Voting and Power

Laruelle, Annick; Valenciano, Federico

doi:10.1007/978-3-642-35929-3_8

“…Here, we want to briefly present a large collection of those and arrange them in a somewhat systematic order. Our classification and listing is based on [3,6,9,29,30,38,51,52,65] 6 . In general terms, a power index on a class V n ⊆ B n of binary games, consisting of n players, is a mapping g : V n → R n .…”

Section: Power Indicesmentioning

confidence: 99%

“…Since the second half of the 20th century, several power indices were formally introduced in order to measure the voting power in collective decision making procedures, see e.g. [6,9,29,51,52] for some surveys and discussions. A huge amount of literature has been devoted to the study of the properties, shortcomings, paradoxes, and axiomatic foundations of several power indices.…”

Section: Introductionmentioning

confidence: 99%

The Inverse Problem for Power Distributions in Committees

Kurz

¹

2014

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Several power indices have been introduced in the literature in order to measure the influence of individual committee members on the aggregated decision. Here we ask the inverse question and aim to design voting rules for a committee such that a given desired power distribution is met as closely as possible. We present an exact algorithm for a large class of different power indices based on integer linear programming. With respect to negative approximation results we generalize the approach of Alon and Edelman who studied power distributions for the Banzhaf index, where most of the power is concentrated on few coordinates. It turned out that each Banzhaf vector of an n-member committee that is near to such a desired power distribution, has to be also near to the Banzhaf vector of a k-member committee. We show that such Alon-Edelman type results are possible for other power indices like e.g. the Public Good index or the Coleman index to prevent actions, while they are principally impossible for e.g. the Johnston index.

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Reflections on Power, Voting, and Voting Power

Holler

¹

,

Nurmi

²

2013

Power, Voting, and Voting Power: 30 Years After

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The inverse problem for power distributions in committees

Kurz¹

2016

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Several power indices have been introduced in the literature in order to measure the influence of individual committee members on the aggregated decision. Here we ask the inverse question and aim to design voting rules for a committee such that a given desired power distribution is met as closely as possible. We present an exact algorithm for a large class of different power indices based on integer linear programming. With respect to negative approximation results we generalize the approach of Alon and Edelman who studied power distributions for the Banzhaf index, where most of the power is concentrated on few coordinates. It turned out that each Banzhaf vector of an n-member committee that is near to such a desired power distribution, has to be also near to the Banzhaf vector of a k-member committee. We show that such Alon-Edelman type results are possible for other power indices like e.g. the Public Good index or the Coleman index to prevent actions, while they are principally impossible for e.g. the Johnston index.Comment: 46 pages, 2 table

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Voting and Power

Cited by 3 publications

References 22 publications

The Inverse Problem for Power Distributions in Committees

The Inverse Problem for Power Distributions in Committees

Reflections on Power, Voting, and Voting Power

The inverse problem for power distributions in committees

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