<HTML><FONT FACE=arial,helvetica><FONT SIZE=2 FAMILY="SANSSERIF" FACE="Arial" LANG="0">Hello Rob and List<BR>
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Recently I've been trying to develop a spreadsheet model to investigate the effect of the use of different voting systems ( Plurality, IRV, Borda, Condorcet and Approval) on the results of elections to a multi-member assembly elected in single districts.<BR>
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I wanted to use in my model an Approval strategy which Approval supporters ( of which I am not one) say will give a result that is satisfactory to the voters. I decided to use Rob LeGrand's strategy A. Rob said the following about strategy A:<BR>
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> Strategy A: Approve all candidates I prefer to the current CRAB<BR>
> first-placer; also approve the first-placer if I prefer him to the<BR>
> second-placer.<BR>
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> [S]trategy A always homes in on the Condorcet winner when one exists<BR>
> and all voters use the same strategy.<BR>
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>My 25-candidate simluations still haven't found a single contradiction to the<BR>
>above statement after over 15000 elections....... <BR>
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Whilst strategy A is undoubtedly good at finding the Condorcet winner (if there is one) in my simulations it only found the Condorcet winner in 96-98 % of contests not 100% of the time.<BR>
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Take the example below:<BR>
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A 380 <BR>
A>B 28<BR>
A>C 9<BR>
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B 80<BR>
B>A 2<BR>
B>C 133<BR>
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C 4<BR>
C>A 13<BR>
C>B 351<BR>
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The Condorcet winner is C beating A by 501 to 419 and beating B by 377 to 243.<BR>
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I used the following assumptions:<BR>
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1/ The voters base their Approval strategy on a 100% accurate Approval poll ( which would be identical to the result of the actual election if all voters had sincerely voted for every candidate they approved of).<BR>
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2/ All candidates given a ranking in the Condorcet election would be approved in a sincere Approval election.<BR>
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The Approval poll in the above election based on these assumptions would have shown the following:<BR>
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A approved by 432 voters<BR>
B approved by 594 voters<BR>
C approved by 510 voters<BR>
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Using strategy A the 215 voters who give a first preference to B approve only B. <BR>
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The 4 C voters approve C, the 13 C>A voters approve C and A and the 351 C>B voters approve only C.<BR>
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The 380 A voters approve A, the 28 A>B voters approve A and B and the 9 A>C voters approve A and C.<BR>
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A 380 approve A<BR>
A>B 28 approve AB<BR>
A>C 9 approve AC<BR>
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B 80 approve B<BR>
B>A 2 approve B<BR>
B>C 133 approve B<BR>
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C 4 approve C<BR>
C>A 13 approve AC<BR>
C>B 351 approve C<BR>
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This gives the following result in the Approval election:<BR>
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A 432 winner<BR>
B 243<BR>
C 377<BR>
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C is the Condorcet winner but A wins using strategy A under Approval.<BR>
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Why am I getting different results, am I applying strategy A incorrectly or am I using different assumptions to the ones you used?<BR>
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David Gamble<BR>
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