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.
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.
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.