[EM] Re: Approval Strategy A- Question for Rob LeGrand
Dgamble997 at aol.com
Dgamble997 at aol.com
Fri Nov 21 12:15:20 PST 2003
Rob LeGrand wrote in response to my post:
>The short answer is that you're allowing the voters to adjust their votes
>only once. With repeated adjustments, the voters would be able to find the
>equilibrium
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)?
My original example:
A 380 A
A>B 28 AB
A>C 9 AC
B 80 B
B>A 2 BA
B>C 133 CB
C 4 C
C>A 13 CA
C>B 351 CB
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.
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:
A 380 A
A>B 28 AB
A>C 9 AC
B 80 B
B>A 2 B
B>C 133 B
C 4 C
C>A 13 CA
C>B 351 C
The results of the second approval opinion poll are A 430, B 243 and C 377.
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:
A 380 A
A>B 28 A
A>C 9 A
B 80 B
B>A 2 BA
B>C 133 BC
C 4 C
C>A 13 C
C>B 351 CB
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:
A 380 A
A>B 28 AB
A>C 9 AC
B 80 B
B>A 2 B
B>C 133 B
C 4 C
C>A 13 CA
C>B 351 C
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?
David Gamble
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