Independence of Approximate Clones with Ordinal Preferences

Théo Delemazure

Keywords: Voting Theory, Computational social choice, Elections, Approximate clones

Abstract: We study different notions of \emph{approximate clones} in elections with ordinal preferences. Informally, two candidates are approximate clones in a preference profile if they are close to being \emph{perfect} clones, which are candidates that are ranked adjacently by all voters. We discuss two measures to quantify this proximity, and we show under which conditions the voting rules that are known to be independent of clones (such as IRV, Ranked Pairs and Schulze) are also independent of approximate clones. In particular, we show that for more than four candidates, none of these rules are independent of approximate clones in the general case. However, we find a more positive result for the case of three candidates. Finally, we conduct an empirical study of approximate clones based on three real-world datasets: votes in local Scottish elections, votes in mini-jury deliberations, and votes of juries in figure skating competitions.

Area: Game Theory and Economic Paradigms (GTEP)

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Submission Number: 1141