On Dedekind’s problem for complete simple games

Sascha Kurz () and Nikolas Tautenhahn ()

International Journal of Game Theory, 2013, vol. 42, issue 2, 437 pages

Abstract: We state an integer linear programming formulation for the unique characterization of complete simple games, i.e. a special subclass of monotone Boolean functions. In order to apply the parametric Barvinok algorithm to obtain enumeration formulas for these discrete objects we provide a tailored decomposition of the integer programming formulation into a finite list of suitably chosen sub-cases. As for the original enumeration problem of Dedekind on Boolean functions we have to introduce some parameters to be able to derive exact formulas for small parameters. Recently, Freixas et al. have proven an enumeration formula for complete simple games with two types of voters. We will provide a shorter proof and a new enumeration formula for complete simple games with two minimal winning vectors. Copyright Springer-Verlag 2013

Keywords: Boolean functions; Dedekind’s problem; Voting theory; Complete simple games; Application of the parametric Barvinok algorithm; 05A15*; 91B12; 94C10; 52B20 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (10)

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DOI: 10.1007/s00182-012-0327-9

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