How similar are two elections?
🤖 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.
Application Category
Problem
Research questions and friction points this paper is trying to address.
election isomorphism
ordinal elections
isomorphic distance
preference orders
computational complexity
Innovation
Methods, ideas, or system contributions that make the work stand out.
isomorphic distance
ordinal elections
NP-completeness
fixed-parameter tractability
preference matching
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