[EM] Efforts to improve on CR's strategy

[Bart Ingles]

Ken Johnson wrote:
> 
> Bart,
> 
> Here's a link to #597,
> http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-April/012689.html
> (Search the text for "num_candidate=10".)

Thanks.  In your 10 candidate, 1 issue trial, are you able to account
for why sincere CR, exaggerated CR, Condorcet, Borda, IRV, and Plurality
all yield exactly the same average across 100,000 elections?  It looks
like top-two Runoff is within 0.1% of the same score.

Stranger still, exaggerated CR should be equivalent to Approval, but the
scores here are wildly dissimilar.

I'm afraid I don't trust the simulation.  There are too many cases where
widely different methods return exactly the same results.  I would
expect this with two candidates (if the optimal strategies are done
correctly), but not with three or more.

Also, I think the Approval strategy used is not what is generally
recognized as optimal zero-info strategy.  You have voters approving all
candidates where CR is >= 0.  The usual "sincere strategy" is to approve
all candidates where CR is greater than the mean CR of all candidates. 
In the two candidate cases, this should give Approval the same score as
the other methods, as one would expect.


> The main problem I saw with Approval occurred when there are many
> candidates, and when everyone votes based on a single election issue. Do
> you know if Merrill simulated this case?

I'm sure he did, but the the cases illustrated in his book use two
issues (two dimensions) with 0.5 correlation between them-- you could
almost say 1-1/2 issues.  The graphs go up to seven candidates, but the
trends are clear enough that you could extrapolate out to 10.

In Merrill's simulations, Condorcet, Borda and Approval all held up well
as the number of candidates increased.  Utility of the runoff methods
and of Plurality dropped steeply as the number of candidates increased.

Bart Ingles