[EM] Proof Borda Count best in the case of fully ranked preference ballots

[Forest Simmons]

On Tue, 19 Feb 2002, Steve Barney wrote:

> Forest:
> 
> What do you think of circular triplets, such as:
> 
> 	A>B>C
> 	B>C>A
> 	C>A>B,
> 
> and reversals, such as:
> 
> 	A>B>C
> 	C>B>A.
> 
> If that is all the information that we have to go on (when ordinal preference
> ballots are used, it is ), shouldn't either of these profiles cancel out
> completely and yield a tie? The Borda Count is the only method which always
> does that, according to Saari's analysis. From that simple fact, argues Saari,
> come voting paradoxes such as non-monotonicity, etc.

The two examples that you give yield ties in every serious method of which
I am aware.

Forest