On the inverse power index problem

DOI10.1080/02331934.2011.587008zbMath1260.91082arXiv1211.6353OpenAlexW3105773719MaRDI QIDQ3165908

Sascha Kurz

Publication date: 19 October 2012

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.6353

Mathematics Subject Classification ID

Decision theory (91B06) Voting theory (91B12) Decision theory for games (91A35)

Related Items (22)

The minimum sum representation as an index of voting power ⋮ The inverse problem for power distributions in committees ⋮ Two-tier voting: measuring inequality and specifying the inverse power problem ⋮ Dimension of the Lisbon voting rules in the EU council: a challenge and new world record ⋮ The cost of getting local monotonicity ⋮ Nearly Optimal Solutions for the Chow Parameters Problem and Low-Weight Approximation of Halfspaces ⋮ Fair representation and a linear Shapley rule ⋮ The inverse Shapley value problem ⋮ Simple voting games and cartel damage proportioning ⋮ Weighted scoring committees ⋮ On \(\alpha\)-roughly weighted games ⋮ Manipulating the quota in weighted voting games ⋮ On the enumeration of some inequivalent monotone Boolean functions ⋮ IMPORTANCE IN SYSTEMS WITH INTERVAL DECISIONS ⋮ A parameterization for a class of complete games with abstention ⋮ On minimum sum representations for weighted voting games ⋮ The power of the largest player ⋮ Weighted committee games ⋮ Heuristic and exact solutions to the inverse power index problem for small voting bodies ⋮ Generating Functions of Weighted Voting Games, MacMahon’s Partition Analysis, and Clifford Algebras ⋮ On influence and compromise in two-tier voting systems ⋮ Minimal proper non-IRUP instances of the one-dimensional cutting stock problem

Cites Work

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• A class of simple games
• On the existence of a minimum integer representation for weighted voting systems
• A computation of the eighth Dedekind number
• New mathematical properties of the Banzhaf value
• Complete simple games
• The inverse Banzhaf problem
• Hierarchies achievable in simple games
• Weighted games without a unique minimal representation in integers
• Every one a Winner or how to Avoid Isomorphism Search when Cataloguing Combinatorial Configurations
• Directed and weighted majority games
• Enumeration of Seven-Argument Threshold Functions
• Enumeration of Threshold Functions of Eight Variables

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