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AlexMennen comments on Stupid Questions Open Thread Round 4 - Less Wrong Discussion

6 Post author: lukeprog 27 August 2012 12:04AM

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Comment author: lukeprog 27 August 2012 12:20:24AM *  8 points [-]

I finally decided it's worth some of my time to try to gain a deeper understanding of decision theory...

Question: Can Bayesians transform decisions under ignorance into decisions under risk by assuming the decision maker can at least assign probabilities to outcomes using some kind of ignorance prior(s)?

Details: "Decision under uncertainty" is used to mean various things, so for clarity's sake I'll use "decision under ignorance" to refer to a decision for which the decision maker does not (perhaps "cannot") assign probabilities to some of the possible outcomes, and I'll use "decision under risk" to refer to a decision for which the decision maker does assign probabilities to all of the possible outcomes.

There is much debate over which decision procedure to use when facing a decision under ignorance when there is no act that dominates the others. Some proposals include: the leximin rule, the optimism-pessimism rule, the minimax regret rule, the info-gap rule, and the maxipok rule.

However, there is broad agreement that when facing a decision under risk, rational agents maximize expected utility. Because we have a clearer procedure for dealing with decisions under risk than we do for dealing with decisions under ignorance, many decision theorists are tempted to transform decisions under ignorance into decisions under risk by appealing to the principle of insufficient reason: "if you have literally no reason to think that one state is more probable than another, then one should assign equal probability to both states."

And if you're a Bayesian decision-maker, you presumably have some method for generating ignorance priors, whether or not that method always conforms to the principle of insufficient reason, and even if you doubt you've found the final, best method for assigning ignorance priors.

So if you're a Bayesian decision-maker, doesn't that mean that you only ever face decisions under risk, because at they very least you're assigning ignorance priors to the outcomes for which you're not sure how to assign probabilities? Or have I misunderstood something?

Comment author: AlexMennen 27 August 2012 12:55:49AM 8 points [-]

So if you're a Bayesian decision-maker, doesn't that mean that you only ever face decisions under risk, because at they very least you're assigning ignorance priors to the outcomes for which you're not sure how to assign probabilities?

Correct. A Bayesian always has a probability distribution over possible states of the world, and so cannot face a decision under ignorance as you define it. Coming up with good priors is hard, but to be a Bayesian, you need a prior.