From Independence of Clones to Composition Consistency: A Hierarchy of Barriers to Strategic Nomination

TL;DR

This paper explores the relationship between independence of clones and composition consistency in social choice functions, identifying a hierarchy of axioms and providing methods to modify rules to satisfy these properties.

Contribution

It clarifies the hierarchy between IoC and CC, identifies a CC-satisfying variant of Ranked Pairs, and offers a method to transform any social choice function to satisfy CC.

Findings

Most common rules are not composition-consistent

A variant of Ranked Pairs satisfies CC

Any neutral social choice function can be modified to satisfy CC

Abstract

We study two axioms for social choice functions that capture the impact of similar candidates: independence of clones (IoC) and composition consistency (CC). We clarify the relationship between these axioms by observing that CC is strictly more demanding than IoC, and investigate whether common voting rules that are known to be independent of clones (such as STV, Ranked Pairs, Schulze, and Split Cycle) are composition-consistent. While for most of these rules the answer is negative, we identify a variant of Ranked Pairs that satisfies CC. Further, we show how to efficiently modify any (neutral) social choice function so that it satisfies CC, while maintaining its other desirable properties. Our transformation relies on the hierarchical representation of clone structures via PQ-trees. We extend our analysis to social preference functions. Finally, we interpret IoC and CC as measures of robustness against strategic manipulation by candidates, with IoC corresponding to strategy-proofness and CC corresponding to obvious strategy-proofness.