Independence of Approximate Clones

TL;DR

This paper investigates how voting rules behave when candidates are nearly perfect clones in ordinal elections, analyzing theoretical conditions and empirical data to understand the impact of approximate clones on election outcomes.

Contribution

It introduces measures for approximate clones, analyzes their effect on clone independence in voting rules, and provides empirical insights from real-world datasets.

Findings

Voting rules independent of perfect clones are generally not independent of approximate clones with four or more candidates.

For three candidates, some voting rules remain independent of approximate clones.

Approximate clones are common in real-world elections, affecting outcome stability.

Abstract

In an ordinal election, two candidates are said to be perfect clones if every voter ranks them adjacently. The independence of clones axiom then states that removing one of the two clones should not change the election outcome. This axiom has been extensively studied in social choice theory, and several voting rules are known to satisfy it (such as IRV, Ranked Pairs and Schulze). However, perfect clones are unlikely to occur in practice, especially for political elections with many voters. In this work, we study different notions of approximate clones in ordinal elections. Informally, two candidates are approximate clones in a preference profile if they are close to being perfect clones. 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 are also independent of approximate clones. In particular, we show that for elections with at least 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 and independence of approximate clones based on three real-world datasets: votes in local Scottish elections, votes in mini-jury deliberations, and votes of judges in figure skating competitions. We find that approximate clones are common in some contexts, and that the closest two candidates are to being perfect clones, the less likely their removal is to change the election outcome, especially for voting rules that are independent of perfect clones.