[EM] Modeling elections

[Adam Tarr]

Blake wrote:

>The "public will" has no clear meaning, as far as I can see.  Some members 
>of the public want one thing, some want something different. There is no 
>unified will.

Yes, but every candidate is some distance from each voter's ideal.  If we 
could count on every voter being completely sincere and expressive, we 
could have the voters rank each candidate in a fine-grained cardinal 
ranking, and pick the candidate with the minimum sum (squared/absolute) 
error.  Of course, we cannot assume a perfectly expressive and sincere 
electorate, so we pick an election method that tries to get as close to 
this as we can.

That's what I mean by "the public will", anyway.

>>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)
>
>Condorcet's method is often accused of favouring the middle candidate. An 
>example that assumed truth would lie in the middle could be accused of 
>making too many centrist assumptions in favour of Condorcet.  My first 
>model takes the opposite position, and puts truth at the far extreme.

I don't mean to imply that the truth is necessarily in the middle, only 
that it is not necessarily on the extreme.  Consider the fact that the 
issue space is not really one-dimensional, but has dozens of 
dimensions.  If the "correct" position is on the extreme in the 1-D 
approximation, this implies that the "correct" position is on an extreme in 
every dimension of the issue space.  Maybe that seems realistic to you, but 
it does not seem realistic to me.  I'd imagine that the correct position is 
on the extreme on some issues, but somewhat moderate on others.

Your last model, with the mean at .7, seems to follow this idea.

>Plurality, Borda, Approval, and Random Candidate are all strongly affected 
>by candidate distribution.  Plurality tends to favour a region that isn't 
>represented by as many candidates.  The others tend to favour a region 
>that has more candidates representing it, at least in the model I used.

This is consistent with our general perceptions of these election methods; 
I'd take this as a sign that your model is not total junk.  Well actually, 
I'm not sure approval would really have this effect, but given your rough 
model of approval strategy it's not too surprising.

>However, in answer to your concerns, here's a slightly different model. 
>The issue space now includes values above as well as below 1.  A value of 
>1 is still optimal, and a candidate's score is equal to 1-abs(v-1), where 
>v is value.

This does answer my concerns, and I consider the results more realistic, 
especially the last one with the slightly skewed candidate 
distribution.  I'd pit a little more faith in the results if it was at 
least a 2-D approximation of the issue space though; it might come out 
different.

-Adam

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