[EM] Re: reccomendations (Scwartz // SC-WMA correction)
chrisbenham at bigpond.com
Mon Sep 6 13:32:54 PDT 2004
Oops! (again). I have discovered that one of the criterion
compliances I claimed for Schwartz:// Symetrically Completed-
Weighted Median Approval was wrong.
> Voters rank the candidates, truncation ok. Non-last equal prefernces
> also ok (but a version that doesn't allow them is also good
> and might be a more practical proposition).
> Eliminate the non-members of the Schwartz set (and henceforth
> continue as though they had never stood).
> Symetrically complete the ballots.
> Now apply the "Weighted Median Approval" method to pick the winner, thus:
> Each (remaining) candidate is assigned a "weight" which is equal to
> the number of first-prefernces they get. The sum of the "weights"
> is equal to the total number of non-empty ballots.
> Each ballot approves the candidate they rank in first-place. If the
> weight of candidates so far approved by a ballot sums to less than
> half the total weight of all the candidates, then that ballot also
> approves the candidate they rank second.
> And so on until each ballot has approved at least half the candidates
> "by weight".
> The candidate with the highest total (thus derived) approval score wins.
If there are three candidates, all in the Schwartz set, then each
ballot approves the two highest-ranked candidates and those
ballots that only rank one candidate approve that candidate and
half-approve the other two.
I wrongly claimed that it meets the Non-Drastic Defense criterion.
32:A>C>B (maybe sincere is A>B>C)
A majority vote B over A, and B no lower than equal first, and yet A
In compliance with the criterion, Winning Votes would have elected B.
Schwartz://SC-WMA seems to have a more severe
Later-no-harm problem. Also, I've been shown some evidence that in some
3-candidate scenarios, the method is more
vulnerable to completely uncountered Burying than is Winning Votes.
So it looks as though compliance with the Sincere Expectation Criterion
(SEC) could be a bit more expensive than I
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