Recognising Multidimensional Euclidean Preferences

Authors

  • Dominik Peters University of Oxford

DOI:

https://doi.org/10.1609/aaai.v31i1.10616

Keywords:

social choice, voting, single-peaked preferences, spatial preferences, recognition problem, computational complexity, ETR, forbidden subprofiles, multidimensional unfolding

Abstract

Euclidean preferences are a widely studied preference model, in which decision makers and alternatives are embedded in d-dimensional Euclidean space. Decision makers prefer those alternatives closer to them. This model, also known as multidimensional unfolding, has applications in economics, psychometrics, marketing, and many other fields. We study the problem of deciding whether a given preference profile is d-Euclidean. For the one-dimensional case, polynomial-time algorithms are known. We show that, in contrast, for every other fixed dimension d > 1, the recognition problem is equivalent to the existential theory of the reals (ETR), and so in particular NP-hard. We further show that some Euclidean preference profiles require exponentially many bits in order to specify any Euclidean embedding, and prove that the domain of d-Euclidean preferences does not admit a finite forbidden minor characterisation for any d > 1. We also study dichotomous preferences and the behaviour of other metrics, and survey a variety of related work.

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Published

2017-02-10

How to Cite

Peters, D. (2017). Recognising Multidimensional Euclidean Preferences. Proceedings of the AAAI Conference on Artificial Intelligence, 31(1). https://doi.org/10.1609/aaai.v31i1.10616

Issue

Section

AAAI Technical Track: Game Theory and Economic Paradigms