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

[Dave Ketchum]

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).