[EM] Re: completing Condorcet using ratings information

[Chris Benham]

Oops!  A  little mistake in my last post, a  "+1"  should  have read 
 "-1".  Correction and some elaboration below.

"Approval Margins":
 High-resolution ratings ballots. Inferring ranking from rating, 
eliminate the non-members of the Schwartz-set.
Of the remaining candidates, each ballot approves those candidates rated 
above average (and half-approves those rated precisely average).
Use the (inferred) rankings to determine the results of  the pairwise 
comparisons between the remaining candidates.
Then  measure the  "defeat strengths" by the differences in the 
candidates' approval scores. On that basis pick the  Ranked Pairs (or 
maybe some other pairwise method at least as good) winner.

James G-A's example:

24: A 100 > B 1 > C 0
24: A 100 > C 1 > B 0
22: B 100 > C 99 > A 0
04: B 100 > C 1 > A 0
01: B 100 > A 1 > C 0
22: C 100 > B 99 > A 0
03: C 100 > A 1 > B 0

100 ballots. A>B>C>A, all 51-49.

All candidates are in the Schwartz set, so each ballot approves those candidates rated above average.

48:A
22:BC
05:B
22:CB
03:C

Approval scores
A: 48
B: 49
C: 47

Pairwise comparisons, with approval margins
A>B 48-49 = -1
B>C 49-47 = +2
C>A 47-48 = -1

If we break the A>B/C>A tie by approval magnitude, then A wins.


Chris Benham