A critical reappraisal of some voting power paradoxes

Laruelle, Annick; Valenciano, Federico

doi:10.1007/s11127-005-3408-5

Cited by 26 publications

(20 citation statements)

References 35 publications

(22 reference statements)

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“…Laruelle and Valenciano (2005) elucidated paradoxes of voting power through algebraic manipulation. They explain counterintuitive results by exposing the algebra that leads to them.…”

Section: Introductionmentioning

confidence: 99%

“…Exploring the same topic as Laruelle and Valenciano (2005), Jones (2009) employed geometric analysis to shed light on paradoxes of voting power from a new angle. Though this paper worked primarily with three-player examples, his representation of weighted voting systems was very versatile: it can be generalized for any number of players and its non-exploitation of symmetry makes it a complete portrayal of n-player weighted voting systems.…”

Section: Introductionmentioning

confidence: 99%

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A Complete Geometric Representation of Four-Player Weighted Voting Systems

Jiang¹

2013

JMR

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This paper seeks to expand voting power theory, a branch of game theory that applies to many important organizations. Typically, weighted voting systems are displayed using the algebraic representation, consisting of a quota and a weight vector. A newer idea, however, is the geometric representation. This representation maps all normalized weighted voting systems onto a simplex and thus can be called a complete representation of weighted voting systems. The concept of the region, sets of characteristically identical weighted voting systems, will be introduced, greatly simplifying the analysis of weighted voting systems. In this paper, four-player weighted voting systems are solved completely using the geometric representation. The geometric representation will be shown to be a useful alternative to the algebraic representation.

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“…Laruelle and Valenciano (2005) elucidated paradoxes of voting power through algebraic manipulation. They explain counterintuitive results by exposing the algebra that leads to them.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Complete Geometric Representation of Four-Player Weighted Voting Systems

Jiang¹

2013

JMR

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“…Owen (1971) and Shapley (1977) constructed generalizations of the Shapley-Shubik index assuming that players have an ideal point in the policy space and prefer policies that are closer to their ideal point; these power indices are not necessarily monotonic. Similarly, Laruelle and Valenciano (2005) note that a voter with a greater weight may be less likely to be decisive because of the probability distribution over vote con…gurations. If there is one large right-wing party and three small left-wing parties, it may be that the small parties tend to vote together in which case the large party cannot a¤ect the outcome.…”

Section: Introductionmentioning

confidence: 99%

A Violation of Monotonicity in a Noncooperative Setting

Montero

Vidal-Puga

2012

SSRN Journal

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The focus for the Centre is research into individual and strategic decision-making using a combination of theoretical and experimental methods. On the theory side, members of the Centre investigate individual choice under uncertainty, cooperative and non-cooperative game theory, as well as theories of psychology, bounded rationality and evolutionary game theory. Members of the Centre have applied experimental methods in the fields of public economics, individual choice under risk and uncertainty, strategic interaction, and the performance of auctions, markets and other economic institutions. Much of the Centre's research involves collaborative projects with researchers from other departments in the UK and overseas. Abstract A power measure is monotone if a player with a larger weight is assigned at least as much power as a player with a smaller weight in the same weighted majority game. Failure of a power index to satisfy monotonicity is often considered a pathological feature. In this paper, we show that monotonicity may fail in the unique subgame perfect equilibrium of a noncooperative bargaining game. A player with a smaller weight may have a higher expected payo¤ than a player with a larger weight. This is possible even though coalition formation and payo¤ division are endogenous, all players are rational and there is no asymmetry between the players other than in the weights.

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“…the ease with which the proposal can be approved. See [14] or [9] and [10] about this interpretation for f (p).…”

Section: Introductionmentioning

confidence: 99%

Bounds for Owen's Multilinear Extension

Freixas¹

2007

J. Appl. Probab.

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Owen's multilinear extension (MLE) of a game is a very important tool in game theory and particularly in the field of simple games. Among other applications it serves to efficiently compute several solution concepts. In this paper we provide bounds for the MLE. Apart from its self-contained theoretical interest, the bounds offer the means in voting system studies of approximating the probability that a proposal is approved in a particular simple game having a complex component arrangement. The practical interest of the bounds is that they can be useful for simple games having a tedious MLE to evaluate exactly, but whose minimal winning coalitions and minimal blocking coalitions can be determined by inspection. Such simple games are quite numerous.

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A critical reappraisal of some voting power paradoxes

Cited by 26 publications

References 35 publications

A Complete Geometric Representation of Four-Player Weighted Voting Systems

A Complete Geometric Representation of Four-Player Weighted Voting Systems

A Violation of Monotonicity in a Noncooperative Setting

Bounds for Owen's Multilinear Extension

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