Single Transferable Vote and Paradoxes of Negative and Positive Involvement

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.