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

2025-02-24

AI Summary

This paper investigates the axiomatic relationship between clone independence (IoC) and composition consistency (CC) in social choice, longstanding properties capturing robustness against clone manipulation. Method: We establish that CC strictly implies IoC—resolving their relative strength for the first time—and develop a PQ-tree-based constructive framework that, in polynomial time, lifts any neutral social choice function to one satisfying CC; we further design the first CC-satisfying variant of Ranked Pairs. Contribution/Results: We prove that major rules—including STV, Schulze, and Split Cycle—violate CC, while CC admits an interpretation as *explicit strategyproofness* (guaranteeing immunity to clone manipulation via transparent, verifiable reasoning), whereas IoC corresponds to standard strategyproofness. Together, they characterize the spectrum of robustness against cloning. Our work introduces a novel axiomatic framework and a computationally tractable construction paradigm for analyzing voting rule robustness.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Knowledge Representation and Reasoning: Preferences
• Machine Learning: Learning Preferences or Rankings

Application Category

• Security and Privacy: Data transparency and provenance
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Relationship between Independence of Clones and Composition Consistency
• Composition consistency of common voting rules
• Robustness against strategic manipulation by candidates

Innovation

• PQ-trees hierarchical representation
• variant of Ranked Pairs
• efficient modification of social choice functions