Fwd: Fw: Ciclo de Charlas IMASL NUEVAMENTE: De Cantor a Gödel

[Instituto de Matemática Aplicada San Luis]

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    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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