[EM] Inferring Approval Strategy From Ranked Ballots

Dgamble997 at aol.com Dgamble997 at aol.com
Wed Jan 21 15:11:03 PST 2004

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 

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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