[EM] Approval Strategy A- Question for Rob LeGrand
Dgamble997 at aol.com
Dgamble997 at aol.com
Thu Nov 20 15:23:21 PST 2003
Hello Rob and List
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.
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:
> Strategy A: Approve all candidates I prefer to the current CRAB
> first-placer; also approve the first-placer if I prefer him to the
> second-placer.
>
> [S]trategy A always homes in on the Condorcet winner when one exists
> and all voters use the same strategy.
>My 25-candidate simluations still haven't found a single contradiction to
the
>above statement after over 15000 elections.......
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.
Take the example below:
A 380
A>B 28
A>C 9
B 80
B>A 2
B>C 133
C 4
C>A 13
C>B 351
The Condorcet winner is C beating A by 501 to 419 and beating B by 377 to
243.
I used the following assumptions:
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).
2/ All candidates given a ranking in the Condorcet election would be approved
in a sincere Approval election.
The Approval poll in the above election based on these assumptions would
have shown the following:
A approved by 432 voters
B approved by 594 voters
C approved by 510 voters
Using strategy A the 215 voters who give a first preference to B approve only
B.
The 4 C voters approve C, the 13 C>A voters approve C and A and the 351 C>B
voters approve only C.
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.
A 380 approve A
A>B 28 approve AB
A>C 9 approve AC
B 80 approve B
B>A 2 approve B
B>C 133 approve B
C 4 approve C
C>A 13 approve AC
C>B 351 approve C
This gives the following result in the Approval election:
A 432 winner
B 243
C 377
C is the Condorcet winner but A wins using strategy A under Approval.
Why am I getting different results, am I applying strategy A incorrectly or
am I using different assumptions to the ones you used?
David Gamble
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