Kemeny ranking is NP-hard for 2-dimensional Euclidean preferences
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The assumption that voters' preferences share some common structure is a standard way to circumvent NP-hardness results in social choice problems. While the Kemeny ranking problem is NP-hard in the general case, it is known to become easy if the preferences are 1-dimensional Euclidean. In this note, we prove that the Kemeny ranking problem is NP-hard for d-dimensional Euclidean preferences with d>=2. We note that this result also holds for the Slater ranking problem.
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