[EM] Condorcet How? Abd

[Kevin Venzke]

Hi Abd,

--- En date de : Sam 10.4.10, Abd ul-Rahman Lomax <abd at lomaxdesign.com> a écrit :
> > It remains bad.
> 
> There is absolutely no way to tell that an outcome is bad
> unless underlying utilities are studied.
> 
> This is a classic vote-splitting outcome.

That's why I prefer the version that doesn't look like a vote-splitting
outcome. In that case the outcome is "bad" because it produces nomination
disincentive. And in general going against majority opinion (which is my
allegation) is usually *not* good for utility.

I can't study the underlying utilities because I don't have them. If I
did I could make them say anything I wanted. I would have to come up
with a general rule anyway, or else give up and say all methods are the
same.

You talk about having multiple rounds of voting. But even if that helps,
it's not something that will always be possible. It's an interesting
subject though.

> My point is that from a mere preference profile, one cannot
> determine who the "best" winner of an election is.
> Preference strength information is necessary. Doing this in
> a real election can be difficult without additional
> constraints, and the most common one is the requirement for
> majority approval.

> > Well, I have assumptions about what tends to maximize
> utility. The ideal
> > scenario for me is that the median voter has 3+ viable
> options to pick
> > from (and not find the choice obvious).
> 
> An assumption about what tends to maximize utility can be
> way, way off. That's what I believe I showed above.

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.

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.

> > > (There may also be some extreme situations where
> the sum of
> > > utilities is not what we want. For example it
> might make
> > > sense to improve the utility of all voters worth
> 10 points
> > > rather than improve the utility of all but one
> voter with 12
> > > points and then kill or otherwise cause a major
> decrease in
> > > utility to that remaining one voter.
> 
> Eh? It might make sense to appoint our favorite the
> dictator, as well. Why bother with these stinkin'
> elections?

Juho said that. I think he's probably right, but in practice I don't think
our information is precise enough to find these situations.

Kevin Venzke