[EM] Quota Limited Weighted Approval (oops! reference to Margins was wrong)
Chris Benham
chrisbenham at bigpond.com
Thu Feb 26 11:16:15 PST 2004
Participants,
Here is my improvement on previous versions of "Weighted Median
Approval" single-winner ranked-ballot method.
Voters rank the candidates. Equal preferences and truncation ok.
(1) Symetrically complete the ballots.
(2) Based on these now symetrically completed ballots, give each
candidate a weight of 1 for each ballot on which it is
ranked in first place. (The total weight of the candidates will now be
equal to the total number of original before-step-1
ballots. Any candidate with a weight equal to or greater than half
the total weight of all the candidates wins).
(3) Each ballot fully approves the highest-ranked candidates whose
combined weight is less than half the total weight of
all the candidates. Each ballot also fractionally approves the next
highest-ranked candidate, so that the combined weight
of the candidates approved by each ballot is equal to half the total
weight of all the candidates.
(4) The candidate with the highest approval score wins.
This method meets (mutual) Majority, Independence of Clones,
Participation, Reverse Symetry, Symetric Completion,
Woodall's Plurality criterion, and Independence of Pareto-Dominated
Alternatives. It is independent of any losers with
no first preferences.
It fails Condorcet, Later-no-harm, Later-no-help, and Steve Eppley's
"resistance to truncation" criterion.
It might be ok regarding his other two "defensive strategy" criteria:
"minimal defense" and "non-drastic defense".
49:A>B
24:B
27:C>B
100 ballots. B is the CW and Borda winner.
Symetrically completing the ballots, this becomes:
49:A>B>C
12:B>A>C
12:B>C>A
27:C>B>A
These ballots give these approvals
49: 1xA, .04167xB
12: 1xB, .5306xA
12: 1xB, .963xC
27: 1xC, .583xB
This gives these final approval scores: A: 55.367, B:51.9158, C:
39.46, so A wins (as in DSC and IRV).
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.)
This example is not the best advertisement for the method, which I like.
Chris Benham
.
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