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cousin_it comments on Bayesian Utility: Representing Preference by Probability Measures - Less Wrong

10 Post author: Vladimir_Nesov 27 July 2009 02:28PM

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Comment author: cousin_it 27 July 2009 02:53:35PM *  1 point [-]

Clever! I would have titled it "Couldness and Shouldness", and inserted some sort of pun about "wouldness" at the end.

I don't quite understand the part about mixing. Did you mean 1 >= alpha > beta >= 0 ? If no, some vectors now have negative coordinates and the polar angle becomes an ambiguous ordering. If yes, that's not the general form: why not use any matrix with nonnegative elements and positive determinant?

And I don't understand the last paragraph at all. If X coordinates of points are given, changing the Y coordinates can reorder the polar angles arbitrarily. Or did you simply mean that composite events stay dependent on simple events?

Sorry if those are stupid questions.

Comment author: Vladimir_Nesov 27 July 2009 03:14:49PM 0 points [-]

Mixing: coefficients can be negative or more than 1, but values of p and q must remain positive (added to the post). This is also a way to drive polar angle of the expected utility of the best point of the sample space to pi/2 (look at the bounding parallelogram in (P,Q)).

You can't move the points around independently, since their coordinates are measures, sums of distributions over specific events, so if you move one event, some of the other events move as well. I'll add an example to the article in a moment.