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Dmytry comments on The Savage theorem and the Ellsberg paradox - Less Wrong

12 14 January 2012 07:06PM

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Comment author: 16 January 2012 04:17:23PM *  2 points [-]

re: Ellsberg paradox.

Sequence of events is important:

• person is presented with first bet question

• person calculates answer to first question (red, very straightforward - you assume that experimenter himself is expected utility maximizer, then he didn't put any green balls into urn. It's so straightforward and obvious and automatic that it's a single step of reasoning and you can't quite see how you make steps)

• person is presented with second bet question.

The second bet question removes the reason to prefer red over green (edit: I.e. the experimenter's act of proposing second bet tells you that the utility maximizing experimenter didn't have any reason to do no-green). Now it is a simple matter of breaking a tie.

It can be immediately seen that (green or blue) is 2/3 of the win (which is clearly the most win you can get if experimenter did not manage to trick you). But it is going to take a fair bit of reasoning to see that the choices red,(red or blue) do not allow the experimenter to screw you over somehow (and any reasoning has probability of error so the reasoning would have to be repeated to make that probability negligible).

You have cake as reward. The reason you like cake is that it provides glucose for the brain to burn. Glucose maximization is fundamentally the same reason why you'd rather choose straightforwardly correct option rather than the option correctness of which has to be shown with quite a bit of glucose-burning reasoning (leaving you with a: less glucose, and b: with less time for other thoughts).

edit: paragraphs, clarity