[EM] Venzke's election simulations

[Warren Smith]

>WDS:   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.

>RBJ: i dunno, Warren.  maybe if the candidate advocates for starving,
torturing, and then killing your kids and other descendants,
relatives.  a holocaust for your ethnic group.  then fouls the entire
environment of your homeland to extract resources for he and his
unworthy buddies.  but i agree, there might be a limit.

--WDS: I think it is clear there is a limit.   If he moves a trillion
times further away than
the cnddt advocating your death, does that make him a trillion times worse?
Seems to me it is simply not possible  to get a trillion times worse.
OK, not convinced? Replace "trillion" with "10^100."   The behavior at
infinity was wrong.

>Venzke: 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?
...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.

--WDS: right.  That is why I suggest using  util=A/sqrt(B+distance^2)
where choose the positive constants A,B to get reasonable behavior.
I admit "reasonable behavior" is somewhat subjective and depends on the
scenarios you are setting up... you've inherently introduced a length
scale the minute you actually set up any scenario..., but you can try
a few scenarios and make sure to use A,B that do something reasonably
sane in them, given the length scale you chose.

And by the way, there really IS a length scale, set by the parameters
defining "a human life." I contend human utility simply is not
scale-free.

Let me elaborate a little since not enough people seem to have "got it."

In issue space, you are assuming there is some utility that depends
only on candidate-voter distance.  Once you assume that, there are two
questions:

(a) What is the right notion of "distance"?
(b) Utility is clearly a MONOTONE DECREASING function f of distance,
but which f to use?

One can make a case L1 distance seems a good answer to (a), at least
better answer than L2 distance.   Or maybe it ought to be L(1.1).

Now I argued re (b) that the function ought to asymptote to a constant
at infinite distance
and further I even feel it should behave like const/x+const   at large
distance x.
Somebody might complain infinity is not a place of great concern in
the real world -- which may or may not be true (actually it might
matter a lot) -- but even if we dodge that debate, just getting the
right QUALITATIVE behavior for f seems important at the least to
prevent you from looking like  a total moron.
   And also I argued utility ought to be a SMOOTH (e.g. everywhere
differentiable)
function of location.  My selection of the formula
   f(x) = A / sqrt(B+x^2)    for some constants A>0, B>0
was not because it was written on a gold tablet from God, it was
simply because this was the simplest formula I could think of that
obeys the desiderata I just mentioned about behavior at infinity,
smoothness, and monotone decreasing.
The attempted formulas
   f2(x) = A/(B+x^2)
   f3(x) = exp(-x^2)
   f4(x) = A/(B+x)
   f5(x) = -x
   f6(x) = -x^2
   f7(x)=sin(x)
would fail to satisfy because of too-fast asymptotic at infinity,
ditto, nonsmooth corner at 0 distance, wrong behavior at infinity and
corner, wrong at infinity, and nonmonotone respectively.

IEVS by the way uses my f-formula and also has Lp distance with
user-choosable p.
I'd recommend Venzke also do that, plus if he wanted to keep his
present thing he could rename it "expected distance" rather than
"utility."

In a sense Venzke is redoing IEVS his own way independently.   That's good since
it is good to have independence and also he's putting in different
voting methods and different strategizing/polling.  Hopefully his
results will mostly agree with mine/IEVS, but hopefully also he will
find something new.

>Venzke:
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.

--well, if you can somehow understand what is "interesting" and bias
your distribution toward interestingness (and somehow justify that
biasing as being realistic, otherwise it is just data fudging) then
you might find RangeNS is no longer best.  I cannot say at present.
I still think at some point you have to settle on some distribution
also you can make a recommendation of some voting system.

IEVS include an option to use what I call "reality based distributions."
That is, there is a database of about 100 real world rank-ballot
elections.  You can
download my dataset to make your own yourself, see
   http://rangevoting.org/TidemanData.html
and if you do it'd be nice to place whatever cleaner nicer bigger set
you get, back
on that CRV webpage.
   Anyhow, IEVS uses a somewhat cheesy hack to generate "randomized
perturbations" of the real elections to get an infinite set of
reality-based fake elections equipped with
reality-based utilities.   Anyhow, roughly speaking, using the reality based
distribution rather than more simpleminded distributions (which IEVS also has)
in practice does not seem to make much difference to my BR results.   Roughly
speaking the same results come out.

But anyway, glad to hear Venzke's sort-of-endorsement of range voting.


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