# [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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