  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.
