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The case against discount rates

March 25, 2012

TLDR:  Why do people care about their current selves so much more than their future selves?   I argue that they shouldn’t, and offer an explanation for why they do.

This will be a somewhat more serious a post than the previous ones, and you will find that posts in certain categories will be more serious than others.  Feel free to filter your readership based on the categories.  That being said, I hope some of you take my argument seriously (and perhaps are moved to change your behavior, to some extent).

It’s generally acknowledged that everybody has a time-discounting rate, i.e. they care about their present self more than their future self.  If you think about the way you act, you’ll find your actions indicate you care more about your present self (e.g. any time you procrastinate on that 10 page paper due next week.  I am as guilty of this as anyone).  In fact, all decision agents (e.g. firms, governments) do this to some extent.

Typically, we think of the amount we value future selves as decreasing exponentially with time.  Why exponentially, as opposed to say, hyperbolically?  Well, 1. it seems exponential in practice, and 2. if you maintain exponential discounting with the same rate across your life, it is consistent with a single utility (if I value my 10 years later self half as much as my present self, then my 10 years later self should value my 20 years later self half as much as himself, and so I should value my 20 years later self a quarter as much as my present self.)  It seems natural that the consistency aspect explains to a large extent why we see exponential discount rates in practice, as well.

But in what sense is this consistency?  If you, in the present, acknowledge that your future self matters less, you must acknowledge that your past self matters more than your current self!  Of course, since we belief time points causally forwards, this has no implications on the way we behave, but it still seems absurd.  If you agree this is absurdity, you should be tempted to conclude that you should care about all versions of yourself equally.  In other words, you should maintain the special case of exponential discounting, but with a discount rate of 0.  (This also feels canonical, and is aesthetically pleasing.)

There are some issues with this.  It means that even if your utility is bounded at any given moment in time, it can be infinite overall (violating the Archimedean property of preferences).  I don’t know exactly what to think of this, but rather than running away from these sorts of issues, it seems better to accept that modeling our values mathematically can be tricky.

However, having a discount rate of 0 doesn’t mean you don’t appear to have a discount rate in practice.  For example, notice that there is some probability of death at all times.  If we model death as a Poisson process, for example (a very unrealistic model, of course), then you get an artificial exponential discount rate, but one which is there with good reason.  Essentially, you should act more in your present self’s interest because, with some probability, your future self may not even be there!  There are other good reasons to maintain a discount rate in practice, like uncertainty about the future, value drift, etc.

I believe this is why people have evolved (i.e. been programmed) to act as if they have discount rates.  In the past, it made a lot of sense for people to do so.  Our biology cleverly reasons, “I really want to have sex with that woman now, because if I don’t, I’ll die of scurvy or get eaten by a lion, and my genes won’t get passed on.”  Now that humans die a lot less, this mechanism is no longer as necessary.  But evolution hasn’t caught up to the ridiculously fast progress humans made in the last couple thousand years, and while death rates are much lower, we continue to be programmed the same way.  As a decision agent, though, it would be best to overcome this instinct.  Using our own cognition, we are able to reason “No, biology – it’s okay.  I can make babies later.  Right now I should probably work on this 10 page paper, which is a more immediate concern.”  Anyways, quit reading this, and go work on your paper!  (I boldly predict/assert that you will not die from scurvy or lions)

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