[EM] Re: Approval Strategy A- Question for Rob LeGrand

[Dgamble997]

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