[EM] Venzke's election simulations

[Warren Smith]

>> 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.

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.

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.

>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.


-- 
Warren D. Smith
http://RangeVoting.org  <-- add your endorsement (by clicking
"endorse" as 1st step)
and
math.temple.edu/~wds/homepage/works.html