<HTML><FONT FACE=arial,helvetica><FONT SIZE=2 FAMILY="SANSSERIF" FACE="Arial" LANG="0">Rob LeGrand wrote in response to my post:<BR>
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>The short answer is that you're allowing the voters to adjust their votes<BR>
>only once. With repeated adjustments, the voters would be able to find the<BR>
>equilibrium <BR>
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Thanks for the information. So am I right in thinking that strategy A gets to the Condorcet winner by a process of iteration. In response to a series of Approval polls the voters alter their choices and end up voting in such a way that they elect the Condorcet winner. Or is it more complex than this in theory (I know it's more complex in reality)?<BR>
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My original example:<BR>
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A 380 A<BR>
A>B 28 AB<BR>
A>C 9 AC<BR>
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B 80 B<BR>
B>A 2 BA<BR>
B>C 133 CB<BR>
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C 4 C<BR>
C>A 13 CA<BR>
C>B 351 CB<BR>
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In the first opinion poll everybody indicates that they will vote for all candidates they sincerely approve giving the poll result A 432, B 594 and C 510.<BR>
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A second opinion poll is conducted and all voters apply strategy A on the basis of the first opinion poll and now say they will vote:<BR>
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A 380 A<BR>
A>B 28 AB<BR>
A>C 9 AC<BR>
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B 80 B<BR>
B>A 2 B<BR>
B>C 133 B<BR>
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C 4 C<BR>
C>A 13 CA<BR>
C>B 351 C<BR>
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The results of the second approval opinion poll are A 430, B 243 and C 377.<BR>
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A third opinion poll is conducted and all voters apply strategy A on the basis of the information in the second opinion. They now indicate they will vote:<BR>
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A 380 A<BR>
A>B 28 A<BR>
A>C 9 A<BR>
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B 80 B<BR>
B>A 2 BA<BR>
B>C 133 BC<BR>
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C 4 C<BR>
C>A 13 C<BR>
C>B 351 CB<BR>
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The results of the third opinion poll are A 419, B 566 and C 501. If voters apply strategy A to the results of this poll we get the Approval choices:<BR>
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A 380 A<BR>
A>B 28 AB<BR>
A>C 9 AC<BR>
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B 80 B<BR>
B>A 2 B<BR>
B>C 133 B<BR>
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C 4 C<BR>
C>A 13 CA<BR>
C>B 351 C<BR>
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this gives the result A 430, B 243 and C 377. This is identical to the result of the second poll. Using strategy A in this case appears to lead to a cycle which alternates A>>B>>A >>B >>A>>....... how do the voters reach an equilibrium point where C is the winner?<BR>
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David Gamble<BR>
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