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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