[EM] Inferring Approval Strategy From Ranked Ballots
Forest Simmons
fsimmons at pcc.edu
Tue Jan 27 19:32:01 PST 2004
Thanks to Dave Gamble for taking the time to do some examples of my idea,
and coming up with one that shows that this approval strategy can indeed
over-look the Condorcet Winner when there is a close three way finish.
It is interesting that this method picked the highest utility candidate
(the Borda winner, C ) in this example.
So we have a method that seems to beat Condorcet on utility (so far,
anyway) yet has good Condorcet efficiency, and suffers none of the clone
problems or favorite burial problems of Borda.
It sounds like it would be worth including in the next round of
simulations either as a self contained method or as a way of simulating
approval strategy in the non-zero info case, i.e. an alternative to
"Strategy A."
Forest
On Wed, 21 Jan 2004 Dgamble997 at aol.com wrote:
> Forrest Simmons wrote:
>
> >How good can we do with a simple rule of conversion of ranked ballots to
> >approval ballots?
>
> >Given a set of preference ballots, let n1, n2, ... be the numbers of top
> >rank votes for candidates c1, c2, ... , respectively. (For now assume that
> >every ballot fully ranks the candidates.)
>
> >Use these numbers n1, n2, ... as weights in the weighted median method for
> >determining the approval cutoff for each ballot.
>
> >That's it, except for a review of the "weighted median method for
> >determining approval cutoffs."
>
> >Suppose the weights are w1, w2, ... . In the present case the w's are the
> >n's . In Joe Weinstein's original proposal, the w's were the respective
> >winning probabilities
>
> This is quite an interesting idea. From looking at a very limited number of
> close examples based on one voting scenario I would guess (with 3 candidate
> contests) that this would find the Condorcet winner (if there is one) about 99%
> of the time.
>
> I did manage to construct an example where this conversion method failed
> though.
>
> 215 A>B>C approve A
> 169 A>C>B approve A
> 109 B>A>C approve BA
> 177 B>C>A approve BC
> 115 C>A>B approve C
> 215 C>B>A approve CB
>
> The Condorcet winner is B narrowly beating A and C.
>
> A v B 499 v 501
> C v B 499 v 501
> A v C 493 v 507
>
> The Approval winner is C ( A 493, B 501 and C 507).
>
> My guess, again, is that this conversion method will only fail in the closest
> of 3 candidates contest.
>
> David Gamble
>
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