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Mike,<br>
Your first impression may be a bit off. The line I gave:<br>
<blockquote type="cite">
<pre>"A candidate whose weight exceeds half the total weight wins outright."</pre>
</blockquote>
is like the majority stopping rule in IRV. It has no effect on the result.
Here is another, perhaps more precise,<br>
wording :<br>
<pre>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
</pre>
<blockquote type="cite"> </blockquote>
WMA <br>
25: Brown Jones<br>
26: Davis Smith Brown<br>
49: Jones Smith Brown<br>
<br>
WMA scores: Brown: 100 Davis: 26 Jones: 74 Smith: 75 <br>
<br>
Brown wins with 100% approval. This method has in common with Bucklin a
severe failure of Later-no-harm, combined<br>
with meeting Later-no-help, to create big incentives to truncate. Here if
the 49 Jones>Smith>Brown voters had truncated<br>
after Smith, then Smith would have won and if they had truncated after
Jones (bullet-voted) then Jones would have won.<br>
<br>
An interesting method that I prefer is WMA-STV. The WMA scores are used
as the fixed elimination schedule for <br>
fractional STV with a majority stopping rule. Taking the above example:<br>
<br>
WMA-STV: Eliminate Davis, which raises Smith's top preference score to 26
(short of a majority), so eliminate <br>
(next on the fixed elimination schedule) Jones, which raises Smith's top
preference score to 75 (a majority) so<br>
Smith wins.<br>
This time if the 49 Jones voters bullet-vote, Smith and Davis are eliminated
but then Brown wins (so the truncation backfires).<br>
<br>
>From what I understand of Forest's post "Bucklin and determining the highest
generalized median rank", Smith in the above<br>
example is the candidate with the highest "generalized" median rank.<br>
<a
href="http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-April/012642.html"><br>
http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-April/012642.html</a><br>
<br>
<br>
Chris Benham<br>
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