# Sniffnoy comments on A summary of Savage's foundations for probability and utility. - Less Wrong

33 22 May 2011 07:56PM

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Comment author: 29 June 2011 11:50:47PM 1 point [-]

Depending on context, it sure looks like these are the right preferences to have.

Sorry, but that is highly nonobvious! Why do you claim that?

Note BTW that your state space is wrong in that it doesn't include differing states of how many green balls there are, but I assume you're just restricting your ordering to those actions which depend only on the color of the ball (since other actions would not be possible in this context).

consistent objective functions

"Consistent" in what sense?

Comment author: 30 June 2011 01:03:48AM 2 points [-]

As to the state space, as you say, we could expand the state space and restrict the actions as you suggest, and it wouldn't matter. But if you prefer we could draw a ball from the urn, set it aside, and destroy the urn before revealing the colour of the ball. At that point colour really is the only state, as I understand the word "state".

As to why it looks right: red is a known probability, green and blue aren't. It seems quite reasonable to choose the known risk over the unknown one. Especially under adversarial conditions. This is sometimes called ambiguity aversion or uncertainty aversion, which is sort of orthogonal to risk aversion.

As for consistency, if you're maximising a single function, you're not going to end up in a lower state via upward-moving steps.

Beyond that I can point to literature on the Ellsberg paradox. The wikipedia page has some info and some resources.

Comment author: 28 November 2011 09:55:17AM 0 points [-]

FWIW, it doesn't seem right to me to mention adversarial situations when that's not given in the problem. Preferring safer bets seems right in the presence of an adversary, but this example isn't displaying that reasoning.

Comment author: 14 January 2012 05:35:17PM 0 points [-]

FWIW, agreed, "not given in the problem". My bad.

Comment author: 15 January 2012 02:53:47AM *  2 points [-]

Betting generally includes an adversary who wants you to lose money so they win it. Possibly in psychology experiments, betting against the experimenter, you are more likely to have a betting partner who is happy to lose money on bets. And there was a case of a bet happening on Less Wrong recently where the person offering the bet had another motivation, demonstrating confidence in their suspicion. But generally, ignoring the possibility of someone wanting to win money off you when they offer you a bet is a bad idea.

Now betting is supposed to be a metaphor for options with possibly unknown results. In which case sometimes you still need to account for the possibility that the options were made available by an adversary who wants you to choose badly, but less often. And you also should account for the possibility that they were from other people who wanted you to choose well, or that the options were not determined by any intelligent being or process trying to predict your choices, so you don't need to account for an anticorrelation between your choice and the best choice. Except for your own biases.