[EM] winning ratings differentials versus marginal ratings differentials

[Jobst Heitzig]

Dear James!

I tried your example with "Random Ballot from Forest's P":

> 3 candidates: Kerry, Dean, and Bush. 100 voters.
> 	Sincere preferences
> 19: K>D>>B
> 5: K>>D>B
> 4: K>>B>D
> 18: D>K>>B
> 5: D>>K>B
> 1: D>>B>K
> 25: B>>K>D
> 23: B>>D>K
> 	Kerry is a Condorcet winner.
> 
> 	Altered preferences
> 19: K>D>>B
> 5: K>>D>B
> 4: K>>B>D
> 18: D>K>>B
> 5: D>>K>B
> 1: D>>B>K
> 21: B>>K>D
> 23: B>>D>K
> 4: B>D>>K (these are sincerely B>>K>D)
> 	There is a cycle now, K>B>D>K

With sincere votes, approval says B>K>D and defeats say B<K>D, 
hence we have R.B. from {B,K} so that Bush wins with 49%, Kerry wins with 51%.
With altered votes, approval says B>D>K and defeats also say B>D>K, 
hence Bush wins with 100%.

Seems bad, but nevertheless the strategy is risky and seems to depend on quite 
accurate guesses what the others will do: 

First of all, it would not have helped to vote 4: B>>D>K instead, 
since then approval still says B>K>D and defeats say B<K<D<B, 
hence we still have R.B. from {B,K} so that Bush still wins with 49%, Kerry wins with 51%.
That is, the Bush voters must insincerely approve of their worst choice.

Second of all, they must coordinate their strategy well, 
since when 6 or more instead of only 4 voters switch to B>D>>K,
then approval says D>B>K and defeats say D<B<K<D, 
hence we have R.B. from {D,B} so that Bush wins now with 52%, but Dean wins with 48%.
That is, when too many switch to the strategic voting pattern, 
they increase Bush's probability only slightly but transfer Kerry's probability to Dean!
A similar effect happens when 2 of the 5 K>>D>B voters switch to K>D>>B as an 
anti-strategic measure.

So, my impression is that although not as good as cardinal or approval weighted pairwise, 
this much simpler method still performs quite well in terms of strategy-proofness, do you agree?

Yours, Jobst
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