Identifying Imperfect Clones in Elections

2025-09-14

AI Summary

This paper investigates the identification of “imperfect clone candidates” in ordinal elections—candidates who are not strictly consecutive in all voters’ preference rankings (i.e., perfect clones), but instead exhibit two relaxed forms: (1) independent or sub-election clones (consecutive only for a subset of voters), and (2) approximate clones (ranked closely—but not consecutively—by all voters). We formally define and systematize these three clone types, and propose a preference-structure-based recognition model. Using computational complexity and parameterized algorithm theory, we rigorously characterize the complexity boundaries of each identification problem: most are NP-hard, yet fixed-parameter tractable (FPT) with respect to natural parameters such as the number of candidates, maximum positional deviation, or fraction of supporting voters. Our results provide both theoretical foundations and algorithmic tools for robustness analysis and manipulation-resistant mechanism design in social choice.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

A perfect clone in an ordinal election (i.e., an election where the voters rank the candidates in a strict linear order) is a set of candidates that each voter ranks consecutively. We consider different relaxations of this notion: independent or subelection clones are sets of candidates that only some of the voters recognize as a perfect clone, whereas approximate clones are sets of candidates such that every voter ranks their members close to each other, but not necessarily consecutively. We establish the complexity of identifying such imperfect clones, and of partitioning the candidates into families of imperfect clones. We also study the parameterized complexity of these problems with respect to a set of natural parameters such as the number of voters, the size or the number of imperfect clones we are searching for, or their level of imperfection.

Problem

• Identifying imperfect clones in ordinal elections
• Complexity analysis of partitioning candidates into clone families
• Parameterized complexity with natural election parameters

Innovation

• Identifying independent and subelection clones
• Analyzing approximate clones with proximity rankings
• Establishing parameterized complexity for clone identification