[EM] Venzke's election simulations

[Kevin Venzke]

Hi Warren,

--- En date de : Mar 8.6.10, Warren Smith <warren.wds at gmail.com> a écrit :
> >> 1. I think using
> utility=-distance
> > is not as realistic as something like
> > utility=1/sqrt(1+distance^2)
> >
> > I claim the latter is more realistic both near 0
> distance
> > and near
> > infinite distance.
> 
> > Why would that be? Do you mean it's more intuitive?
> 
> --because utility is not unboundedly large.  If a
> candidate gets
> further from you, utility does not get worse and worse
> dropping to
> -infinity.
> No.   Eventually the candidate as he moves
> away approaches the worst
> he can be for you, which is, say, advocating your death,
> and then
> moving the candidate twice as far away doesn't make him
> twice as bad
> from your perspective, and 10X as far doesn't make him 10X
> worse.  It
> only makes him a little worse.
> 
> So my formula behaves better near infinity.

A difficulty with this is that you have to know where this reduction in
effect (of distance) occurs in comparison to where the voters are. In
other words are there really voters who advocate policies so bad for me
that I can't feel any difference among them, while they can?

> Also, near 0 distance, it seems plausible there is a smooth
> generic
> peak, like the valley in U, not in V which has a
> corner.    Hence
> again my formula more realistic near 0.
> Why should there be a singularity at 0?  Shouldn't
> utility depend
> smoothly on location?
> If it should, then you must refuse to permit corners.

This seems to have the same difficulty, of where is the curve? Suppose 
the issue is how close the bus will drop me off to my stop. Maybe there 
is a curve... Maybe 1 meter isn't twice as good as 2 meters. But maybe
1 mile is twice as good as 2 miles. Within a simulation it's not clear
what we're talking about.

> Incidentally the formula could be
>   A/sqrt(B+distance^2)
> where A and B are positive constants chosen to yield
> reasonable results.
> 
> 
> >> 2. It has been argued that L2 distance may not be
> as
> > realistic as L1 distance.
> > L2=euclidean
> > L1=taxicab
> 
> > That's interesting. I wonder what arguments were
> used.
> 
> --well, it was claimed.   It's
> debatable.   If I differ from you on 3
> issues, that ought
> to be 3X as bad as 1 issue, not sqrt(3) times as bad.
> It seems to make some sense.

Yes, I'm thinking it makes sense at the moment.
 
> >Well, it would be better to cycle over some of the
> locations, but taking
> the average over all possible locations would not be very
> good evidence
> either, since not all locations are equally likely.
> 
> --average over the correct nonuniform distribution of
> location-tuples.
> I admit, what that is, is not obvious :)
> But eventually you'll have to summarize in one number, which means 
> you have to
> do this.  With some luck it may turn out not to matter
> too much which
> distribution is chosen from among a few reasonable ones.

I think it's more likely that rather than guess at the correct 
distribution, I would try to categorize all possible scenarios according
to noteworthy effects.

It's pretty clear to me that if you just toss out candidates randomly,
RangeNS will usually win. It just happens that in the scenarios I pick
out as being of interest to me, RangeNS isn't usually winning. So I would
like to investigate this to find exactly what are the circumstances that
cause methods like Bucklin or DAC to prevail.

Kevin Venzke