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<font size="2" color="#808080">Charla del IMASL</font>
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<b> </b><dd><font face="Calibri" size="3"><font face="Arial
Rounded MT Bold" color="#009900"><b><span
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<dd><font face="Calibri" size="3"><font face="Arial Rounded MT
Bold" color="#009900"><b><span style="line-height:
17px;">"Measuring Power in Weighted Voting: The
Generating Function Method"</span></b></font><br
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<dd><span
style="color:rgb(68,68,68);font-size:15px;line-height:21px">A
cargo de: <b>Profesor Peter Tannenbaum </b></span><br
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<span
style="color:rgb(68,68,68);font-size:15px;line-height:21px">(Fulbright
Specialist Program, California State University Fresno)</span></dd>
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<p> Fecha: Martes 5 de Marzo - 12:10 hs<br>
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<p> Lugar: Aula 1, 1er piso Edificio IMASL<br>
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<p><font face="Calibri" size="3"><span
style="color:rgb(68,68,68);line-height:21px">Abstract: </span></font></p>
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<div><span
style="font-family:Calibri;font-size:12pt;color:rgb(51,51,51);line-height:17px">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 </span><span
style="font-family:Calibri;font-size:12pt;display:inline;color:rgb(51,51,51);line-height:17px">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.)</span></div>
<div><font face="Calibri" size="3"><span
style="display:inline;color:rgb(51,51,51);line-height:17px"><br>
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<div><font face="Calibri" size="3"><span
style="display:inline;color:rgb(51,51,51);line-height:17px">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. <br>
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</span></font></div>
<div><font face="Calibri" size="3"><span
style="display:inline;color:rgb(51,51,51);line-height:17px">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.</span></font></div>
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