Mensuração de Índices de Poder em Jogos de Votação Ponderada por Simulação de Monte-Carlo (Measurement of Power Indexes in Weighted Voting Games by Monte-Carlo Simulation)

Moacir Manoel Rodrigues Jr (, Volmir Eugênio Wilhelm (

1Universidade Regional de Blumenau/Universidade Federal do Paraná
2Universidade Federal do Paraná

This paper appears in: Revista IEEE América Latina

Publication Date: March 2016
Volume: 14,   Issue: 3 
ISSN: 1548-0992

This paper aims to present a simulation model, through the Monte Carlo method that measures the Power Index of the Banzhaf and Shapley-Shubik. The problematic has been prepared taking into consideration the complexity involved in the calculation these indices for large voting commissions. The study involved one simulation model for each power index, and made two simulations, the first with 10 thousand coalition and other with 100 thousand coalition successively repeated for 200 times. The results pointed to confirm the potential of the established simulation. The results presented absolute errors mean less than 10^(-3)for model with 10 thousand simulations and less than 10^(-4) for model with 100 thousand simulations. Likewise, analyzing linear correlation between the standard deviation of the estimates and the absolute error, it was confirmed that the standard deviation could be understood as a factor of control of the estimated error. It was concluded by satisfaction of aim of the research and verification of the Monte Carlo simulation as a potentially applicable to estimated Power Indexes Banzhaf and Shapley-Shubik.

Index Terms:
Shapley-Shubik Index, Banzhaf Index, Monte-Carlo Simulation.   

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