[EM] Responses to some of Forest's ideas

[Forest Simmons]

On Tue, 10 Jul 2001, Rob LeGrand wrote in part:

> utility given sincere votes, but surprisingly it doesn't seem to be the SU
> champ of Condorcet methods.  The best one I've found is what I call Borda(wv):
> 
> 1. Calculate the pairwise matrix.
> 2. For each entry Pij, set it to zero if it's less than Pji (this is the step
>    that makes it different from Borda).
> 3. Calculate a score for each candidate by subtracting its column sum from its
>    row sum.
> 4. Pick the candidate with the highest score.
> 
> My simulations haven't found an example for which Borda(wv) fails to choose the
> Condorcet winner, or even within the Smith set, and I haven't been able to
> construct a contrived example.  Can anyone show that Borda(wv) is or isn't a
> Condorcet method?  I don't expect Borda(wv) to have as many desirable
> properties as the best Condorcet methods, though.
> 

This method is a kind of cross or hybrid between Borda and Copeland, so it
is not surprising that it would have high SU and a tendency to pick the CW
when there is one. However, the following example shows that it doesn't
always pick the CW:

51 ABCDE
49 BCDEA

Borda(wv) gives the win to B with a score of 249 compared to the CW's
score of 204.

Forest