The Nakamura numbers for computable simple games

نویسندگان

  • Masahiro Kumabe
  • H. Reiju Mihara
چکیده

The Nakamura number of a simple game plays a critical role in preference aggregation (or multi-criterion ranking): the number of alternatives that the players can always deal with rationally is less than this number. We comprehensively study the restrictions that various properties for a simple game impose on its Nakamura number. We find that a computable game has a finite Nakamura number greater than three only if it is proper, nonstrong, and nonweak, regardless of whether it is monotonic or whether it has a finite carrier. The lack of strongness often results in alternatives that cannot be strictly ranked. Journal of Economic Literature Classifications: C71, C69, D71.

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عنوان ژورنال:
  • Social Choice and Welfare

دوره 31  شماره 

صفحات  -

تاریخ انتشار 2008