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

[Chris Benham]

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 AGS is its smallest such score against any other candidate. A coalition's 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