Ciclos de Charlas del IMASL
Instituto de Matemática Aplicada San Luis
imasl en unsl.edu.ar
Vie Mar 1 11:15:55 ART 2013
Charla del IMASL
**
**
*"Measuring Power in Weighted Voting: The Generating Function Method"*
A cargo de: *Profesor Peter Tannenbaum *
(Fulbright Specialist Program, California State University Fresno)
Fecha: Martes 5 de Marzo - 12:10 hs
Lugar: Aula 1, 1er piso Edificio IMASL
Abstract:
In many voting situations voters are not all equal, and it is desirable
to recognize their differences. A weighted voting system is a system of
voting in which the differences among the voters are formally recognized
by giving different voters control over a different number of votes:
voter 1 controls w1 votes, voter 2 controls w2 votes, etc. Weighted
voting systems are most common when the voters are institutions
(countries, provinces, financial institutions, etc.)
One of the fundamental questions in a weighted voting system is how much
power each voter holds over the decision-making process. This question
is non-trivial because the power of a voter is not linearly related to
the weight of that voter---in fact, the relation between weights and
power is very complicated and non-linear. There are two classical
approaches for computing the power of a voter in a weighted voting
system: the Shapley-Shubik measure of power and the Banzhaf measure of
power. The Banzhaf measure uses ordinary coalitions (subsets) of the
voters, and the calculations are of the order of 2! computations; the
Shapley-Shubik measure uses sequential coalitions (permutations) of the
voters, and the calculations are of the order of n! computations. Either
way, traditional calculations are impractical for voting systems with n
> 30.
In this talk I will: (a) describe the Banhaf and Shapley-Shubik methods
for computing power (both in a deterministic as well as a probabilistic
situation); (b) describe a new method (the method of generating
functions) that allows us to efficiently calculate power for very large
weighted voting systems, and (c) illustrate the efficiency of the
generating function method with an example of a probabilistic weighted
voting system with n =51 players.
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