How similar are two elections?

2025-02-01

Journal of computer and system sciences (Print)

AI Summary

This study addresses the problem of measuring the similarity between two ordinal elections with identical numbers of candidates and voters, under the requirement that the measure be invariant under relabeling of both candidates and voters. To this end, the work proposes the first distance notion for elections that satisfies isomorphism invariance, defined by aligning candidate labels and finding an optimal bijection between voters that minimizes the total distance between matched preference orders. The authors show that election isomorphism can be decided in polynomial time, yet two natural variants of the isomorphism-invariant distance are both NP-complete and hard to approximate. Fixed-parameter tractable (FPT) algorithms are developed with respect to several natural parameters, including the number of voters and the number of distinct preference types. The technical approach integrates techniques from graph isomorphism testing, combinatorial optimization, and parameterized complexity analysis.

Technology Category

Constraint Satisfaction and Optimization: Distributed CSP/OptimizationGame Theory and Economic Paradigms: Social Choice / VotingSearch and Optimization: Combinatorial Optimization

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsEconomics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environmentsSecurity and Privacy: Large-scale security measurements

Problem

• election isomorphism
• ordinal elections
• isomorphic distance
• preference orders
• computational complexity

Innovation

• isomorphic distance
• ordinal elections
• NP-completeness
• fixed-parameter tractability
• preference matching