[EM] Re: Weighted Mean Approval
Chris Benham
chrisbenham at bigpond.com
Fri Apr 9 22:34:01 PDT 2004
Mike,
Your first impression may be a bit off. The line I gave:
>"A candidate whose weight exceeds half the total weight wins outright."
>
is like the majority stopping rule in IRV. It has no effect on the
result. Here is another, perhaps more precise,
wording :
Weighted Mean Approval .
Voters rank the candidates, equal preferences ok.
Each candidate is given a weight of 1 for each ballot on which that
candidate is ranked alone in first place, 1/2 for each ballot on
which that candidate is equal ranked first with one other candidate,
1/3 for each ballot on which that candidate is ranked equal first with
two other candidates, and so on so that the total of all the weights
equals the number of ballots.
Then approval scores for each candidate is derived thus: each ballot
approves all candidates that are ranked in first or equal first place
(and does not approve all candidates that are ranked last or equal
last). Subject to that, if the total weight of the approved candidates
is less than half the total of number of ballots, then the candidate/s
on the second preference-level are also approved, and the third, and so
on; stopping as soon as the total weight of the approved candidates
equals or exceeds half the total mumber of ballots.
The candidate with the highest approval score wins.
Take this recently discussed Bucklin example:
25:Brown>Jones>Davis>Smith
26:Davis>Smith>Brown>Jones
49:Jones>Smith>Brown>Davis
Weights: Brown: 25 Davis: 26 Jones: 49 Smith: 0
WMA
25: Brown Jones
26: Davis Smith Brown
49: Jones Smith Brown
WMA scores: Brown: 100 Davis: 26 Jones: 74 Smith: 75
Brown wins with 100% approval. This method has in common with Bucklin
a severe failure of Later-no-harm, combined
with meeting Later-no-help, to create big incentives to truncate. Here
if the 49 Jones>Smith>Brown voters had truncated
after Smith, then Smith would have won and if they had truncated
after Jones (bullet-voted) then Jones would have won.
An interesting method that I prefer is WMA-STV. The WMA scores are
used as the fixed elimination schedule for
fractional STV with a majority stopping rule. Taking the above example:
WMA-STV: Eliminate Davis, which raises Smith's top preference score to
26 (short of a majority), so eliminate
(next on the fixed elimination schedule) Jones, which raises Smith's top
preference score to 75 (a majority) so
Smith wins.
This time if the 49 Jones voters bullet-vote, Smith and Davis are
eliminated but then Brown wins (so the truncation backfires).
From what I understand of Forest's post "Bucklin and determining the
highest generalized median rank", Smith in the above
example is the candidate with the highest "generalized" median rank.
http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-April/012642.html
Chris Benham
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