[EM] [ER] FBC-complying Margins-like method (?)
Chris Benham
chrisbenham at bigpond.com
Mon Dec 19 09:49:54 PST 2005
Kevin, Warren, other FBC freaks,
I've recently had an idea for a FBC-complying Margins method.
"Voters rank the candidates, equal-ranking and truncation allowed.
(1) Make pairwise comparisons. Treating pairwise defeats by margins
that are smaller
than or equal to the number of ballots on which both candidates are
ranked equal-top
as pairwise equalities, eliminate candidates that are not in the
smallest non-empty set of
candidates that are pairwise undefeated by any outside-the-set candidates.
(2)If more than one candidate remains, drop eliminated candidates from
the ballots and
then delete ballots that make no ranking distinction between remaining
candidates, and repeat
step 1.
(3) Repeat steps 1 and 2 as many times as possible. (If at any stage
only one candidate remains
then that candidate is the winner.)
(4) If after step 3 more than one candidate remains, then with ballots
that rank both the candidates in
a pairwise comparison equal-top used to modify the defeat margins by
counting as whole single votes
for the pairwise loser (so that some margins can be negative, but not so
that any pairwise defeats can
be reversed); change the pairwise defeat by a smallest margin to an
equality; and as in step 1 again
eliminate candidates that are not in the smallest non-empty set of
candidates that are pairwise undefeated
by any outside-the-set candidates.
(5) If more than one candidate remains, then again drop eliminated
candidates from the ballots and then
delete ballots that make no ranking distinction between remaining
candidates.
(6) Keep repeating steps 4 and 5 until only one candidate remains."
In common with MDD,ER-Bucklin(whole) I think it meets Majority for
Solid Coalitions and Condorcet(Gross).
But unlike that method, it meets Independence from Irrelevant Ballots.
Chris Benham
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