When maximizing utility doesn’t

Jun 4 JDN 2460100

Expected utility theory behaves quite strangely when you consider questions involving mortality.

Nick Beckstead and Teruji Thomas recently published a paper on this: All well-defined utility functions are either reckless in that they make you take crazy risks, or timid in that they tell you not to take even very small risks. It’s starting to make me wonder if utility theory is even the right way to make decisions after all.

Consider a game of Russian roulette where the prize is $1 million. The revolver has 6 chambers, 3 with a bullet. So that’s a 1/2 chance of $1 million, and a 1/2 chance of dying. Should you play?

I think it’s probably a bad idea to play. But the prize does matter; if it were $100 million, or $1 billion, maybe you should play after all. And if it were $10,000, you clearly shouldn’t.

And lest you think that there is no chance of dying you should be willing to accept for any amount of money, consider this: Do you drive a car? Do you cross the street? Do you do anything that could ever have any risk of shortening your lifespan in exchange for some other gain? I don’t see how you could live a remotely normal life without doing so. It might be a very small risk, but it’s still there.

This raises the question: Suppose we have some utility function over wealth; ln(x) is a quite plausible one. What utility should we assign to dying?


The fact that the prize matters means that we can’t assign death a utility of negative infinity. It must be some finite value.

But suppose we choose some value, -V, (so V is positive), for the utility of dying. Then we can find some amount of money that will make you willing to play: ln(x) = V, x = e^(V).

Now, suppose that you have the chance to play this game over and over again. Your marginal utility of wealth will change each time you win, so we may need to increase the prize to keep you playing; but we could do that. The prizes could keep scaling up as needed to make you willing to play. So then, you will keep playing, over and over—and then, sooner or later, you’ll die. So, at each step you maximized utility—but at the end, you didn’t get any utility.

Well, at that point your heirs will be rich, right? So maybe you’re actually okay with that. Maybe there is some amount of money ($1 billion?) that you’d be willing to die in order to ensure your heirs have.

But what if you don’t have any heirs? Or, what if we consider making such a decision as a civilization? What if death means not only the destruction of you, but also the destruction of everything you care about?

As a civilization, are there choices before us that would result in some chance of a glorious, wonderful future, but also some chance of total annihilation? I think it’s pretty clear that there are. Nuclear technology, biotechnology, artificial intelligence. For about the last century, humanity has been at a unique epoch: We are being forced to make this kind of existential decision, to face this kind of existential risk.

It’s not that we were immune to being wiped out before; an asteroid could have taken us out at any time (as happened to the dinosaurs), and a volcanic eruption nearly did. But this is the first time in humanity’s existence that we have had the power to destroy ourselves. This is the first time we have a decision to make about it.

One possible answer would be to say we should never be willing to take any kind of existential risk. Unlike the case of an individual, when we speaking about an entire civilization, it no longer seems obvious that we shouldn’t set the utility of death at negative infinity. But if we really did this, it would require shutting down whole industries—definitely halting all research in AI and biotechnology, probably disarming all nuclear weapons and destroying all their blueprints, and quite possibly even shutting down the coal and oil industries. It would be an utterly radical change, and it would require bearing great costs.

On the other hand, if we should decide that it is sometimes worth the risk, we will need to know when it is worth the risk. We currently don’t know that.

Even worse, we will need some mechanism for ensuring that we don’t take the risk when it isn’t worth it. And we have nothing like such a mechanism. In fact, most of our process of research in AI and biotechnology is widely dispersed, with no central governing authority and regulations that are inconsistent between countries. I think it’s quite apparent that right now, there are research projects going on somewhere in the world that aren’t worth the existential risk they pose for humanity—but the people doing them are convinced that they are worth it because they so greatly advance their national interest—or simply because they could be so very profitable.

In other words, humanity finally has the power to make a decision about our survival, and we’re not doing it. We aren’t making a decision at all. We’re letting that responsibility fall upon more or less randomly-chosen individuals in government and corporate labs around the world. We may be careening toward an abyss, and we don’t even know who has the steering wheel.

Reasons for optimism in 2022

Jan 2 JDN 2459582

When this post goes live, we will have begun the year 2022.

That still sounds futuristic, somehow. We’ve been in the 20th century long enough that most of my students were born in it and nearly all of them are old enough to drink (to be fair, it’s the UK, so “old enough to drink” only means 18). Yet “the year 2022” still seems like it belongs in science fiction, and not on our wall calendars.

2020 and 2021 were quite bad years. Death rates and poverty rates surged around the world. Almost all of that was directly or indirectly due to COVID.

Yet there are two things we should keep in perspective.

First, those death rates and poverty rates surged to what we used to consider normal 50 years ago. These are not uniquely bad times; indeed, they are still better than most of human history.

Second, there are many reasons to think that 2022—or perhaps a bit later than that, 2025 or 2030—will be better.

The Omicron variant is highly contagious, but so far does not appear to be as deadly as previous variants. COVID seems to be evolving to be more like influenza: Catching it will be virtually inevitable, but dying from it will be very rare.

Things are also looking quite good on the climate change front: Renewable energy production is growing at breathtaking speed and is now cheaper than almost every other form of energy. It’s awful that we panicked and locked down nuclear energy for the last 50 years, but at this point we may no longer need it: Solar and wind are just that good now.

Battery technology is also rapidly improving, giving us denser, cheaper, more stable batteries that may soon allow us to solve the intermittency problem: the wind may not always blow and the sun may not always shine, but if you have big enough batteries you don’t need them to. (You can get a really good feel for how much difference good batteries make in energy production by playing Factorio, or, more whimsically, Mewnbase.)

If we do go back to nuclear energy, it may not be fission anymore, but fusion. Now that we have nearly reached that vital milestone of break-even, investment in fusion technology has rapidly increased.


Fusion has basically all of the benefits of fission with none of the drawbacks. Unlike renewables, it can produce enormous amounts of energy in a way that can be easily scaled and controlled independently of weather conditions. Unlike fission, it requires no exotic nuclear fuels (deuterium can be readily attained from water), and produces no long-lived radioactive waste. (Indeed, development is ongoing of methods that could use fusion products to reduce the waste from fission reactors, making the effective rate of nuclear waste production for fusion negative.) Like both renewables and fission, it produces no carbon emissions other than those required to build the facility (mainly due to concrete).

Of course, technology is only half the problem: we still need substantial policy changes to get carbon emissions down. We’ve already dragged our feet for decades too long, and we will pay the price for that. But anyone saying that climate change is an inevitable catastrophe hasn’t been paying attention to recent developments in solar panels.

Technological development in general seems to be speeding up lately, after having stalled quite a bit in the early 2000s. Moore’s Law may be leveling off, but the technological frontier may simply be moving away from digital computing power and onto other things, such as biotechnology.

Star Trek told us that we’d have prototype warp drives by the 2060s but we wouldn’t have bionic implants to cure blindness until the 2300s. They seem to have gotten it backwards: We may never have warp drive, but we’ve got those bionic implants today.

Neural interfaces are allowing paralyzed people to move, speak, and now even write.

After decades of failed promises, gene therapy is finally becoming useful in treating real human diseases. CRISPR changes everything.

We are also entering a new era of space travel, thanks largely to SpaceX and their remarkable reusable rockets. The payload cost to LEO is a standard measure of the cost of space travel, which describes the cost of carrying a certain mass of cargo up to low Earth orbit. By this measure, costs have declined from nearly $20,000 per kg to only $1,500 per kg since the 1960s. Elon Musk claims that he can reduce the cost to as low as $10 per kg. I’m skeptical, to say the least—but even dropping it to $500 or $200 would be a dramatic improvement and open up many new options for space exploration and even colonization.

To put this in perspective, the cost of carrying a human being to the International Space Station (about 100 kg to LEO) has fallen from $2 million to $150,000. A further decrease to $200 per kg would lower that to $20,000, opening the possibility of space tourism; $20,000 might be something even upper-middle-class people could do as a once-in-a-lifetime vacation. If Musk is really right that he can drop it all the way to $10 per kg, the cost to carry a person to the ISS would be only $1000—something middle-class people could do regularly. (“Should we do Paris for our anniversary this year, or the ISS?”) Indeed, a cost that low would open the possibility of space-based shipping—for when you absolutely must have the product delivered from China to California in the next 2 hours.

Another way to put this in perspective is to convert these prices per mass in terms of those of commodities, such as precious metals. $20,000 per kg is nearly the price of solid platinum. $500 per kg is about the price of sterling silver. $10 per kg is roughly the price of copper.

The reasons for optimism are not purely technological. There has also been significant social progress just in the last few years, with major milestones on LGBT rights being made around the world in 2020 and 2021. Same-sex marriage is now legally recognized over nearly the entire Western Hemisphere.

None of that changes the fact that we are still in a global pandemic which seems to be increasingly out of control. I can’t tell you whether 2022 will be better than 2021, or just more of the same—or perhaps even worse.

But while these times are hard, overall the world is still making progress.