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lymen 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: endoself 16 January 2011 03:29:54AM *  2 points [-]

I admit that I'm relatively new to these concepts so I apologize in advance if my post is a bit scatterbrained or in the wrong post, but it's just a thought.

It's good that you are trying to learn and that you posted. There are misconceptions, which I will proceed to pick apart in extreme detail :), but, if I do this well, you will learn something and come to a deeper understanding of the concepts.

While the lottery would accomplish that preference, it is not the best way to do so. By being a game of chance, lotteries may only be run by the government, so some of the money that would go to the one person goes to the government instead. While people might also prefer that the government has money, they could donate to the government (or to a charity) separately. Also, bundling the two things into one action fixes the ratio between the amount of money given to each. This is neutral if fixed at the desired ratio and of negative utility if fixed at a suboptimal ratio. It would only be considered good to most people if the people who want a lower rate of lottery tax are few enough that they cannot start their own lottery-like system, so they are forced to pay the higher taxes desired by the rest of the ticket buyers in order to play.

Also, the person that benefits is randomly selected. Would it not be preferable to chose someone with above-average need for the money? Even if the ticket buyers would not think so, surely they could think of some criteria that is better than random . In general, the lottery shows no signs of being optimized for this preference. Since you're new here, you may not have read http://lesswrong.com/lw/hu/the_third_alternative/ . I highly recommend it.

Since people would think that buying a lottery ticket that they knew would not be able to win would be ridiculous, we can tell that none of these considerations are what matters. People buy lottery tickets because of the benefit to themselves and, since this is irrational in all but the few cases where utility is concave up in money (and people's participation in the lottery does not depend on how well it conforms to a certain concave up utility function), it is unlikely that the concern for other possible winners, which is minimal on its own, makes it rational for them.

Comment author: lymen 17 January 2011 07:22:26AM 0 points [-]

Ahh, right. Thanks for that point. I forgot you can't have hidden motivations if they're not conscious.

Also, I've read the third alternative article but I'm not really seeing what you were trying to say by posting it.

My original thought was that when you have a choice between torturing a person for fifty years or letting 3^^^^3 people experience a dust speck in the eye, I'd pick the 3^^^^3 people getting the dust speck.

However, from an outsider's standpoint, would you rather give 3^^^^3 people a penny or one person a billion dollars (you're not included in either party). I for one might decide to give the billion dollars because at least it has some value (I'm not really happy about giving 3^^^^3 people one penny each, even if 3^^^^3 pennies is worth a lot more than a billion dollars).

Comment author: endoself 17 January 2011 10:34:32AM 0 points [-]

The point of the third alternative is that an action is not good because it is preferable to some "default action", but because it is preferable to all possible actions that you can think of. If it is rational for some people to buy lottery tickets, it is because it is the best use of their money, not because it is better than saving. If there is a more efficient way to accomplish the same goals, than rational people would not buy lottery tickets.

I for one might decide to give the billion dollars because at least it has some value (I'm not really happy about giving 3^^^^3 people one penny each, even if 3^^^^3 pennies is worth a lot more than a billion dollars).

What percentage of people would have a major life change because of a single extra penny? A tiny fraction, but multiply that number by 3^^^^3 and you can do vastly more good than by giving one person $1 billion.

I'm not quite sure what you mean in your first sentence. People can and do have hidden motivations that they are not consciously aware of depending on the definition of motivation.

Comment author: Will_Sawin 17 January 2011 06:18:23PM 0 points [-]

If a penny has no value, and another penny has no value, and a third penny has no value, ....

then 100 billion pennies must have no value.

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?

or

  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.