Only if you discretize them prematurely. A "true" bayesian, w/ infinite computing power, has exactly one choice; picking their utility f(x).https://twitter.com/enkiv2/status/816405431610445825 …
If you want to have no preferences over all possible outcomes, that would be valid. (But strange - am I misunderstanding?)
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this also applies if there exists a y,z such that y!=z but f (y)=f (z). Reality is a low information game.
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most decisions cannot be distinguished even with infinite computation because we don't have perfect knowledge.
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