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

[Kristofer Munsterhjelm]

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".