On the Number of Group-Separable Preference Profiles

  • Alexander KarpovEmail author


The paper studies group-separable preference profiles. Such a profile is group-separable if for each subset of alternatives there is a partition in two parts such that each voter prefers each alternative in one part to each alternative in the other part. We develop a parenthesization representation of group-separable domain. The precise formula for the number of group-separable preference profiles is obtained. The recursive formula for the number of narcissistic group-separable preference profiles is obtained. Such a profile is narcissistic group-separable if it is group-separable and each alternative is preferred the most by exactly one voter.


Schröder paths Schröder numbers Separable permutations Permutation patterns Narcissistic preferences 



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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.National Research University Higher School of EconomicsMoscowRussia
  2. 2.Institute of Control ScienceRussian Academy of ScienceMoscowRussia

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