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<font size="2"><b><br>
</b></font><b> <dd><font size="2" color="#808080">Charla del
IMASL</font> </dd>
</b><dd><b><font size="4" color="#000080">“</font></b><font
face="Calibri" size="3"><font face="Arial Rounded MT Bold"
color="#009900"><b><span style="line-height: 17px;"></span></b></font></font></dd>
<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
style="line-height:21px;color:rgb(68,68,68)">
</font> </dd>
<dd><font size="2"> </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
style="line-height:21px;color:rgb(68,68,68);font-size:15px">
<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>
</p>
<p> Lugar: Aula 1, 1er piso Edificio IMASL<br>
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<p><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>
<div><font face="Calibri" size="3"><span
style="color:rgb(68,68,68);line-height:21px"><br>
</span></font></div>
<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>
</span></font></div>
<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>
<br>
</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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