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
- Re: [EM] Approval Strategy A- Question for Rob LeGrand Dgamble997
- Re: [EM] Approval Strategy A- Question for Rob LeGrand Kevin Venzke
- [EM] Re: Approval Strategy A- Question for Rob LeGrand Rob LeGrand
- Re: [EM] Approval Strategy A- Question for Rob LeGrand Gervase Lam
- RE: [EM] Approval Strategy A- Question for Rob LeGr... James Gilmour
- Re: [EM] Approval Strategy A- Question for Rob LeGr... Kevin Venzke
- RE: [EM] Approval Strategy A- Question for Rob LeGrand Gervase Lam