Power balance and apportionment algorithms for the United States Congress

Hemaspaandra, Lane A.; Rajasethupathy, Kulathur S.; Sethupathy, Prasanna; Zimand, Marius

doi:10.1145/297096.297106

Cited by 8 publications

(4 citation statements)

References 13 publications

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“…Before ending the class, I turn this all a bit on its head, by introducing the notion of power indices, and giving examples showing that, due to that notion, the connection between number of representatives and power is far more subtle than one might think, and thus that trying to match votes closely to proportional quotas may not be the right goal to have (see [13] and the references therein for more background and empirical studies in this direction).…”

Section: Computer Science Gladiators Day/lightning Research Daysmentioning

confidence: 99%

That Most Important Intersection

Hemaspaandra

2018

Adventures Between Lower Bounds and Higher Altitudes

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This article describes the design and components of a Knuthstyle problem-solving course for undergraduate students, including example problems. The hope is that the course approach is flexible and adaptable enough that it will be relatively portable, and yet will provide a course that for both teacher and students falls in that most important intersection: the intersection of what one can do quite well, and what one can do with much passion and joy.

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Section: Computer Science Gladiators Day/lightning Research Daysmentioning

confidence: 99%

That Most Important Intersection

Hemaspaandra

2018

Adventures Between Lower Bounds and Higher Altitudes

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“…We are also looking for fresh computational approaches to apportionment. An overview of apportionment is available in [22].…”

Section: Algorithmic and Technical Issuesmentioning

confidence: 99%

Efficient Algorithm for Designing Weighted Voting Games

Aziz

Paterson

Leech

2007

2007 IEEE International Multitopic Conference

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Abstract-Weighted voting games are mathematical models, used to analyse situations where voters with variable voting weight vote in favour of or against a decision. They have been applied in various political and economic organizations. Similar combinatorial models are also encountered in neuroscience, threshold logic, reliability theory and distributed systems.The calculation of voting powers of players in a weighted voting game has been extensively researched in the last few years. However, the inverse problem of designing a weighted voting game with a desirable distribution of power has received less attention. We present an elegant algorithm which uses generating functions and interpolation to compute an integer weight vector for target Banzhaf power indices. This algorithm has better performance than any other known to us. It can also be used to design egalitarian two-tier weighted voting games and a representative weighted voting game for a multiple weighted voting game.

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“…In a country divided into districts it makes sense to give each district voting power proportional to its population (consider, e.g., the US House of Representatives or various decision making processes within the European Union). In fact, the power that various apportionment methods give to the US states in its House of Representatives has been studied in terms of how well it is proportional to the sizes of the states [HRSZ98]. In a business setting, stockholders in a company might hope to have voting power proportional to the amount of stock they own.…”

Section: Introductionmentioning

confidence: 99%

The Complexity of Power-Index Comparison

Faliszewski

Hemaspaandra

Algorithmic Aspects in Information and Management

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We study the complexity of the following problem: Given two weighted voting games G and G that each contain a player p, in which of these games is p's power index value higher? We study this problem with respect to both the Shapley-Shubik power index [SS54] and the Banzhaf power index [Ban65, DS79]. Our main result is that for both of these power indices the problem is complete for probabilistic polynomial time (i.e., is PP-complete). We apply our results to partially resolve some recently proposed problems regarding the complexity of weighted voting games. We also study the complexity of the raw Shapley-Shubik power index. Deng and Papadimitriou [DP94] showed that the raw Shapley-Shubik power index is #P-metriccomplete. We strengthen this by showing that the raw Shapley-Shubik power index is many-one complete for #P. And our strengthening cannot possibly be further improved to parsimonious completeness, since we observe that, in contrast with the raw Banzhaf power index, the raw Shapley-Shubik power index is not #P-parsimonious-complete.

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Power balance and apportionment algorithms for the United States Congress

Cited by 8 publications

References 13 publications

That Most Important Intersection

That Most Important Intersection

Efficient Algorithm for Designing Weighted Voting Games

The Complexity of Power-Index Comparison

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