[EM] math 103 website - Arrow & Saari

[Markus Schulze]

Dear Forest,

you wrote (9 Jan 2002):
> How are "strategical nomination" problems and the clone
> problems related?

There are two kinds of strategical nominations: clones and
irrelevant alternatives.

An election method violates "Independence from Irrelevant
Alternatives" when there are situations where you can
increase the winning probability of a given already running
candidate by introducing an additional candidate.

An election method violates "Independence from Clones"
when there are situations where you can (1) increase or
decrease the probability that a candidate of a given set
of clones is elected by introducing additional clones to
this set of clones or (2) increase or decrease the
probability that a given candidate is elected by introducing
additional clones to a set of clones to which this candidate
doesn't belong.

"Independence from Irrelevant Alternatives" and "Independence
from Clones" describe two different nomination strategies.

Examples: Random Candidate meets "Independence from Irrelevant
Alternatives" and violates "Independence from Clones". Tideman's
Ranked Pairs method meets "Independence from Clones" and violates
"Independence from Irrelevant Alternatives".

Markus Schulze