[EM] Election-Methods Digest, Vol 54, Issue 18

[fsimmons at pcc.edu]

These diagrams with increasing sigma are very helpful and enlightening.

Note that on the left end (with small sigma) the diagrams of all the methods are like the diagrams for the 
Condorcet method.

As Raph mentioned, increasing sigma is equivalent to shrinking the candidate configuration without 
changing its shape.  So if increasing sigma can squeeze out a Condorcet winner, then shrinking the 
configuration can also squeeze out the Condorcet winner.

Imagine starting with a non-normal distribution with a sharp, infinite central peak at the origin of a coordinate 
system, say with a probability density function given by rho = (1/r)/e^r, where r is the distance from the 
origin.

With a distribution like this we would expect that a candidate at the origin would be most representative of 
the population.  And indeed, in any pairwise contest this candidate would have the majority of the votes.

But (under IRV) if we have two other candidates (good cop and bad cop) that move in on opposite sides of 
the origin, they will eventually squeeze out this condorcet winner, transferring the win to the lesser evil of the 
two "cops," i.e. the one closer to the ideal position, the origin, which is still occupied by the erstwhile 
Condorcet winner, now merely an IRV loser.

For this to work they don't have to be on diametrically opposite sides (though that makes it happen 
sooner).  They only have to make sure that the distance between them stays larger than the distance from 
either of them to the origin by at least one percent, say.

If there is some kind of anti-squeeze criterion that is supposed to prevent this kind of behavior, then IRV fails 
it grossly.

I think this squeeze problem is damning enough by itself.  But the diagrams also make clear the 
unacceptable extent of the non-monotonicity problem (even with nice smooth symmetrical normal 
distributions).

Forest


> From: Brian Olson 
> Subject: [EM] Voting space graphs, varying sigma
> To: Election Methods Mailing List 
> Message-ID: <7D38A1C4-3898-48B4-A139-AACC576075CD at bolson.org>
> Content-Type: text/plain; charset=us-ascii; format=flowed; delsp=yes
> 
> http://bolson.org/voting/sim_one_seat/20081203/
> 
> Tight population grouping at the left moving to widely spread on 
> the 
> right.