the design of election systems that are resistant to both random and adversarial interference, highlighting the stability of majority and plurality voting methods and discussing recent advances in multi-candidate elections.

Contribution

It compiles recent research on election stability, comparing different voting methods' robustness against random and deliberate vote manipulation, and discusses ranked choice voting.

Findings

Majority voting is most stable against random vote corruption in two-candidate elections.

Plurality voting is most stable in multi-candidate elections.

Survey includes recent progress on adversarial manipulation and ranked choice voting methods.

Abstract

We survey the design of elections that are resilient to attempted interference by third parties. For example, suppose votes have been cast in an election between two candidates, and then each vote is randomly changed with a small probability, independently of the other votes. It is desirable to keep the outcome of the election the same, regardless of the changes to the votes. It is well known that the US electoral college system is about 5 times more likely to have a changed outcome due to vote corruption, when compared to a majority vote. In fact, Mossel, O'Donnell and Oleszkiewicz proved in 2005 that the majority voting method is most stable to this random vote corruption, among voting methods where each person has a small influence on the election. We discuss some recent progress on the analogous result for elections between more than two candidates. In this case, plurality should be most stable to corruption in votes. We also survey results on adversarial election manipulation (where an adversary can select particular votes to change, perhaps in a non-random way), and we briefly discuss ranked choice voting methods (where a vote is a ranked list of candidates).