Characterization of Transitive Individual Preferences for Quasi-Transitive Collective Preference under Simple Games

1976 ◽  
Vol 17 (2) ◽  
pp. 308 ◽  
Author(s):  
Maurice Salles
Keyword(s):  
Simple Games ◽  
Individual Preferences ◽  
Collective Preference

scholarly journals On the characterization of weighted simple games

2017 ◽  
Vol 83 (4) ◽  
pp. 469-498 ◽  
Author(s):  
Josep Freixas ◽  
Marc Freixas ◽  
Sascha Kurz
Keyword(s):  
Simple Games

scholarly journals ON GAMES OF PERFECT INFORMATION: EQUILIBRIA, ε–EQUILIBRIA AND APPROXIMATION BY SIMPLE GAMES

2005 ◽  
Vol 07 (04) ◽  
pp. 491-499 ◽  
Author(s):  
GUILHERME CARMONA
Keyword(s):  
Payoff Function ◽  
Perfect Information ◽  
Perfect Equilibrium ◽  
Simple Games ◽  
Original Game ◽  
Approximation Sequence ◽  
Perfect Equilibria

We show that every bounded, continuous at infinity game of perfect information has an ε–perfect equilibrium. Our method consists of approximating the payoff function of each player by a sequence of simple functions, and to consider the corresponding sequence of games, each differing from the original game only on the payoff function. In addition, this approach yields a new characterization of perfect equilibria: A strategy f is a perfect equilibrium in such a game G if and only if it is an 1/n–perfect equilibrium in Gn for all n, where {Gn} stands for our approximation sequence.

scholarly journals Voting Method Based on an Average Gap Assessment

2019 ◽  
Vol 12 (3) ◽  
pp. 1176-1186
Author(s):  
Zoinabo Savadogo ◽  
Abdoulaye Compaore ◽  
Pegdwinde Ousseni Fabrice Ouedraogo
Keyword(s):  
Social Choice ◽  
Political System ◽  
Electoral Systems ◽  
Individual Preferences ◽  
Voting System ◽  
Voting Methods ◽  
The Individual ◽  
Collective Preference ◽  
Voting Method ◽  
Democratic Political System

The theory of social choice is the study of voting methods. In the literature manystudies have been conducted for the development of a fair voting system, that is to say a voting method that allows to aggregate the individual preferences in a collective preference representing in the most possible faithfull way individual preferences. Yet some voting methods do not allow to obtain a consensus. So there are a lot of paradoxes in electoral systems and related results in the theory of social choice are also paradoxical. This is the case, for example, with Arrow’s theorem showing that no voting method can simultaneously verify a restricted list of  roperties that are desirable in a democratic political system. That is to mean that the search for a system that makes it possible to reach a consensus remains a concern in the theory of social choice. In this article we have combined various voting methods based on grading, scoring or approving to contribute to literature with a new voting system filling fair properties.

scholarly journals Weightedness and structural characterization of hierarchical simple games

2013 ◽  
Vol 65 (3) ◽  
pp. 181-189 ◽  
Author(s):  
Tatiana Gvozdeva ◽  
Ali Hameed ◽  
Arkadii Slinko
Keyword(s):  
Structural Characterization ◽  
Simple Games

scholarly journals An Axiomatization for Two Power Indices for (3,2)-Simple Games

2019 ◽  
Vol 21 (01) ◽  
pp. 1940001 ◽  
Author(s):  
Giulia Bernardi ◽  
Josep Freixas
Keyword(s):  
Power Index ◽  
Power Indices ◽  
Simple Games ◽  
Banzhaf Index ◽  
Null Player

The aim of this work is to give a characterization of the Shapley–Shubik and the Banzhaf power indices for (3,2)-simple games. We generalize to the set of (3,2)-simple games the classical axioms for power indices on simple games: transfer, anonymity, null player property and efficiency. However, these four axioms are not enough to uniquely characterize the Shapley–Shubik index for (3,2)-simple games. Thus, we introduce a new axiom to prove the uniqueness of the extension of the Shapley–Shubik power index in this context. Moreover, we provide an analogous characterization for the Banzhaf index for (3,2)-simple games, generalizing the four axioms for simple games and adding another property.

scholarly journals A Generalization of Arrow’s Lemma on Extending a Binary Relation

2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Athanasios Andrikopoulos
Keyword(s):  
Abelian Group ◽  
Social Choice ◽  
Binary Relation ◽  
Abelian Groups ◽  
Extension Theorem ◽  
Impossibility Theorem ◽  
Binary Relations ◽  
Extension Theorems ◽  
Individual Preferences

By examining whether the individualistic assumptions used in social choice could be used in the aggregation of individual preferences, Arrow proved a key lemma that generalizes the famous Szpilrajn’s extension theorem and used it to demonstrate the impossibility theorem. In this paper, I provide a characterization of Arrow’s result for the case in which the binary relations I extend are not necessarily transitive and are defined on abelian groups. I also give a characterization of the existence of a realizer of a binary relation defined on an abelian group. These results also generalize the well-known extension theorems of Szpilrajn, Dushnik-Miller, and Fuchs.

Morphological Characterization of Mycobacteriophage R1

1974 ◽  
Vol 32 ◽  
pp. 254-255
Author(s):  
B. L. Soloff ◽  
T. A. Rado
Keyword(s):  
Carbon Source ◽  
Stationary Phase ◽  
Growth Phase ◽  
Minimal Medium ◽  
Morphological Characterization ◽  
Logarithmic Growth Phase ◽  
Complete Lysis ◽  
Lysogenic Culture ◽  
Logarithmic Growth

Mycobacteriophage R1 was originally isolated from a lysogenic culture of M. butyricum. The virus was propagated on a leucine-requiring derivative of M. smegmatis, 607 leu−, isolated by nitrosoguanidine mutagenesis of typestrain ATCC 607. Growth was accomplished in a minimal medium containing glycerol and glucose as carbon source and enriched by the addition of 80 μg/ ml L-leucine. Bacteria in early logarithmic growth phase were infected with virus at a multiplicity of 5, and incubated with aeration for 8 hours. The partially lysed suspension was diluted 1:10 in growth medium and incubated for a further 8 hours. This permitted stationary phase cells to re-enter logarithmic growth and resulted in complete lysis of the culture.

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