[EM] Re: are ranked pairs and river Schwartz-consistent?

[Chris Benham]

James G-A  and anyone interested,
The meaning of my last post might not be completely clear, because I 
twice omitted the word "minimum" in my explanation
of  the  "Descending minimum Augmented Gross Score"  method.
Here are the two sentences, corrected:

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.

And here is the whole (corrected) post.

James,
Interesting,  maybe this casts some light on the mystery of  why  the 
Smith set is mentioned much more often the  Schwartz set.
Does any problem arise with  RP, River etc. if  a line is simply added 
at the front  "Eliminate non-members of the Schwartz set"?

Your example:

5: RSAT
5: TARS
4: STAR
4: RAST
3: TRAS
3: SATR
2: ATRS
2: SRAT
1: ASRT
1: TRAS

Out of curiosity, I determined the winner of one of the methods Woodall 
discusses,
"Descending minimum Augmented Gross Score" (DminAGS) which he says meets 
"Condorcet(Net)", meaning
that the winner is always in the Smith set (which he calls the 
"Condorcet(Net)Top Tier").
A candidate's "augmented gross score" against another candidate is its 
pairwise score against that
candidate based on the symetrically completed ballots, that is with 
"abstainers" and those who vote
them equal all contributing a half-vote to each of the two candidates.
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.
All possible coalitions are thus scored (including single candidates). 
Those candidates not in the
coalition with the highest score are eliminated. Any remaining 
candidates who are not in the coalition
with the second highest score are eliminated, and so on until one remains.

My table of scores:

  S   T   A   R
S  x   19  14  10

T  11  x   13  18

A  16  17  x   15

R  20  12  15  x

The coalitions with their min. scores:
STA 10, STR 13, SAR 12, TAR 11,
ST 10, SA 10, SR 12, TA 11, TR 11, AR 12,
S 10, T 13, A 15, R 12.

The "coalition" with the highest score is A, so all the other candidates 
are eliminated and A wins.

Using an on-line vote counter, I see that A is also unequivocally 
elected by Beat Path (Schulze and
LeGrand), Simpson (aka MM), and Raynaud.

> From your post I now know that DminAGS is not equivalent to 
> River(Margins).



Chris Benham












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