Independence of Approximate Clones

2026-01-28

AI Summary

Perfect clones are exceedingly rare in real-world elections, yet approximate clones are widespread, rendering the classical Independence of Clones axiom inadequate. This work systematically formalizes the notion of approximate clones and introduces two quantitative measures to assess candidate proximity. Through a combination of theoretical analysis and empirical investigation, it examines how prominent ordinal voting rules behave under the presence of approximate clones. Theoretically, it is shown that while certain rules remain robust in three-candidate settings, they generally violate approximate clone independence when four or more candidates are present. Empirically, the study demonstrates that approximate clones frequently occur in real elections and that the closer such clones are to being perfect, the less likely their removal is to alter the election outcome.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Knowledge Representation and Reasoning: Preferences
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• independence of clones
• approximate clones
• ordinal elections
• voting rules
• social choice theory

Innovation

• approximate clones
• independence of clones
• ordinal elections
• voting rules
• empirical analysis