An axiomatization of success

In this paper we give an axiomatic characterization of three families of measures of success defined by Laruelle and Valenciano (2005) for voting rules.power indices, voting power, collective decision-making, axiomatization

POTENTIAL, VALUE AND PROBABILITY

This paper focuses on the probabilistic point of view and proposes a extremely simple probabilistic model that provides a single and simple story to account for several extensions of the Shapley value, as weighted Shapley values, semivalues, and weak (weighted or not) semivalues, and the Shapley value itself. Moreover, some of the most interesting conditions or notions that have been introduced in the search of alternatives to Shapley's seminal characterization, as 'balanced contributions' and the 'potential', are reinterpreted from this same point of view. In this new light these notions and some results lose their 'mystery' and acquire a clear and simple meaning. These illuminating reinterpretations strongly vindicate the complementariness of the probabilistic and the axiomatic approaches, and shed serious doubts about the achievements of the axiomatic approach since Nash's and Shapley's seminal papers in connection with the genuine notion of value.Coalition games, value, potential

A CRITICAL REAPPRAISAL OF SOME VOTING POWER PARADOXES

Power indices are meant to assess the power that a voting rule confers a priori to each of the decision makers who use it. In order to test and compare them, some authors have proposed "natural" postulates that a measure of a priori voting power "should" satisfy, the violations of which are called "voting power paradoxes". In this paper two general measures of factual success and decisiveness based on the voting rule and the voters' behavior, and some of these postulates/paradoxes test each other. As a result serious doubts on the discriminating power of most voting power postulates are cast.Voting power, decisiveness, success, voting rules, voting behavior, postulates, paradoxes.

An axiomatization of success

In this paper we give an axiomatic characterization of three families of measures of success defined by Laruelle and Valenciano (2005) for voting rules

ASSESSMENT OF VOTING SITUATIONS: THE PROBABILISTIC FOUNDATIONS

In this paper we revise the probabilistic foundations of the theory of the measurement of 'voting power' either as success or decisiveness. For an assessment of these features two inputs are claimed to be necessary: the voting procedure and the voters' behavior. We propose a simple model in which the voters' behavior is summarized by a probability distribution over all vote configurations. This basic model, at once simpler and more general that other probabilistic models, provides a clear conceptual common basis to reinterpret coherently from a unified point of view di.erent power indices and some related game theoretic notions, as well as a wider perspective for a dispassionate assessment of the power indices themselves, their merits and their limitations.Voting rules, voting power, decisiveness, success, power indices

Probabilistic power indices for games with abstention

S'introdueixen vuit índexs de poder que admeten una interpretació probabilística per les normes de votació amb abstenció o amb tres nivells d'aprovació en l'entrada. S'analitzen les semblances i diferències entre els índexs estàndards coneguts pels jocs simples i per les extensions per aquest context més general. Es conclou la feina proporcionant procediments basats en la generació de funcions per jocs(3,2) extensibles a jocs (j,k).Preprin

Alocação de recursos baseado em desempenho : uma aplicação de Voting Games ao programa REHUF

Orientador : Prof. Dr. Volmir Eugênio WilhelmTese (doutorado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Métodos Numéricos em Engenharia. Defesa: Curitiba,31/07/2015Inclui referências : f. 142-153Área de concentração : Programação matemáticaResumo: A problemática da alocação de recursos é uma linha de estudo em diferentes áreas do conhecimento. Modelos aplicados a esta realidade surgem com diferentes características e em diferentes cenários. O governo federal brasileiro, por meio do Programa de Reestruturação dos Hospitais Universitários (REHUF), criou uma política de alocação de recursos à Hospitais Universitários (HU) com intuito de melhorar suas instalações e serviços. O questionamento que surge é como distribuir estes recursos para os 45 HUs vinculados ao Ministério da Educação de forma que seja pautado no desempenho operacional das entidades. Dá-se então o objetivo desta pesquisa como: Modelar a conciliação dos Voting Games, por meio dos Índices de Poder de Shapley-Shubik e Banzhaf, aos problemas de alocação de recursos com base no desempenho para Hospitais Universitários participantes do REHUF.. Os Jogos Cooperativos de Votação, admitidos aqui como Jogos de Maioria Ponderada, são utilizados para mensurar o poder que um jogador/eleitor possui em um comissão eleitoral onde há ponderação quanto a quantidade de votos de cada membro. A temática do desempenho está inserida no passo inicial da avaliação do desempenho, que é a sua mensuração. Para a mensuração do desempenho foram usados os Métodos de Apoio a Decisão Multicritério: T-ODA, TOPSIS, VIKOR, PROMETHEE II. Os Índices de Poder de Shapley-Shubik e Banzhaf foram estimados por meio de simulação de Monte-Carlo. Foram obtidos oito modelos de distribuição de recursos, sendo fruto da combinação de quatro métricas de desempenho e dois Índices de Poder. Os resultados apontam para as especificidades de cada modelo e que os Índices de Banzhaf e Shapley-Shubik, aplicados a grandes comissões eleitorais, obtém valores próximos entre si. Os modelos baseados nos métodos T-ODA e TOPSIS tenderam a favorecer entidades com desempenho menor. O modelo que utiliza a mensuração VIKOR de desempenho, admite uma maior concentração de recursos a HUs com maior desempenho. Os resultados da aplicação do método PROMETHEE II destacam variações distribuídas igualmente para todos os níveis de desempenho. Conclui-se assim que os modelos híbridos propostos se mostraram robustos corroborando com o que preconiza a literatura de que a construção dos Índices de Poder satisfaz os princípios da justiça e equidade entre os jogadores. Palavras-chaves: Problemas de Votação. Métodos de Apoio a Decisão Multicritério. Alocação de Recursos. Avaliação de Desempenho.Abstract: The problem of resource allocation is a study line in different areas of knowledge. Models applied to this reality arise with different features and in different scenarios. The Brazilian government, through the University Hospitals Restructuring Program (REHUF), created an investment policy in University Hospitals (UH) with purpose of improve its facilities and services. The question that arises is how to allocate these funds to the 45 HUs linked to the Ministry of Education as it was ruled into the operating performance of the entities. The objective of this research was given as: Modeling the conciliation of the Voting Games, through the Power Indexes of Shapley-Shubik and Banzhaf, to the resource allocation problem based on performance for University Hospitals participants REHUF. The Cooperative Games of Voting, admitted here as Weighted Majority Games, are used to measure the power that a player/voter has in an election commission where there is weight as the amount of votes of each member. The performance theme was inserted in the first step of performance evaluation, which is the measurement. For measuring the performance was used the Multiple Criteria Decision Making: T-ODA, TOPSIS, VIKOR, PROMETHEE II. The Power Indexes Banzhaf and Shapley-Shubik were estimated using Monte Carlo simulation. Obtained eight resource allocation models, being the result of the combination of four performance metrics and two Power Indexes. The results point to the specifics of each model and the Indexes of Banzhaf and Shapley-Shubik, applied to large commissions, gets values very close to each other. The models based on T-ODA and TOPSIS methods tended to favor entities with lower performance. The model uses the VIKOR performance measurement, accepts a higher concentration of funds to HUs with higher performance. The results of the application of PROMETHEE II method out equally distributed variations for all levels of performance. It is therefore concluded that the proposed hybrid models are robust confirming what literature recommends that the construction of the Power Index satisfy the principles of justice and equity among the players. Keywords: Voting Problems. Multiple-Criteria Decision Analysis. Allocation of Resources. Performance Evaluation