[EM] Why I think IRV isn't a serious alternative

[fsimmons at pcc.edu]

 Greg,

When someone asks for examples of IRV not working well in practice, they are usually protesting against 
contrived examples of IRV's failures.  Sure any method can be made to look ridiculous by some unlikely 
contrived scenario.

I used to sympathize with that point of view until I started playing around with examples that seemed natural 
to me, and found that IRV's erratic behavior was fairly robust.  You could vary the parameters quite a bit 
without shaking the bad behavior.

But I didn't expect anybody but fellow mathematicians to be able to appreciate how generic the pathological 
behavior was, until ...

... until the advent of the Ka-Ping Lee and B. Olson diagrams, which show graphically the extent of the 
pathology even in the best of all possible worlds, namely normally distributed voting populations in no more 
than two dimensional issue space.

These diagrams are not based upon contrived examples, but upon benefit-of-a-doubt assumptions.  Even 
Borda looks good in these diagrams because voters are assumed to vote sincerely.

Each diagram represents thousands of elections decided by normally distributed sincere voters.

I cannot believe that anybody who supports IRV really understands these diagrams.  Admittedly, it takes 
some effort to understand exactly what they represent, and I regret that the accompaning explanations are 
too abstract for the mathematically naive.  They are a subtle way of displaying an immense amount of 
information.

One way to make more concrete sense out of these diagrams is to pretend that each of the "candidate" 
dots actually represents a proposed building site, and that the purpose of each simulated election is to 
choose the site from among these options.

Each of the other pixels in the diagram represents (by its color) the outcome the election would have (under 
the given method) if a normal distribution of voters were centered at that pixel.

So each pixel of the diagram represents a different election, but with the same candidates (i.e. proposed 
construction sites).

Different digrams explore the effect of moving the candidates around relative to each other, as well as 
increasing the number of candidates.

With a little practice you can get a good feel for what each diagram represents, and what it says about the 
method it is pointed at (as a kind of electo-scope).

On result is that IRV shows erratic behavior even in those diagrams where every pixel represents an election 
in which there is a Condorcet candidate.

My Best,

Forest
 
 
 
 
 
 
 
 
 
 
 
 
 
 
gre