2022
DOI: 10.48550/arxiv.2202.03185
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Euclidean preferences in the plane under $\ell_1$, $\ell_2$ and $\ell_\infty$ norms

Abstract: We present various results about Euclidean preferences in the plane under ℓ1, ℓ2 and ℓ∞ norms. We show that Euclidean preference profiles under norm ℓ1 are the same as those under norm ℓ∞, and that the maximal size of such profiles for four candidates is 19. Whatever the number of candidates, we prove that at most four distinct candidates can be ranked in last position of an Euclidean preference profile under norm ℓ1, which generalizes the case of one-dimensional Euclidean preferences (for which it is well kno… Show more

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