[EM] Head to Head Comparison of Election Methods

[Markus Schulze]

Dear Paul,

you wrote (8 Jun 1999):
> Perhaps Steve Eppley's program would help us to do some statistical
> analysis on the space of possible outcomes. Does Steve provide this
> program for others to try? Particularly, I'm interested in
> determining how serious a problem Dumais voting encounters with
> similar candidates. I would also like to examine the space of
> possibilities where intuitively I see some severe problems (my
> intuition could be very wrong).

I remember that once two scientists were asked to calculate the
probability of an occurence of a violation of monotonicity
when there are only three candidates and the votes are distributed
randomly and IRO is used. Although the question was clear and offered
only one interpretation, both scientists came to totally different
results. The one scientist (= Crispin Allard) calculated a probability
of only 0.002% and concluded that, were STV to be used in the UK,
there would be "less than one incidence every century of monotonicity
failure." The other scientist (= Dominique Lepelley) calculated a
probability of 5.74% and concluded that "it seems difficult to claim
that monotonicity paradoxes are extremely rare and have no practical
relevance."

Markus Schulze