What I wrote last time is about as simple as you get. Canceling the
smallest margin cancels a three-member cycle, leaving the strongest
member as CW. Could take more canceling for more complex, and thus
rarer, cycles.
Dave Ketchum
On Nov 10, 2009, at 7:54 AM, Kristofer Munsterhjelm wrote:
Dave Ketchum wrote:
Trying some fresh thinking for Condorcet, and what anyone should be
able to see in the X*X array. I am ignoring labels such as Schulze
and Ranked Pairs - this is human-doable and minimal effort -
especially with normally having a CW and most cycles having the
minimal three members.
1. Look at any pair of candidates. Loser is not the CW (there
can be a tie in any comparison here - NOT likely in a normal
election, but we have to be prepared with responses for such).
2. If there are other possible CWs, repeat step 1 with latest
winner and one of them.
3. If there are other candidates latest winner has not been
compared with, compare it with each of them.
4. If winner wins each of these, it is CW.
5. Winner and each who beat it in step 4 are cycle members. Also,
any candidate beating any of these is also a cycle member.
IF there is a CW, it should win - anything else is a complication,
even if some math makes claims for the something else.
Otherwise a simple cycle resolution should apply. Simply
canceling the smallest margin has been thought of - that value
means minimum difference in vote counts between actual and what is
assumed.
Note that each cycle member would be CW if remaining cycle
members were ignored.
As to voting:
Equal ranks permitted.
Write-ins permitted, and such a candidate wins with the same
vote counts as if nominated.
As to clones, strategy, primaries, and runoffs - all seem best
ignored, though only a nuisance if some are determined to involve
such.
Okay, so let's see which *simple* cycle breaker provides as much as
possible. To do that, we'll need to find out what simplicity means,
and how to define "as much as possible".
That could be interesting in itself.
Ranked Pairs (or River) seems nice, but even it may be too complex.
Sports usually employ Copeland (but modified); perhaps that could be
used - but Copeland is indecisive. One can add Smith compliance by
checking for a CW among the first n ranked in the output, then n-1,
then n-2 and so on, but that might also be too complex.
Of course, if simplicity is paramount (i.e. we want very simple) we
could just go with "break it by whoever beats the Plurality winner
by the greatest amount" or plain old minmax (candidate with least
worst defeat wins) or LR (greatest sum of victories wins).
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