[EM] Modeling elections

[Adam Tarr]

Blake wrote:

>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?

Well no, there is some right answer, even if it is not clear at the 
time.  But in my opinion, your fallacy is thinking that the "best" election 
method will more reliably hone in on it.  I think we're better off just 
trying to get good reflections of the public will, then imagining that we 
can deduce which portions of the public are right.

That said, I still find your idea interesting, and I could be wrong about 
my objections, so I'd like to see your results with a more realistic 
model.  Here's my problem with your model: you assume that a voter can 
identify where they, or a candidate, lies on a "rightness" scale.  In 
reality, the voters only know where they and the candidates lie on the 
issue space.  So in order to model this idea accurately, you need to assign 
a "rightness" function that maps any point on the issue space to the 
interval [0,1].  (or (-infinity, 1] as you have it modeled)

The only case where this is equivalent to your approach is when we have a 
one-dimensional issue space, and the "rightness" function is a linear; i.e. 
one extreme is "correct".  As an example of a difference, if the "correct" 
answer in the 1-D issue space is toward the middle, then you will have 
voters on the left and the right of the political center who are equally 
"correct" but will vote for completely different candidates.

My advice is to model the election with various candidate and voter 
distributions along the issue space, combined with various "rightness" 
models that put the "correct" point at various positions along the issue 
space.  Rightness of each candidate could be determined by either absolute 
or squared distance from the "correct" point.  You could try a 1-D issue 
space, and then see if adding dimensions changes your results.

-Adam

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