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vs. "randomized" decision rules, as they are called in decision theory
("stochastic learning algorithm" means something different to me, but
maybe I'm just misinterpreting your posting).

Picking an opinion from a pool of experts randomly is clearly not a
particularly good randomized decision rule in most cases.  However,
there are cases in which properly chosen randomized decision rules are
important (any good introduction on Bayesian statistics should discuss
this).  Unless there is an intelligent adversary involved, such cases
are probably mostly of theoretical interest, but nonetheless, a
randomized decision rule can be "better" than any deterministic one.

					Thomas.