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Will_Sawin comments on Lotteries: A Waste of Hope - Less Wrong

28 Post author: Eliezer_Yudkowsky 13 April 2007 05:36AM

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Comment author: Desrtopa 17 January 2011 06:43:13PM 0 points [-]

But the utility of a penny is not necessarily the same as one hundredth of the utility of a hundred pennies. If you distribute a great deal of money by giving many people a single penny, you may have disbursed less utility than if you gave a fraction of that money all to one person.

Comment author: Will_Sawin 17 January 2011 07:22:35PM -1 points [-]

If I give one person X amount of money, I can do this N times for N different people, producing on average U(X) utility each time.

If I give N people X/N amount of money, and do this N times for the same N people, I must be producing, on average, the same U(X) of utility, since I have produced the same result with the same number of iterations.

Do you expect:

  1. That the first person I give money to will benefit more than the average person?


  1. That the first penny I give people will benefit less than the average penny?

If so, why?

Comment author: Desrtopa 17 January 2011 07:47:51PM 0 points [-]

The second.

It's not controversial that the marginal utility of money decreases when you've got a lot of it. Another dollar is worth less to a millionaire than a beggar. But you also have a lot more than a hundred times as many purchasing options with a dollar than with a penny, so I think it's likely that the utility of money is described by an S curve.

Comment author: Will_Sawin 17 January 2011 08:33:17PM 1 point [-]

This would make sense if everyone started with $0, or an exact round number of dollars, which seems like an odd scenario. However, if that's your assumption, I agree with you.

Comment author: Desrtopa 17 January 2011 08:40:40PM *  2 points [-]

I suppose I incorporated that assumption without really thinking about it. Now that you mention it, that would be a pretty odd situation.

Depending where on the the curve the slope levels off, it might still result in greater utility to give one person a lot of money than to distribute the same amount of money in one cent units to very many people, but if you assume that a majority of the people are already middle class, that's probably not the case.

Comment author: orthonormal 17 January 2011 10:13:26PM 1 point [-]

I think the confusion here is more of a sorites paradox than anything about expected utility. You can't imagine a single extra penny changing anyone's outcome, but you can imagine it for a hundred extra pennies.

I think that's a mistaken intuition; for instance, you could be about to buy something small, realize you're a few cents short, and either cancel the transaction or use the "Take a Penny" jar; but the probabilities of doing either will actually change (for social reasons) depending on whether you're, say, 3, 4 or 5 cents short of the total.

It's rather like the way that being one more second late out the door can either get you to the office at the exact same time, or twenty minutes later, depending on the bus schedule.

Comment author: Desrtopa 17 January 2011 10:24:50PM 0 points [-]

Utility clearly isn't linear with money, but I think you're probably right that that intuition had something to do with my drawing the conclusion I did.