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On the Non-Emptiness of Solution Concepts for Voting Games

Author

Listed:
  • Nicolas Andjiga
  • Boniface Mbih

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique)

  • Issofa Moyouwou

Abstract

The non-emptiness of cores of voting games not only depends on the dominance relation, but also on the properties of individual preferences. In this paper, we enrich the panorama of existing non-emptiness results (for core concepts and the stability set) by providing their counter-parts when one moves from monotonic voting games to non monotonic ones; or from the assumption of individual preferences as linear orders to that of those preferences as weak orders. We mainly show how these two types of movements modify the three characteristic numbers associated with theorems on refinements of the core and the 1-stability set of voting games, namely the Nakaruma number (Nakamura [1979]), the Andjiga-Mbih number (Andjiga and Mbih [2000]) and the Andjiga-Moyouwou number (Andjiga and Moyouwou [2006]).

Suggested Citation

  • Nicolas Andjiga & Boniface Mbih & Issofa Moyouwou, 2025. "On the Non-Emptiness of Solution Concepts for Voting Games," Post-Print hal-05107308, HAL.
    • Handle: RePEc:hal:journl:hal-05107308
    DOI: 10.3917/redp.351.0025
    as

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