[EM] IIA Theory

[Markus Schulze]

Dear Craig,

you wrote (7 Oct 1999):
> At 01:00 07.10.99 , Markus Schulze wrote:
> > I prefer the following wordings:
> >
> [A]
> > Deterministic Independence from Irrelevant Alternatives:
> >
> >   Suppose, that candidate A would have not been elected
> >   if candidate B hadn't run. Then -if candidate B does run-
> >   candidate A must not be elected.
> >
> [B]
> > Stochastic Independence from Irrelevant Alternatives:
> >
> >   Suppose, that candidate A would have been elected with
> >   the probability p if candidate B hadn't run. Then
> >   -if candidate B does run- the probability that candidate
> >   A is elected must not be larger than p.
> >
> > Markus Schulze
>
> I show that my IFPP passes wording [A], at least for 1 and
> 2 winner 3 candidate elections. Wording [B] probably ought
> be rejected.

Of course, I presumed that the opinions of the voters are
"transitive" and "independent." Transitivity means that if a
given voter prefers candidate A to candidate B and if this voter
prefers candidate B to candidate C, then he also prefers
candidate A to candidate C. Independence means that the opinion
of a given voter about a given candidate doesn't change when
another candidate is added or removed.

Those who claim that FPP-like election methods meet IIA
presume that the opinions of the voters are not independent.
They presume that if a candidate is removed those voters
who would have otherwise voted for him are so disappointed
that they stay home instead of voting for their then most
favourite candidate.

You wrote (7 Oct 1999):
> Regarding [B], the use of the word "chance" is a 'probable'
> mistake isn't it?
> Q: What method has semi-random results and requires a strict
> rule?
> Q: Mr Schulze!: is that rule "[B]" intended to be applied to
> elections that do not use preferential voting (partly random
> FPTP, or games or athletes contests?).
> This is a rule that is imprecise due to the use of the word
> probaility.

I didn't use the term "chance."

There is no contradiction in [B]. Even if an event is random
you can make concrete statements about probabilities and
expectations.

When I discuss election methods with other people, I observe
very frequently, that other people try to circumvent the paradox
of voting simply by saying that they use "some random mechanisms"
in those problematic cases. The intention of [B] is to urge
these people to say which random mechanism should be used.

You wrote (7 Oct 1999):
> Have you been reading too many books or something: or this
> is motivated out of consideration the semi-random STV?

Does that mean that New Zealanders don't read books???

By the way, I think that at least you read the wrong books.
Saari's geometric terminology makes sense only if you have
already agreed with him that the Borda method is best.

Borda and Saari implicitely presume that there is an even
distribution of the candidates. But if there is an even
distribution of the candidates then of course the Borda
method is best because then every pairwise comparison has
the same independent importance.

Markus Schulze