taw comments on Exterminating life is rational - Less Wrong

17 Post author: PhilGoetz 06 August 2009 04:17PM

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Comment author: taw 07 August 2009 04:54:13PM 0 points [-]

Nothing about utility maximization model says utility function is unbounded - the only mathematical assumptions for a well behaved utility function are U'(x) >= 0, U''(x) <= 0.

If the function is let's say U(x) = 1 - 1/(1+x), U'(x) = (x+1)^-2, then it's a properly behaving utility function, yet it never even reaches 1.

And utility maximization is just a model that breaks easily - it can be useful for humans to some limited extent, but we know humans break it all the time. Trying to imagine utilities orders of magnitude higher than current gets it way past its breaking point.

Comment author: Nick_Tarleton 07 August 2009 05:35:44PM *  6 points [-]

Nothing about utility maximization model says utility function is unbounded

Yep.

the only mathematical assumptions for a well behaved utility function are U'(x) >= 0, U''(x) <= 0

Utility functions aren't necessarily over domains that allow their derivatives to be scalar, or even meaningful (my notional u.f., over 4D world-histories or something similar, sure isn't). Even if one is, or if you're holding fixed all but one (real-valued) of the parameters, this is far too strong a constraint for non-pathological behavior. E.g., most people's (notional) utility is presumably strictly decreasing in the number of times they're hit with a baseball bat, and non-monotonic in the amount of salt on their food.