[EM] The Unique Winning Alliance method

[Markus Schulze]

Dear Rob,

you wrote (4 Aug 2003):
> What's interesting is that in both situations, SSD and Ranked Pairs
> choose either A or C (down to a tiebreaker) - they avoid the candidates
> who might not be in the Nash set. Although actually restricting the
> election to the Nash set is not monotonic, do good Condorcet methods
> tend to pick winners in the Nash set anyway? Are there cases where
> they don't?

Example:

   A  B  C  D
A  0  1 -5  4
B -1  0  6 -2
C  5 -6  0 -3
D -4  2  3  0

The Nash Set is ACD. SSD, Ranked Pairs, MinMax, Kemeny-Young, and
Smith//Borda would choose candidate B.

You wrote (4 Aug 2003):
> Are they justified?

As you say, these cases are justified by the fact that "restricting
the election to the Nash set is not monotonic."

Markus Schulze