[EM] Re: reccomendations (Scwartz // SC-WMA correction)

Chris Benham 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

Chris  Benham

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