Discounting rates

I was looking through the archives of Overcoming Bias, and came across an interesting discussion of discounting rates. The question asked is: Do you prefer to save one person from torture today, or 132 persons in a century? If you have a discounting rate of 5% yearly, then you are indifferent between these two options, and the assertion is that this is immoral – you ought always to prefer to save the 132 people, even if your decision won’t take effect for another century.

This got me to thinking; but it seems to me that the invocation of torture interferes with clear thought, so I won’t go there right away. I’ll start with thinking about where discounting rates come from in the first place. In other words, suppose you are given the option of a dollar now, or a dollar and five cents in a year. If the rate of interest is 5%, you shouldn’t care unless you really need a dollar right now. If you don’t need it right away, you could stash it in your bank, and lo and behold, you’ll have 1.05 in a year, so what does it matter? (Modulo the value of liquidity, that is.) In other words, money in the future is worth less than money now – I have to offer you that extra five cents to get you to wait a year. Why is that? A dollar is a dollar, no? (Again, modulo the value of having the dollar available, and I can get around this by baking it into my interest rate.) Or to put it differently, do you prefer a chocolate now, or in a year? It shouldn’t matter; the pleasure of eating it is the same either way. To say that you prefer it now – or equivalently, to say that you want some extra chocolate as payment for waiting a year – is to discriminate against your future self.

Now, you have a perfect right to discriminate against your future self; only you will suffer for that judgement. It might still be interesting to discover why people do so, but one cannot very well call it immoral. But the case is not as clear with other people. Suppose I, the rich philanthropist, offer to get clean water for one African family today, or for two families in twenty years. Now, you happen to know that if I invest the money for one family’s clean water today, then in twenty years I can pay for three families and have some money left over; so by good discounting principles you ought to ask for the one family now. But now you are causing measurable harm to someone else merely because they happen to be in the future. Do you have a right to do this? Dr Yudkowsky argues that you do not: helping two families is better than helping one even if you have to wait a while.

A possible counterargument is that this gets you into an infinite loop. Suppose, instead of helping that one family today, I invest the money; then as I outlined above, I can help three families in twenty years. Well and good, if we’re not time-discounting altruism then that’s what I should do. But hang on, what’s privileged about twenty years? Why not wait forty years, and help nine families? Sixty years, and twenty-seven? I end up waiting for all time and never helping anyone at all! I need a discounting rate, by this argument, to get anything done. But I think this argument fails; it assumes an infinite population of families needing help. In actual fact there are a finite number of such families; as long as my investments grow faster than their population, there will come a point when I can help everyone, and that’s the point I ought to prefer, as having the maximal altruistic impact. Even if my investment grows more slowly, the Universe can only contain so many needy families. At some point a given exponentially growing investment will control a sufficiently large percentage of the economy to help that maximum number of families.

At this point I think it’s helpful to go back to the personal discount rate. I discriminate against my future self. I have a right to do so, as it hurts only me, but why do I do it? I think the answer is that my future self is not certain to exist. Suppose I say “A dollar now, or a dollar in a year”. The reason I prefer a dollar now is the higher probability – even if only a very little higher – that I will get to spend it. If the offer were “A dollar now, or a dollar in a year, and I guarantee that you’ll be around to spend it”, then certainly I would take the latter. But nobody really has the power to make such an offer, which is why we discount our possibly-nonexistent future self, and we do it so automatically that we are not even quite sure why.

With this in mind, let’s go back to the families. One family helped now, or two in twenty years. By the usual discounting procedure I ought to prefer the current family; but that discount operates as though I were thinking of myself. There is some finite probability I will not be here in twenty years; but the probability that there won’t be any poor Africans in need of water is much lower than that. So there’s still a discount rate, but it’s much lower. This resolves the dilemma: I can prefer the two families helped even after discounting, by understanding where discounting comes from and applying it correctly.

Now we have the weaponry to go back to the torture. Save a man from torture now, or 132 in a century? Well, really, how likely is it that the person making this offer genuinely has the power to ensure the torture of 132 people a century from now? Not very; so we intuitively assign a high discounting rate to the question, and save the current victim, who presumably is in his torturer’s clutches right now, and the electricity will start at the touch of a button. If I really believed that the questioner had such power, then I’d have to save the 132 people rather than the one. Likewise for the question of saving Bruno from the stake: If I really believed someone had the power to go back in time and stop the burning, I would value Bruno’s life equally with contemporary lives. If I had lived in the time of Bruno, and really believed that saving Bruno would with certainty lead to a burning at the stake in 2008, I would likewise be indifferent between the two. But to live in the time of Bruno, and be offered the choice of Bruno today, or 1,226,786,652 burnings in 2008, would strain my credulity; I would very reasonably not believe that my questioner had any such power, discount the billion burnings at a much greater rate than 5%, and end up saving Bruno.

In other words, discounting rates are not a hard-to-defend time preference, they are a perfectly reasonable probability preference. It is eminently rational to prefer a certain dollar to a 99% chance of a dollar, or to be indifferent between a certain dollar and a 50% chance of two dollars. The difficulty arises when the probability difference is disguised by making the question one of time.


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Filed under Economics

One response to “Discounting rates

  1. Pingback: Irrationally high discount rates « Ynglinga Saga and other stories

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