nyan_sandwich comments on Terminal Bias - Less Wrong

18 [deleted] 30 January 2012 09:03PM

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Comment author: thelittledoctor 30 January 2012 10:28:19PM *  3 points [-]

Risk aversion as a terminal value follows pretty naturally from decreasing marginal utility. For example imagine we have a paperclip-loving agent whose utility function is equal to sqrt(x), where x is the number of paperclips in the universe. Now imagine a lottery which either creates 9 or 25 paperclips, each with 50% probability - an expected net gain of 17 paperclips. Now give the agent a choice between 16.5 paperclips or a run of this lottery. Which choice maximizes the agent's expected utility?

Comment author: [deleted] 30 January 2012 10:47:42PM 3 points [-]

That's not risk aversion, it's just decreasing marginal utility. They look different to me.

And it's still not a terminal value, it would be instrumental.

Comment author: Eugine_Nier 31 January 2012 04:07:40AM 3 points [-]

That's not risk aversion, it's just decreasing marginal utility. They look different to me.

They're really mathematically equivalent ways of expressing the same thing. If they look different to you that's a flaw in your intuition, you may want to correct it.

Comment author: [deleted] 31 January 2012 04:37:02AM 0 points [-]

Ok, let's taboo "risk aversion", I'm talking about what a minimax algorithm does, where it comes up with possibilities, rates them by utility, and takes actions to avoid the worst outcomes. This is contrasted to a system that also computes probabilities to get expected utilities, and acts to maximize that. Sure you can make your utility function strongly concave to hack the traits of the minimax system into a utility maximizer, but saying that they are "mathematically equivalent" seems to be missing the point.

Comment author: Eugine_Nier 31 January 2012 05:01:39AM 4 points [-]

That's called "certainty effect" and no one is claiming that it's a terminal value.

Comment author: [deleted] 31 January 2012 06:08:35AM 0 points [-]

Ok, thanks for the terminology help.