Forming Coalitions and Measuring Voting Power

Holler, Manfred J.

doi:10.1111/j.1467-9248.1982.tb00537.x

Cited by 206 publications

(123 citation statements)

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“…Interesting results related to voting power and power index were obtained by Holler (1982Holler ( , 1984Holler ( , 1995Holler ( , 1997. However, in some cooperative games, the players' choices are influenced or restricted by political institutions.…”

Section: Contribution Of Lloyd Shapley To Game Theorymentioning

confidence: 99%

Modification of Shapley Value and its Implementation in Decision Making

Zaremba¹,

Zaremba²,

Suchenek

2017

Foundations of Management

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Abstract:The article presents a solution of a problem that is critical from a practical point of view: how to share a higher than usual discount of $10 million among 5 importers. The discount is a result of forming a coalition by 5 current, formerly competing, importers. The use of Shapley value as a concept for co-operative games yielded a solution that was satisfactory for 4 lesser importers and not satisfactory for the biggest importer. Appropriate modification of Shapley value presented in this article allowed to identify appropriate distribution of the saved purchase amount, which according to each player accurately reflects their actual strength and position on the importer market. A computer program was used in order to make appropriate calculations for 325 permutations of all possible coalitions. In the last chapter of this paper, we recognize the lasting contributions of Lloyd Shapley to the cooperative game theory, commemorating his recent (March 12, 2016) descent from this world.

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Section: Contribution Of Lloyd Shapley To Game Theorymentioning

confidence: 99%

Modification of Shapley Value and its Implementation in Decision Making

Zaremba¹,

Zaremba²,

Suchenek

2017

Foundations of Management

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“…The PGI index is also called the Holler-Packel index due to the axiomatization of Holler andPackel (1983). Napel in (1999), (2001) showed the independence and non-redundancy of the Holler and Packel axioms.…”

Section: The König and Bräuninger's Index (Or Zipke Index)mentioning

confidence: 99%

“…The Public Good index (PGI) was defined by Holler in (1982). The PGI considers the coalition value to be a public good.…”

Section: The König and Bräuninger's Index (Or Zipke Index)mentioning

confidence: 99%

“…Some indices have been derived from existing values; i.e., the Shapley and Shubik (1954) as well as the Banzhaf (1965) and the Coleman (1971). Other power indices were formulated exclusively for simple games; i.e., the Public Good index (Holler, 1982), the Deegan and Packel index (1978), and the Johnston index (1978). In this paper, we analyze some values and power indices well-defined in the social context where the goods are public; e.g., the Public Good index, the Public Good value, the Public Help index (Bertini et al, 2008), the König and Bräuninger index (1998) also called the Zipke index (Nevison et al, 1978), and the Rae index (1969).…”

Section: Introductionmentioning

confidence: 99%

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On Public Values and Power Indices

Bertini

Stach²

2015

dmms

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Abstract.In this paper, we analyze some values and power indices from a different point of view that are well-defined in the social context where the goods are public. In particular, we consider the Public Good index (Holler, 1982), the Public Good value (Holler and Li, 1995), the Public Help index (Bertini et al., 2008), the König and Bräuninger index (1998) also called the Zipke index (Nevison et al., 1978), and the Rae index (1969). The aims of this paper are: to propose an extension of the Public Help index to cooperative games; to introduce a new power index with its extension to a game value; and to provide some characterizations of the new index and values.

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“…Both the Deegan-Packel index [15] and the Holler index [20] are based on the notion of minimal winning coalitions. Minimal winning coalitions are significant with respect to coalition formation.…”

Section: Other Power Indicesmentioning

confidence: 99%

Power Indices in Spanning Connectivity Games

Aziz

Lachish

Paterson

et al. 2009

Lecture Notes in Computer Science

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Abstract. The Banzhaf index, Shapley-Shubik index and other voting power indices measure the importance of a player in a coalitional game. We consider a simple coalitional game called the spanning connectivity game (SCG) based on an undirected, unweighted multigraph, where edges are players. We examine the computational complexity of computing the voting power indices of edges in the SCG. It is shown that computing Banzhaf values is #P-complete and computing ShapleyShubik indices or values is NP-hard for SCGs. Interestingly, Holler indices and Deegan-Packel indices can be computed in polynomial time. Among other results, it is proved that Banzhaf indices can be computed in polynomial time for graphs with bounded treewidth. It is also shown that for any reasonable representation of a simple game, a polynomial time algorithm to compute the Shapley-Shubik indices implies a polynomial time algorithm to compute the Banzhaf indices. This answers (positively) an open question of whether computing Shapley-Shubik indices for a simple game represented by the set of minimal winning coalitions is NP-hard.

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Forming Coalitions and Measuring Voting Power

Cited by 206 publications

References 5 publications

Modification of Shapley Value and its Implementation in Decision Making

Modification of Shapley Value and its Implementation in Decision Making

On Public Values and Power Indices

Power Indices in Spanning Connectivity Games

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