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

[Steve Barney]

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.

SB

--- In election-methods-list at y..., Forest Simmons <fsimmons at p...> wrote:
> 
> On Mon, 18 Feb 2002, Steve Barney wrote:
> 
> > Just so you know, in the case of fully ranked ordinal preference ballots,
> > Donald Saari has claimed to have proven, mathematically, that the Borda
Count
> > is the optimal procedure in the sense that it produces the smallest number,
all
> > together, of paradoxical outcomes. 
> 
> A paradox is a paradox only as long as our intuition remains uneducated.
> 
> What is counterintuitive to Saari may or may not be counterintuitive to
> me or you.
> 
> The number of counterintuitive properties that a method resolves is in the
> mind of the beholder.
[...]
> 
> Forest


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