Your first impression may be a bit off. The line I gave:
is like the majority stopping rule in IRV. It has no effect on the result. Here is another, perhaps more precise,"A candidate whose weight exceeds half the total weight wins outright."
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