Single Transferable Vote and Paradoxes of Negative and Positive Involvement

TL;DR

This paper investigates involvement paradoxes in single transferable vote elections, showing how increased participation can paradoxically change winners and losers, with analysis and real-world examples from Scottish elections.

Contribution

It provides the first detailed analysis of involvement paradoxes in STV, including worst-case scenarios and empirical examples from actual elections.

Findings

Involvement paradoxes can occur under STV, affecting election outcomes.

Worst-case scenarios demonstrate the potential for paradoxical results.

Real Scottish election data illustrates these paradoxes in practice.

Abstract

We analyze a type of voting paradox which we term an involvement paradox, in which a candidate who loses an election could be made into a winner if more of the candidate's non-supporters participated in the election, or a winner could be made into a loser if more of the candidate's supporters participated. Such paradoxical outcomes are possible under the voting method of single transferable vote (STV), which is widely used for political elections throughout the world. We provide a worst-case analysis of involvement paradoxes under STV and show several interesting examples of these paradoxes from elections in Scotland.