The option value of civilization

Hi Tyler, I’m a longtime reader of MR and your more recent books.  I enjoyed Stubborn Attachments and was particularly interested in your discussion of the social discount rate.  Like you, I’m inclined to think that this rate should be very low, if not zero.  But more importantly, I think discounting is the wrong financial metaphor to use when discussing the moral worth of the present vs. the future.  Instead, we should look to option pricing theory.  As strange as it seems, option theory provides a neat way to unify many of the claims in Stubborn Attachments, and it gives us arguments for other important claims.  I’m a mortgage-backed securities trader, so embedded mispriced (or unpriced) optionality is always on my mind.

The key idea is that the total moral worth of the universe has some positively skewed distribution: there are more ways for things to be good than there are for it to be bad.  Let’s take this as a given for now; towards the end of this message I explore the consequences of relaxing this assumption.  If the moral worth of the universe has a distribution like this, we can draw an analogy to the payout profile of a call option.  We can imagine that we own an option on the underlying process that generates historical outcomes.

The first thing to recognize is that there’s a fundamental difference between the value of the option, and the value of the underlying.  Translated to moral terms, we should distinguish between the value of present, and the ultimate moral worth of the universe.  The former is just one input in calculating the latter, and the latter should be our primary concern.  We are only indirectly exposed to the value of the present.  We are also exposed to other factors, including the volatility of the historical process, and the social discount rate.

Let’s consider these in turn.  Options theory tells us that the value of an option increases in volatility — a trader would say that an option has positive “vega.”  Thus it makes perfect sense to see you arguing in Stubborn Attachments (and TGS and TCC) for increased social dynamism, risk taking, and openness to innovation.  If we can increase upside volatility, or reduce downside volatility, that’s even better than a symmetric increase in volatility.  My sense is that you view human rights as a way to mitigate downside risk.  This framework implies that some degree of downside mitigation can be traded for upside, a view which seems to be consistent with your view of human rights.

In the option-theoretical framework, the value of an option is decreasing in the discount rate.  But while the specific choice of discount rate changes the overall value of the option, it doesn’t change the sign of any of the sensitivities.  One advantage of this framework is that it can incorporate any particular social discount rate, without affecting the broader conclusions.

We can restate other common questions in this jargon.  Let’s start with the question of the value of the present vs. the value of the future.  In my view, that language is confused.  The value of the future is unknowable and can’t be affected directly.  We should stop talking as if we can.  We can only affect things like the value of the present and the volatility and overall trajectory of the historical process.  Rather than asking about the value of the present vs. the future, we should simply ask “how much should we care about the present, relative to the other things we can affect directly?”  In options jargon, the “delta” of an option is the derivative of the option’s value with respect to the value of the underlying process.  In moral terms, delta is interpreted as the derivative of the moral worth of the universe with respect to the value of the present.  “How much should we care about the present?” can be restated as “What is the delta the option?”

In standard theory, delta is positive (obviously) and increasing in the value of the underlying process.  That is, the second derivative of an option’s value with respect to the value of the underlying process is also positive.  Translated to moral terms: the more valuable the present, the more we should care about it.  This is intuitive, at least to me.  If you think the potential value of the future is vastly greater than the value of the present (i.e. if you think our option is only slightly in-the-money) you should care less about the value of the present.  But if the option is deep in-the-money — if civilization is secure and of great value — we should care more about increasing its value.

We can also think about partial sensitivities.  The most interesting is the sensitivity of delta with respect to volatility: as volatility increases, delta decreases.  In moral terms: the greater the range of historical outcomes, the less we should care about the precise moment we’re in now.  If we think history is highly dynamic, that the space of potential outcomes is very large, and that the far future can be vastly more valuable than the present, we should care less about the specific value of the present.  Similarly, if we think we’re close to the end of history, we should focus on incremental tweaks to improve the value of the present.  The arguments in Stubborn Attachments clearly tend toward the former view.

Finally, we can return to the original assumption, that the value of the future is biased to the upside.  I don’t think you argue for this explicitly, but it’s implied in your idea of Crusonia plants.  What would a negative or inverse Crusonia plant look like?  Could one even exist?  I think it’s vastly more likely for civilization and value to simply be wiped out, than it is for a monstrously evil future to occur.  But if you disagree, you can account for it in the option framework.  The more likely an evil future, the more symmetric (and less option-like) our payout profile.  You can think of humanity as owning some combination of a long call and a short put.  If our portfolio contains equal positions in each, our total delta is 1 — implying that the value of our options position is identical to the value of the underlying.  Translated into moral terms: the more symmetric we think future outcomes are, the more we should care about the present.

This is a new framework for me, but I think it is useful.  I’m sure there are other implications that haven’t yet occurred to me.  I can’t imagine I’m the first to come up with this framework: after all, Cowen’s Second Law states that there’s a literature on everything.  There’s perhaps some precedent in Nassim Taleb’s work and his popularization of options theory and its usefulness in non-financial contexts.  I’m sure someone in the Effective Altruism community has kicked these ideas around; I’m just not aware of it.  If you know of any related work, I’d love to be pointed in the right direction.

That is from MR reader CK.


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