Lumifer comments on Mean of quantiles - Less Wrong Discussion
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It's somewhat subjective. There is no law of the universe that says one approach is right and the other is long (so long as you avoid inconsistencies, which the policy selection idea does.) There is no objective way to compress an entire distribution down to a single value.
Do you want to select a distribution that contains the best average future? Do you want to select from a distribution that contains the best median future? Or do you want something in between? What do we, humans, actually want?
Ah. We finally get to interesting questions :-)