[EM] Condorcet How? Abd

[Kevin Venzke]

Hi Abd,

--- En date de : Dim 11.4.10, Abd ul-Rahman Lomax <abd at lomaxdesign.com> a écrit :
> > In a given election yes, it is easy to miss the mark.
> But in general,
> > aiming for the median voter is the most reliable.
> (That is assuming you
> > don't know utilities, which I'm really not sure you
> showed how to find.)
> > To see this, you assume utility is based on issue
> space distance, and
> > that the voters aren't distributed unevenly.
> 
> I didn't show how to find utilities, I only showed various
> possibilities consistent with the votes.

Yes, and my response is what can I possibly do with that? You used one
method that was rather Borda-like in character. One can't evaluate methods
using a Borda-like criterion or you'll end up advocating something 
Borda-like.

> To study voting system performance, I'm saying, one must
> *start* from utilities, not from preference order without
> preference strength information. Voter behavior is not
> predictable without preference strength information.
> Strategy, in general, doesn't make sense without an
> understanding of preference strength.

We sort of have been doing this when Juho questions the story behind my
scenarios.

> > Thus when you have a situation where every voter
> chimed in on some
> > question, and they didn't do that for any other
> question, you should
> > expect (on average) a utility problem when the outcome
> goes against the
> > majority opinion.
> 
> I'll agree that this is the "norm." However, it can go
> drastically wrong.
> 
> How can we detect the exceptions?

Right, that's the question.

> Sure, the majority criterion and the condorcet criterion
> are usually a sign of good performance, but it is obvious
> that exceptions exist, and we should not denigrate a voting
> system if it, under an exception condition, it violates the
> criteria!

I wouldn't, no. But I would presumably have some model that explains why
violation of the criterion worked.

> I was just pointing out that the outcome you claimed was
> obviously bad wasn't. It might be that, on average, this
> outcome would be poorer than the other, 

Yes, I'm afraid that's what I call "bad." If I didn't call this "bad" I
would also have to be pretty undecided about the resolution of most 
two-candidate FPP elections.

> but it was not a truly bad outcome, 
> under reasonable assumptions of likely
> utility, the first utility scenario I gave, which used Range
> 2 utilities, i.e., normalized and rounded off so as to make
> all the votes sincere and sensible. The bullet voters then
> had equal bottom utilities for the other candidates, and
> those who ranked had stepped utilities. Simple. And showing
> that A was, indeed (with these assumptions, which seem
> middle-of-the-road to me), the utility maximizer, by a
> fairly good margin!

This was the Borda-like thing I mentioned above.

> You can make a contrary assumption, that the A voters were
> "strategic." That they "really" would be happy with B. I'm
> assuming, instead, that their votes would be sincere. And
> likewise the votes of the other voters.
> 
> Look, A *almost* has a majority in first preference. I'm
> very suspicious of claims that an election outcome is
> "terrible" if it depends on some close-shave majority that
> failed.

You are really missing my complaint then. According to your stepped
utility analysis C voters don't like B that much at all. If they know
that the method interprets such votes that way, then it is really bad 
to vote sincerely for C.

I initially read your last paragraph with disbelief. In my interpretation,
C and his votes are just noise. The task of the election method is to pick
the right candidate between A and B, just as it would be in FPP (where C
would probably have died off pre-election). To be unable to do this is
quite useless in my view.

--- En date de : Dim 11.4.10, Abd ul-Rahman Lomax <abd at lomaxdesign.com> a écrit :
> > This should rather say, if I proposed utilities behind
> the scenario, I
> > could make those utilities say anything I wanted.
> 
> I pointed out some extremes, which reveal as the ideal
> winner A, B, or C. In other words, you are apparently
> agreeing with me.

Yes.

> However, I believe that I showed that a
> middle-of-the road assumption about underlying utilities,
> with stated assumptions that were not designed to make it
> turn out some particular way, A could indeed be the best
> winner.

Yes you did.

> (I did not set out to "prove" that A was the best winner,
> but rather just to attempt to infer utilities from the
> voting patterns, which didn't allow me to assume equal
> ranking except at the bottom).
> 
> The matter hinges on the A voters, who are, after all,
> almost a majority. Why did none of them rank B or C? The
> only reasonable assumption is that they have strong
> preference, and that's what ices it.

I'm happy to say that A voters have a strong preference, but why should
only the A voters get to benefit from this? Are you saying the other
voters don't have a strong preference against A?

> This is the classic
> reason to violate the Condorcet or Majority criteria: a
> strong preference of a minority, particularly when the
> margin is thin.
> 
> If, in fact, B and C were true clones, with only minor
> preference between them, the assumption of a significant
> reduction of utility between them (which is the other factor
> that lowers the rating for B and C) would fail.
> 
> If the method allowed equal ranking, we'd see that in the
> votes, and B might win. The A votes would be the same, the B
> bullet voters would be the same, but the other B and C
> voters would equal rank B and C. Because of the B bullet
> voters, B would win by a small majority.
> 
> So my result for A could be an artifact of the voting
> system not allowing equal ranking. I used Range 2, which
> doesn't give a lot of room for "creative interpretation."
> That was much easier with Range 10, as I showed. With Range
> 2, there wasn't any other reasonable way to interpret the
> votes. 

It's possible that with equal ranking it would be different, but if we
are not going to ask a method to behave unless voters use equal ranking,
I guess we could just use Approval.

Kevin Venzke