# [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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