[EM] Modeling elections

[Blake Cretney]

  Richard Moore wrote:

> Blake Cretney wrote:
> > Anyway, I hope I didn't make any errors.  If anyone is interested in my
> > Python code, I'll post it on my web site.  I have a feeling not 
> everyone
> > is going to agree with the assumptions of my model, so let the debate
> > begin.
>
> I don't know what all of your assumptions are -- particularly, what 
> sort of
> strategy was used for Approval; I guess for Borda and Condorcet you used
> sincere rankings only?

Sincere for everything.  For approval, a voter "approved" of all 
candidates that were closer to that voter than the average for that voter.

>>  I've recently been experimenting with modeling elections.  I'm 
>> particularly interested in models that take the view that there is a 
>> right answer, with voters varying in their ability to see the best 
>> solution.  This is quite different than looking at the election as an 
>> opportunity for each person to express the utility of an option to 
>> them, in the hopes of maximizing perceived utility.
>
>
> It does sound a little strange. This might be a good model for an 
> election
> to decide which baseball team is the best -- there should be a right 
> answer
> (or possibly three or more, since the teams compete pairwise so there can
> be cycles), and maybe some observers will be more able than others to see
> which team is best. But political elections aren't like that.

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 think I can explain the drop in Approval performance. Note the 
> following
> result:
>
>> Here's one last one.  I went back to the normal distribution, but set 
>> the candidate standard deviation to 0.25, resulting in a candidate 
>> field superior to the voters.
>>
>> plurality 0.540424844931
>> approval 0.767877868695
>> borda 0.747518871757
>> random 0.788082777819
>> condorcet 0.668325197385
>>
>> Not surprisingly, random candidate becomes the best.
>
>
> In this case Approval got a lot better. Approval seems to be particularly
> sensitive to candidate distribution in your model, and I observed this
> in my sims as well. Here's what happens: When candidates are clustered
> in some local region of issue space, there is a tendency of Approval
> to skew towards that region in simulations of this sort. After thinking
> about it a while, I realized that this isn't real-world voter behavior.
> Imagine two clone candidates in an Approval election. Each voter will
> either approve both, or disapprove both. But if the clones become the
> two front-runners, then each one only has a 50% chance. This is then
> equivalent to the situation where the clones are represented by a
> single proxy, and if that proxy wins, she will pick one of the clones
> at random to be the winner. The proxy will not pick up any additional
> votes by representing two (or any number of) candidates. If they are
> only near-clones, then the effect will be diminished, but should still
> be very strong. The more they are separated, the weaker the effect,
> with the effect vanishing when the candidates are all evenly spread
> out.
>
> The difference between the simulation and the real world is this:
> A simulated voter will examine its utilities, giving each of the
> clones the same weight as the other candidates (or in proportion
> to the weights of the other candidates, if non-ZI), in order to
> calculate its Approval cutoff point. A simulated voter that opposes
> the clones will thus go farther in compromising, whereas one that is
> on the clone's side will compromise less. A real voter *who is aware
> that the clones are clones* will understand that they can't both
> win, and will divide that weight by the number of members of the
> clone set, and thus arrive at a different cutoff point.
>
> Of course, this does mean that not recognizing clone candidates
> could put a voter at a strategic disadvantage. But to some extent
> most voters do this already: Suppose there "isn't a dime's worth
> of difference" between the Democrat and the Republican, and that
> clone set has a 98% chance of winning. Then each of the two
> candidates has a 49% chance of winning, and this fact isn't lost
> on the voter who doesn't realize they are clones. Unfortunately,
> it's a lot more subtle when the clone set has only a 20% chance
> of winning.

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.

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.

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.

---
Blake Cretney


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