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

Chris Benham chrisbenham at bigpond.com
Mon Sep 6 13:32:54 PDT 2004

```Hello,
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)
45:B>A>C
23:C=B>A

A majority vote B over A,  and B no lower than equal first, and yet  A
wins.

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
thought.

Chris  Benham

```