[EM] The Unique Winning Alliance method

[Markus Schulze]

Dear Rob,

you wrote (3 Aug 2003):
> The properties of this method:
> (...)
> * It is _not_ monotonic. The share that someone gets of the UWA might
> go down if they get additional votes. It's a surprising flaw, but a
> necessary outcome of the almost-IIAC-ness.
> (...)
> * It is almost IIAC. Certainly, if a member of the Nash Set drops out, it
> will change the result, but that member would have had a chance to win,
> so he isn't especially irrelevant.  The result stays the same if anyone
> outside the Nash Set leaves.  This does not break Arrow's Theorem
> because Arrow does not allow for non-deterministic methods.

You wrote (3 Aug 2003):
> However, the property it has - which could be called Very Local IIA,
> but which you point out is not the same as regularity - is interesting.

4) What does "almost IIAC" resp. "Very Local IIA" mean in this context?
Does it mean that an additional candidate who isn't in the new Nash Set
cannot change the winning probability of an already running candidate?

5) Could you give a concrete example where the Nash Set differs from
the Uncovered Set? (The "Uncovered Set" is the set of candidates who
beat every other candidate with a path of length 1 or 2. In other
words: When "X >= Y" means that the number of voters who strictly
prefer candidate X to candidate Y isn't strictly smaller than the
number of voters who strictly prefer candidate Y to candidate X,
then candidate A is in the "Uncovered Set" if & only if for every
other candidate B at least one of the following two statements is
valid: [1] A >= B. [2] There is a candidate C with A >= C >= B.)

******

You wrote (3 Aug 2003):
> Aside: Where did the // in method names come from, anyway?

Lowell Bruce Anderson has introduced this terminology. "X//Y"
means that, at first, election method X is applied. But when
election method X doesn't lead to a unique winner but to a set
of potential winners, then all candidates who are not in this
set of potential winners are eliminated and election method
Y is applied to the remaining candidates.

Markus Schulze