[EM] Re: completing Condorcet using ratings information
Chris Benham
chrisbenham at bigpond.com
Tue Jun 22 23:22:02 PDT 2004
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
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