How Similar Are Two Elections
THIRTY-THIRD AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE / THIRTY-FIRST INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE / NINTH AAAI SYMPOSIUM ON EDUCATIONAL ADVANCES IN ARTIFICIAL INTELLIGENCE(2019)
摘要
We introduce the ELECTION ISOMORPHISM problem and a family of its approximate variants, which we refer to as d-ISOMORPHISM DISTANCE (d-ID) problems (where d is a metric between preference orders). We show that ELECTION ISOMORPHISM is polynomial-time solvable, and that the d-ISOMORPHISM DISTANCE problems generalize various classic rank-aggregation methods(e.g., those of Kemeny and Litvak). We establish the complexity of our problems (including their inapproximability) and provide initial experiments regarding the ability to solve them in practice.
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