army1987 comments on Open Thread, February 15-29, 2012 - Less Wrong

3 Post author: OpenThreadGuy 15 February 2012 06:00AM

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Comment author: [deleted] 25 February 2012 10:58:33AM *  4 points [-]

I've just seen the Wikipedia article for the ‘overwhelming gain paradox’:

Harford illustrates the paradox by the comparison of three potential job offers:

  • In Job 1, you will be paid $100, and if you work hard you will be paid $200.
  • In Job 2, you will be paid $100, and if you work hard you will have a 1% chance of being paid $200.
  • In Job 3, you will be paid $100, and if you work hard you will have a 1% chance of being paid $1billion.

Most people will state that they will choose to work hard in jobs 1 and 3, but not job 2 [2]. In Job 1, working hard is obvious because there is a clear reward for doing so. In Job 2, it seems a bad choice because the likelihood of a reward is so low. But in Job 3, working hard becomes the preferable choice, because the potential gain is so overwhelming that any chance - no matter how small - of obtaining it is seen as worthwhile. This appears irrational and paradoxical, because jobs 2 and 3 are identical 99% of the time.

Why the hell would anyone consider that a paradox? ISTM that it is completely reasonable for an utility function to be such that the disutility of working harder would be exceeded both by the utility of extra $100 and by 0.01 times the utility of extra $999,999,900, but not by 0.01 times the utility of extra $100. (If anything, I would consider anything else to be paradoxical, for people for whom the disutility of working at all is exceeded by the utility of getting $100 in the first place.)