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.
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.