Caplan and Yudkowsky bet at 1-1 odds whether humanity would be exterminated from the surface of the Earth by 2030. How it works is Caplan pays Yudkowsky $100 in 2017 (when the bet began). If humanity is still living on the surface on the Earth in 2030 then Yudkowsky owes Caplan $200 plus 5% annual interest. See here for details.

I don't think Yudkowsky was taking this bet seriously, which somewhat invalidates it, but let's pretend the bet was in good faith. Does the bet actually work?

Some people criticized the bet on the grounds that it relied on Yudkowsky's honesty and interest rates staying similar. I don't think either of these are an issue. The bet contains a clause to deal with interest rates going haywire and there's no way even a psychopathic machiavellian Yudkowsky would trash his public reputation for a mere CPI-adjusted $200. Moreover, accounting for interest rates is something all time-displaced bets need to deal with. It's just an annoying fact of quantitative finance.

There's a bigger problem with the Caplan-Yudkowsky bet. The bet only makes sense from the perspective of Caplan. There's no direct way for Yudkowsky to intentionally profit from it except indirectly, via financial derivatives, unless our annihilation becomes certain.

Consider the most conservative approach. Yudkowsky invests his $100 in the stock market at 5% annual interest for 13 years. There are two possible outcomes: Either the world ends or it doesn't. If the world ends, Yudkowsky gains exactly nothing from the bet, because he never spent the money. If the world doesn't end then Yudkowsky simply loses money. If Yudkowsky is to profit from the bet, then he must spend money before the world ends in 2030.

Suppose it's 2029. Yudkowsky is confident that the world will end on January 1, 2030. There's no reason to preserve capital, so he blows all of his money on cocaine, prostitutes and a cryogenic vault. If the world ends, then great! But if the world doesn't end then Caplan doesn't get paid back. Yudkowsky can't spend the money as long as there is a chance the world will survive.

In other words, Yudkowsky can only benefit from the $100 by going bankrupt. (Unless interest rates change. Caplan notes that "this is primarily a bet that annualized real interest rates stay below 5.5%". Which is true. But what's interesting is the "End-of-the-World" part, not the 5.5% interest rate.)

It's plausible that financial derivatives might work around this problem, but unless Yudkowsky is using them (unlikely for a bet this small) then this bet was just an indirect way of buying a genuine probability estimate from Bryan Caplan. The only way Yudkowsky can earn money from this bet is via unintended edge cases where he survives the apocalypse (e.g. by being off-planet). Or where our doom has become certain, but it hasn't happened yet, and where money value is still meaningful.

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14 comments, sorted by Click to highlight new comments since: Today at 4:27 PM

This seems silly. Yudkowsky could just do extra talks, work extra hours, etc. right before 2029 ends if he's immediately unable to pay Bryan Caplan back. I gather that Yudkowsky thinks theres a lumpy chance of the world ending all over the 2020s, and not a specific high chance at January 1st, 2030. Even if he did, he could still have engineered payments in trenches because Yudkowsky has human capital he can use as long as the world continues to exist.

So the bet is capped at Yudkowsky's ability to earn extra income on the margin, to meet unforseen circumstances and whatever payment plan they can agree to, but this problem is obviously not insolvable.

You're right. I have edited the post to remove the bit about tying up capital. That part was wrong.

You claim that Eliezer can't spend the money and your argument requires that assumption. But I don't see anything in the bet itself requiring that?

Not directly, but that's not quite what I'm getting at. What I really mean is that Eliezer is honor-bound to maintain enough collateral to repay Caplan in case the world survives. [Edit: lc pointed out a flaw in that logic.]

One way Eliezer could benefit from this bet (which I left out in my post) is by spending literally all of his money and then suddenly earning back the $200 right before he has to repay Caplan. But that would require him to literally bankrupt himself, which outweights any benefit he could accrue from this bet. (Except in the world I already noted where our doom becomes certain.)

He's unlikely to bankrupt himself, precisely because it would have bad effects. But, that doesn't mean he doesn't benefit from the extra $100! Instead, it means he has an additional $100 cushion to avoid bankruptcy, and is in fact $100 better off than if he didn't have that $100, conditional on the world ending before the deadline. 

ETA: and planning to earn it back right before the deadline is perfectly rational on the assumption that the likelihood of the world ending is very high. It only doesn't make sense if he doesn't actually believe in what he's betting on!

$100 is only useful if you spend it or invest it. If Yudkowsky spends it, that means he burdned through all his other investments and bankrupted himself. And it makes no sense to invest it because he only keeps the money if the world ends and investments become worthless.

No, imagine he has some utility function with one term that depends on spending money (e.g. consumer goods) and another term that depends on having money (preserving optionality/avoiding bankruptcy).

In equilibrium, Eliezer will divide his money between saving and spending money to maximize the total utility of those terms.

If he has an extra $100, he has an extra $100. He will divide it in some manner between those terms and be, in fact, better off. It isn't important how precisely he divides it. 

If he expects the world to end, very little resources should be allocated to savings for expenses expected to occur after the end of the world. If the world doesn't end, then he will suddenly have to pay $200. As it approaches the deadline and he expects the world not to end, he will now be worse off as he has to reallocate resources to paying off the debt. But in expectation, if he initially expects the world to end with high probability, he is still better off having the $100.

It seems to me like that benefit is very marginal compared to the simple expected value loss if the world survives.

Edit: Caplan wins alpha but Yudkowsky wins mere liquidity.

If he's confident enough it seems like a very good expected value: If Yudkowsky is right, he's getting an infinity% return on investment (since Caplan gave him $100 that he'll never have to pay back).

In the limit of high expectation of the world ending, the expected value loss if the world survives goes to zero, so we've now established that the bet can, in fact, work.

With respect to the actual values, given that the bet is for an amount of money small relative to expected income, I'd expect fairly linear effects where the expected utility cost* of doing extra work/spending less to accumulate $200 in the future is pretty close to twice the utility cost of having $100 more to spend now, such that if the chance of the world ending is greater than 50% it makes sense to make the bet.

(*ignoring discount rates, wage rate changes etc., which aren't the point)

Further edit: if the world is likely to end, yes Yudkowsky wins alpha.

How it works is Caplan pays Yudkowsky $100 in 2017 (when the bet began). If humanity is still living on the surface on the Earth in 2030 then Caplan owes Yudkowsky $200 plus 5% annual interest. See here for details.

Typo/Transpositional error: Yudkowsky owes Caplan 200$ plus 5% annual interest.

Fixed. Thanks.

Caplan and Yudkowsky bet at 2-1 odds

It's a 1:1 bet, not a 2:1 bet. If you give me $100 now and I give you $200 if a fair coin lands heads, this is equivalent to you making a $100 1:1 bet on the fair coin landing heads. This is because you'll net $100($200-$100) if the coin lands heads, and I'll net $100 if the coin doesn't land heads.

Fixed. Thank you.