[EM] Modeling elections

Wed May 8 17:37:07 PDT 2002

  Adam Tarr wrote:

> 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.

I'm not trying to find a method that will, as if by magic, always find 
the best candidate.  Just a method that does better than the others, 
using the most reasonable models.

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.

> 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)

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.  Nevertheless, Condorcet does quite well, giving high results 
that are not unduly affected by the distribution of candidates.  This 
brings up the other point of my model.  It shows that 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.

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.  So, the maximum score of 1 is achieved at value 1, 
this decreases to 0 at v=0 and v=2, and falls to negative below 0 and 
above 2.  Then I used distributions analogous to the ones I previously 
tested.  BTW, my scripts are at http://vote.sourceforge.net/sim/sim.zip

These examples, and the ones I previously used, are obtained by altering 
the appropriate lines in the script in the vsim folder.  I'll explain 
vsim2 later.  The scripts use Python 2.2 or higher.

First, normal distribution, mean=1, s.d.=.5.  This time, values both 
above and below 1 are used.  I'll call this the balanced 1-d model.
plurality 0.703732381822
approval 0.888929794719
borda 0.910319787896
random 0.59812059214
condorcet 0.9219711185

This model tends to be more favourable to all methods, especially 
Condorcet, so that now Condorcet beats Borda even when the candidate 
distribution is as good as the voter distribution.  It also helps 
approval, which now scores substantially better than plurality. 
 Remember that previously plurality did better than approval for these 
distributions.

Next, even candidate distribution between 0 and 2.

plurality 0.775341660814
approval 0.860249223585
borda 0.878064937439
random 0.50257630386
condorcet 0.896420423701

Slight dip in all methods except plurality, likely caused by a dip in 
the score of the best candidate available.  Plurality did better because 
fewer candidate in the middle means less vote-splitting.  We don't see 
the same tendency for candidate distribution to affect the results of 
approval/borda/random when the best candidate is in the middle.

Next, normal candidate distribution mean=1, s.d.=1

plurality 0.774218920792
approval 0.785293410838
borda 0.854024430868
random 0.208517235585
condorcet 0.872729383067

Next, I used a candidate distribution of mean=.7,s.d.=.5

plurality 0.734637910454
approval 0.772200872852
borda 0.877108080746
random 0.536090215074
condorcet 0.914025094745

---
Blake Cretney (vote.sourceforge.net)

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