Dear all :-
Professor Halpern is correct that when people speak of "Ellsberg's
problem" or paradox, they typically mean the three-color
version. Konrad's version also was in the discussion, and perhaps he
finds that it more transparently makes the point about 'ambiguity
aversion.'
In both problems, the majority response is easily recognized as "maximin
expected value" [because there are only two distinct prizes, it is impossible
to distinguish "expected value" from "expected utility" behaviorally]. Apart
from its evident popularity, normative cases for maximin exist.
Among the best known and best developed for the general use of the
strategy is of course Isaac Levi's. Levi is especially lucid on
incompletely specified probabilities, such as we see in the
three-color version (and arguably often in life, too).
Ellsberg's remarks about ambiguity are also interesting. After all,
maximiners really are, among other things and in some sense and whether or not
intentionally, ambiguity averse.
Ellsberg wrote a well-known critique of maximin in competitive
games. Maybe then, Ellsberg's contribution on this point was to find
an original unsavory-sounding thing to say about maximin (a genuine
feat, given the volume of sneers by then in the literature - timidity,
drowning, ...), a strategy for which he plainly had little enthusiasm.
In any case, it is wonderful that this should come up in the
thread. Professor Zadeh's work can be profitably viewed as an
extended and rich meditation on maximin decision and inference. I
doubt he would describe it that way, but it is not really an offensive
thing to say.
Best.
Paul
