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

[Dave Ketchum]

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.

Dave Ketchum

On Nov 8, 2009, at 6:33 AM, Kristofer Munsterhjelm wrote:

> robert bristow-johnson wrote:
>> On Nov 5, 2009, at 1:35 PM, Kristofer Munsterhjelm wrote:
>>> robert bristow-johnson wrote:
>
>>>> i don't think a sequence of elimination rounds would be okay, but  
>>>> the method of picking the biggest loser for each round needs to  
>>>> be debated.  i am not sure what would be best.
>>>
>>> Are you referring to IRV here?
>> no.  i mean if there is a Condorcet cycle, as an alternative to  
>> Schulze or Ranked Pairs or whatever, you could start with the Smith  
>> Set and, with some meaningful metric, eliminate a candidate deemed  
>> to be the biggest loser, then rerun the superficial Condorcet tally  
>> (just see if there is a Condorcet winner among the candidates left)  
>> and repeat until a Condorcet winner is apparent from the candidates  
>> left over.
>
> I've been browsing old posts of this list, and I've encountered the  
> idea or method of "sprucing up", which may be of interest in this  
> respect:
>
> http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2004-December/014372.html
>
> The relevant post for determining cycles is here:
>
> http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2004-December/014373.html
>
> and basically says that, in public elections, and in every election  
> if the base method passes certain criteria, the question of how to  
> resolve cycles can be reduced to drawing the borders of three  
> regions of a triangle. The complexity of the question has thus been  
> reduced quite a bit, even if it is now very abstract.
>
> On another note, Condorcet cycles don't have to be resolved through  
> elimination. Also, there may be subsets of the Smith or Schwartz  
> set, such as the uncovered (Landau, Fishburn) set, that have just  
> one candidate even when the former sets have multiple, that can be  
> used to resolve the cycles. Picking uncovered candidates confers  
> protection against certain forms of strategy, as well.
>
> All of this is theoretical, since the methods are too clumsy for  
> public proposal, but one has to start somewhere :-)
>
>>> You're right. If I were to guess, I'd say that in most situations,  
>>> unless the electorate is small or uncertain, there will be a CW;  
>>> however, once the method has been adopted, parties will try to  
>>> coordinate strategies to induce a cycle,
>> really?  Terry B (also a Burlington resident) told me that, and i  
>> find that to be an untested hypothesis.  since the parties do not  
>> know who will benefit from a cycle (who can tell the future?), i  
>> really have my doubts about that.
>
> They'll try, but that doesn't necessarily mean they'll succeed. If  
> the method resists the initial strategy, they would eventually give  
> up. In the case of STV, vote management did work (but it was very  
> risky), and so the parties continued, adding noise to the system. I  
> do think the "good" methods (River, MAM/Ranked Pairs, Schulze, etc)  
> will manage to resist the initial attempts at coordinated strategy,  
> but it does emphasize that you need some resistance to strategy in  
> order to survive the metaphorical birth of fire.
>
> Some strategies could be maintained longer than others. Those that  
> involve manipulation of the candidate set would be easier for a  
> party than those that involve electoral strategy, for instance; so a  
> method should be cloneproof (which the three I mentioned are), and  
> should be independent of as many alternatives as possible (the three  
> are all independent of candidates not in the Smith set, and River is  
> also independent of Pareto-dominated alternatives).
>
> The voters themselves might also strategize. Such strategy would be  
> less coordinated, but this is where the critics of Condorcet focus  
> their efforts: if a large share of the electorate "bury" candidates  
> (vote A > ... > B instead of A > B > ... because B "is a threat"),  
> then you can get bad outcomes. The question here is whether the  
> public will actually do that.
>
>> in Burlington Vermont, Repubs who voted for their candidate as  
>> their first pick actually helped elect (with IRV) the candidate  
>> they liked the least and that would not have happened if it was  
>> Condorcet.  they are mistaken in their belief that their candidate  
>> (the FPTP winner) should have won, but i can understand their voter  
>> regret in that their vote for their guy actually caused the  
>> election of the candidate they liked the least.
>
> Yes, it brings to mind a few pictures I saw on the web.
>
> http://www.braindoll.net/vote/#Which%20version%20is%20best%20%28or: 
> %20Grudgeless%20Match%20between%20the%20Tomorrow%20Twins%29.3.1
>
> FPTP's football field is nearly vertical, IRV's is better but still  
> has a hill in it (minor parties are safe as long as they're minor,  
> but when they start getting large, they'll interfere with the runoff  
> process). Condorcet's is flat :-)
>
>>> There's certainly precedence for this,
>> not with Condorcet there is.  it's never been used in a government  
>> election.
>
> I meant more broadly. The parties will *try*, but will they succeed?  
> Depends on the method.
>
>>> Unlike FairVote et al, we don't have a strong voice saying "Hey  
>>> public, if you think Plurality sucks, implement [method here]".
>> but if FairVote won't keep all of their eggs in the IRV basket,  
>> then we need someone to do the same for Condorcet.
>
> FairVote doesn't? I thought their problem was that they had  
> "committed" to IRV as the electoral method from heaven, and thus  
> they have to stick with it rather than, for instance, say "Oh, oops,  
> we were wrong, turns out that system is actually better".