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

[Kristofer Munsterhjelm]

robert bristow-johnson wrote:
> On Nov 5, 2009, at 9:30 AM, Kristofer Munsterhjelm wrote:
> 
>> robert bristow-johnson wrote:
>>> being pretty much completely converted to the condorcet faith, i have 
>>> no problem with non-monotonicity that happens to non-condorcet 
>>> winners.  i still do not understand any realistic scenario where 
>>> non-monotonicity affects the condorcet winner.
>>
>> What is your opinion regarding methods, such as Nanson, Baldwin, and 
>> Raynaud, that are nonmonotonic when there is no Condorcet winner?
> 
> i dunno any of those methods (references would be nice, but i can google 
> for them).  the only methods i know about are Ranked pairs, Schulze (but 
> i haven't dug into the actual method to search out all beatpaths and 
> rank them), Kemeny-Young.  i see that Nanson is on the list at 
> Wikipedia, but not Baldwin nor Raynaud (at least by those names).

Baldwin is described on the same page as Nanson. In short, Baldwin is 
Borda IRV whereas Nanson is below-average Borda runoff (all candidates 
with below average Borda score are eliminated). These, while not nearly 
as good as Schulze and Ranked Pairs, might be more palatable to a public 
that has been sold IRV.

Though, if minimal change to IRV is the objective, bottom two runoff 
works: instead of eliminating the Plurality loser, do a "runoff" 
(pairwise contest) between the two candidates with least Plurality 
votes, then eliminate the loser - thus the Condorcet winner is never 
eliminated. Or even simpler: keep eliminating until there's a CW among 
the remaining candidates, then that candidate wins.

None of these are summable and they're not monotone either, so I would 
definitely prefer Ranked Pairs or Schulze.

Raynaud goes like this: repeatedly eliminate the loser of the strongest 
pairwise defeat until only one candidate remains. This is summable, but 
not monotone.

> simplicity and sufficient transparency is important to have public 
> confidence.  otherwise i would probably just jump on the Schulze bandwagon.

Ranked Pairs might be good here. If you can get the one you're 
explaining it to, to understand the pairwise way of thinking, then it 
"easily" follows that if you're going to build a ranking for society 
itself piece by piece, the stronger defeats should be considered before 
the weaker ones, and there you have Ranked Pairs.

On the other hand, more organizations use Schulze than Ranked Pairs, so 
it comes down to which inspires greater confidence: simplicity or a 
record of use.

> 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?

>> Do Condorcet winners appear often enough in reality that it is not a 
>> problem?
> 
> since no government yet uses Condorcet, i don't think any of us know the 
> answer.

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, because that's the only way 
they can game the system. There's certainly precedence for this, in how 
the various parties in STV New York tried to employ vote management to 
get more than their fair share of the local council.

> but for there to be a paradox, you would need a situation where there is 
> no predictable voter alignment along a single dimensioned political 
> spectrum.  you would need to have (in 2000) a lot of Nader voters who 
> choose Bush over Gore as their second choice, and Bush voters that 
> sincerely choose Nader over Gore, something i really do not expect.

Perhaps the existence of Condorcet would permit variety to the point 
that the political spectrum becomes multidimensional? For instance, 
there might be left-right and unitary-federalist. With the right 
distributions, these can lead to cycles. Whether or not that 
diversification will actually happen is a question to which I don't know 
the answer.

> while having *something* meaningful in law to deal with a Condorcet 
> cycle, i really think that the lack of "the perfect solution" to the 
> paradox problem (that likely will never happen in a real election with 
> real candidates) should not be used as a block to adopting Condorcet in 
> general.  what to do with a cycle can be adjusted at a later time.

That might be a problem, because we discuss many different Condorcet 
variants on the EM list. Unlike FairVote et al, we don't have a strong 
voice saying "Hey public, if you think Plurality sucks, implement 
[method here]".