[EM] River method - a refinement, minor computational evidence, and a generalized IPDA criterion ISDA

[Dr.Ernie Prabhakar]

Hi Jobst,

On Apr 24, 2004, at 5:49 AM, Jobst Heitzig wrote:
> Def. INDEPENDENCE OF STRONGLY DOMINATED ALTERNATIVES (ISDA):
> Removing a strongly dominated alternative must not change the winner.
> X is STRONGLY DOMINATED by an alternative Y if
> (i) Y beats X
> and, for all Z distinct from X,Y:
> (ii)  if Z beats Y, Z beats X even stronger,
> (iii) if Z beats X, Y beats X even stronger,
> (iv)  if X beats Z, Y beats Z even stronger, and
> (v)   if Y beats Z, Y beats X even stronger.
>
> In the general case, Pareto-dominated alternatives are also strongly
> dominated but not vice versa, hence ISDA is then stronger than IPDA. As
> Steve already pointed out for Pareto-dominated alternatives, such
> strongly dominated alternatives might be easily be found by a losing
> party and be added strategically to change the winner, which should not
> be possible.

Very impressive.  Just to make sure I understand, are you effectively 
saying that ISDA means that removing -or- adding an SDA shouldn't 
change the results?

Also - I didn't know this, perhaps you did - there's now a very nice 
Wiki writeup on MAM:

http://en.wikipedia.org/wiki/Maximize_Affirmed_Majorities

I'd love to see a similar article on the River; in fact, if you write 
it, I'd be happy to help Wikify it, if that's a barrier.

-- Ernie P.
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