[EM] Modeling elections

[Richard Moore]

Blake Cretney wrote:
> What are they like?  I don't think they're like choices of favourite ice 
> cream.
> 
> Consider the following.  I, and 10 other people, want to buy a big tub 
> of ice cream to split between us.  They all prefer chocolate, and I 
> prefer vanilla.  So, I argue that chocolate is not the rational 
> preference.  They don't think this is a sensible argument to take.  If 
> anyone is capable of changing preference, they argue, then I should. 
> This would increase the utility of the inevitable choice of vanilla. Of 
> course, converting all preferences to chocolate would have the same 
> benefit, but this would appear more difficult, and there is no reason 
> the prefer vanilla to chocolate in general.
> 
> Now, consider that I, and 10 other people want to decide how a society 
> should be governed.  They are all conservatives where as I am a liberal. 
> I try to argue the perceived advantages of liberalism, but they argue 
> that this is just the same situation as with the ice cream.  It makes no 
> sense to argue that a person should be a particular political opinion. 
> And if people are capable of change, it should be me who changes, since 
> this would make the result more pleasing to me, and there is no real 
> advantage between the two ideologies.
> 
> So, would you agree with that argument?

I'm not sure what your point is so I'll just elaborate on mine and you
can tell me where you disagree.

If we're voting to see which is the best baseball team, or the highest
mountain, or the brightest star in the sky, we are voting on something
that can be measured independently of the opinions of the voters. There
is one best answer (except maybe in the baseball case, where our
independent test would consist of playing the teams off against each
other, and there could emerge a cyclic tie).

Political elections and ice cream flavors are more similar to each
other than they are to the case of voting on something objective. So,
while it is possible that peer pressure may cause some voters to
change their opinion, that doesn't mean that the election is attempting
to find the one best answer. Rather, I see the election as attempting
to find the best-fit answer. (Notwithstanding Hitler/Stalin/Washington
examples -- If you tried to devise an "objective" test to weed out the
dictators and extremists you'll never get the population to agree
as to what questions would be on the test, so you're back to looking
for the best-fit candidate.)

> I think that analysis is close to being right, but I'm going to raise a 
> few objections.  It isn't clear what you mean by the term "clone".  I 
> don't think you mean clones using Tideman's definition.  I interpret you 
> as meaning that the candidates are essentially the same.

Yes, I mean that they occupy the same point in issue space. So every
voter will assign the same utility to each of the clones, or in a sincere
ranking they will be ranked the same (or adjacently) on every voters
ballot.

> All my candidate distributions were random, either from a normal or an 
> even distribution.  I think you would have trouble finding a firm 
> definition of when candidates are essentially the same, and when they 
> are not.  It's like looking at a starry night sky.  You would observe 
> some clumping (as even random distributions tend to look clumped).  But 
> you wouldn't be able to firmly define some stars as clone stars by their 
> proximity in the night sky.  So, I don't think it is as simple as 
> recognizing similar candidates, and then adapting one's strategy.

The candidates don't have to be exact clones to see the effect; the effect
varies with their proximity to each other. You would see this effect with
4 candidates all occupying the same quadrant of a 2-D space, even if the
four were occupying the four corners of that quadrant. The intensity of
the effect might be lessened, though.

If it seems unrealistic to confine the candidates to two (or some other
small number of) dimensions, because each voter may have issues with
some particular candidates that aren't shared by the other voters, then
just extend the issue space to as many dimensions are needed to represent
those private issues. I don't think this will negate the effect, however,
especially since I think public issues will dominate in most voters'
decisions, and since there is a lot of correlation of positions on
different issues, which Forest pointed out tends to collapse the issue
space.

Even with a large number of dimensions, you could always divide your
space into two half-hypercubes (label A and B). Then, supposing you run
your simulations with 5 candidates drawn at random. 1/32 of the time,
all candidates will be in the A half, and 1/32 of the time, all candidates
will be in the B half. But the orientation of the dividing hyperplane is
arbitrary, so the actual probability of all candidates being in the
same half-hypercube is going to be considerably more than 1/16. I think
even though the candidates aren't clustered tightly, there could be a
significant gravitation towards the denser (in candidate population)
half.

In your model, with "best" (highest score on some objective measure)
at one extreme end of the space, if you adjust the probability density
so that more candidates are closer to the opposite extreme, then the
gravitation will be towards that opposite extreme; if you adjust the
probability density so that more candidates are closer to the "best",
then the gravitation will be towards the "best".

In my model, the "best" (best-fit, actually) would be at or near the
center of the issue space, and skewing the distribution would always
tend to pull the result away from the center.

> I think you are right that more candidates in a region of the issue 
> space tends to pull the result in that direction in Borda, Approval, and 
> Random Candidate.  But this isn't quite the same as saying that it is 
> the result of clumping.  For example, it may be that better teachers 
> result in better test scores.  So test scores would be affected by 
> teacher quality distribution.  But I wouldn't characterize this as the 
> effect of clumps of good teachers.  That is, clumps of teachers at 
> similar, level of ability.  It's the over-all distribution, not the clumps.

If competency is an issue, as your last paragraph implies, then add a
dimension for that, too. Naturally, we hope that most voters will demand
competency as well as agreement on issues before they give their approval
to a candidate, but that seems not to always be the case.

  -- Richard

----
For more information about this list (subscribe, unsubscribe, FAQ, etc), 
please see http://www.eskimo.com/~robla/em