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Participants,<br>
Here is my improvement on previous versions of "Weighted Median Approval"
single-winner ranked-ballot method.<br>
<br>
Voters rank the candidates. Equal preferences and truncation ok.<br>
(1) Symetrically complete the ballots.<br>
(2) Based on these now symetrically completed ballots, give each candidate
a weight of 1 for each ballot on which it is<br>
ranked in first place. (The total weight of the candidates will now be equal
to the total number of original before-step-1<br>
ballots. Any candidate with a weight equal to or greater than half the
total weight of all the candidates wins).<br>
(3) Each ballot fully approves the highest-ranked candidates whose combined
weight is less than half the total weight of<br>
all the candidates. Each ballot also fractionally approves the next highest-ranked
candidate, so that the combined weight<br>
of the candidates approved by each ballot is equal to half the total weight
of all the candidates.<br>
(4) The candidate with the highest approval score wins.<br>
<br>
This method meets (mutual) Majority, Independence of Clones, Participation,
Reverse Symetry, Symetric Completion,<br>
Woodall's Plurality criterion, and Independence of Pareto-Dominated Alternatives.
It is independent of any losers with <br>
no first preferences.<br>
It fails Condorcet, Later-no-harm, Later-no-help, and Steve Eppley's "resistance
to truncation" criterion. <br>
It might be ok regarding his other two "defensive strategy" criteria: "minimal
defense" and "non-drastic defense".<br>
<br>
49:A>B<br>
24:B<br>
27:C>B<br>
100 ballots. B is the CW and Borda winner.<br>
<br>
Symetrically completing the ballots, this becomes:<br>
49:A>B>C<br>
12:B>A>C<br>
12:B>C>A<br>
27:C>B>A<br>
<br>
These ballots give these approvals <br>
49: 1xA, .04167xB<br>
12: 1xB, .5306xA<br>
12: 1xB, .963xC<br>
27: 1xC, .583xB<br>
<br>
This gives these final approval scores: A: 55.367, B:51.9158, C: 39.46,
so A wins (as in DSC, Margins and IRV).<br>
<br>
If all the 24 B voters vote B>C, then Majority says "not A", and B wins.(an
example of the method failing Later-no-help.)<br>
<br>
This example is not the best advertisement for the method, which I like.<br>
<br>
Chris Benham <br>
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