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James G-A and anyone interested,<br>
The meaning of my last post might not be completely clear, because I twice
omitted the word "minimum" in my explanation<br>
of the "Descending minimum Augmented Gross Score" method.<br>
Here are the two sentences, corrected:<br>
<br>
<pre>A candidate's minimum AGS is its smallest such score against any other candidate. A coalition's minimum
AGS is the smallest AGS of any of the candidates in the coalition against any of the candidates outside
of the coalition.</pre>
And here is the whole (corrected) post.<br>
<br>
<div class="moz-text-flowed"
style="font-family: -moz-fixed; font-size: 13px;" lang="x-western">James,
<br>
Interesting, maybe this casts some light on the mystery of why the Smith
set is mentioned much more often the Schwartz set. <br>
Does any problem arise with RP, River etc. if a line is simply added at
the front "Eliminate non-members of the Schwartz set"? <br>
<br>
Your example: <br>
<br>
5: RSAT <br>
5: TARS <br>
4: STAR <br>
4: RAST <br>
3: TRAS <br>
3: SATR <br>
2: ATRS <br>
2: SRAT <br>
1: ASRT <br>
1: TRAS <br>
<br>
Out of curiosity, I determined the winner of one of the methods Woodall discusses,
<br>
"Descending minimum Augmented Gross Score" (DminAGS) which he says meets
"Condorcet(Net)", meaning <br>
that the winner is always in the Smith set (which he calls the "Condorcet(Net)Top
Tier"). <br>
A candidate's "augmented gross score" against another candidate is its pairwise
score against that <br>
candidate based on the symetrically completed ballots, that is with "abstainers"
and those who vote <br>
them equal all contributing a half-vote to each of the two candidates. <br>
A candidate's minimum AGS is its smallest such score against any other candidate.
A coalition's minimum AGS is the smallest AGS of any of the candidates in
the coalition against any of the candidates outside of the coalition. <br>
All possible coalitions are thus scored (including single candidates). Those
candidates not in the <br>
coalition with the highest score are eliminated. Any remaining candidates
who are not in the coalition <br>
with the second highest score are eliminated, and so on until one remains.
<br>
<br>
My table of scores: <br>
<br>
S T A R <br>
S x 19 14 10 <br>
<br>
T 11 x 13 18 <br>
<br>
A 16 17 x 15 <br>
<br>
R 20 12 15 x <br>
<br>
The coalitions with their min. scores: <br>
STA 10, STR 13, SAR 12, TAR 11, <br>
ST 10, SA 10, SR 12, TA 11, TR 11, AR 12, <br>
S 10, T 13, A 15, R 12. <br>
<br>
The "coalition" with the highest score is A, so all the other candidates
are eliminated and A wins. <br>
<br>
Using an on-line vote counter, I see that A is also unequivocally elected
by Beat Path (Schulze and <br>
LeGrand), Simpson (aka MM), and Raynaud. <br>
<blockquote type="cite">From your post I now know that DminAGS is not equivalent
to River(Margins). <br>
</blockquote>
<br>
<br>
Chris Benham <br>
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