On Dedekind’s problem for complete simple games

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 deco...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:International journal of game theory Ročník 42; číslo 2; s. 411 - 437
Hlavní autoři: Kurz, Sascha, Tautenhahn, Nikolas
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer-Verlag 01.05.2013
Springer [[2009-]]
Springer Nature B.V
Témata:
Algorithms
Behavioral/Experimental Economics
Boolean
Codes
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Economics and Finance
Enumeration
Game Theory
Games
Integer programming
Linear programming
Operations Research/Decision Theory
Social and Behav. Sciences
Studies
Voters
Voting theory
91B12
52B20
Boolean functions
Dedekind’s problem
Complete simple games
Application of the parametric Barvinok algorithm
94C10
05A15
ISSN:0020-7276, 1432-1270
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí: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.
Bibliografie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0020-7276
1432-1270
DOI:10.1007/s00182-012-0327-9