[EM] The Unique Winning Alliance method

[Markus Schulze]

Dear Rob,

it has been proven by Prasanta K. Pattanaik and Bezalel Peleg
("Distribution of power under stochastic social choice rules,"
ECONOMETRICA, vol. 54, p. 909-921, 1986) that there is no
preferential paretian non-dictatorial single-winner method
that meets regularity.

"Regularity" says that an additional candidate cannot increase
the winning probability of an already running candidate. Thus,
regularity can be considered a probabilistic generalization of
Arrow's independence from irrelevant alternatives. Therefore,
I doubt that it is possible to get less manipulable single-
winner methods by making them less deterministic.

However, I have some questions about Unique Winning Alliance:

1) What is the exact definition for the "Nash Set"? (Please don't
use game theoretical terminology.)

2) Could you give an explicite example where the Smith Set differs
from the Nash Set?

3) What are, in your opinion, the advantages of Unique Winning
Alliance compared e.g. to Smith//RandomDictatorship? (At least,
Smith//RandomDictatorship is monotonic.)

Markus Schulze