[EM] About non-monotonicity and non-responding to previous posts...

[Kristofer Munsterhjelm]

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).