I’ve now edited that section. Old version and new version here for posterity.
Old version:
None of these is very satisfactory! Intuitively speaking, Alice and Bob want to come to an agreement where respect for both of their interests is built in. For example, they might want the EUM they form to value fairness between their two original sets of interests. But adding this new value is not possible if they’re limited to weighted averages. The best they can do is to agree on a probabilistic mixture of EUMs—e.g. tossing a coin to decide between option 1 and option 2—which is still very inflexible, since it locks in one of them having priority indefinitely.
Based on similar reasoning, Scott Garrabrant rejects the independence axiom. He argues that the axiom is unjustified because rational agents should be able to follow through on commitments they made about which decision procedure to follow (or even hypothetical commitments).
New version:
These are all very unsatisfactory. Bob wouldn’t want #1, Alice wouldn’t want #2, and #3 is extremely non-robust. Alice and Bob could toss a coin to decide between options #1 and #2, but then they wouldn’t be acting as an EUM (since EUMs can’t prefer a probabilistic mixture of two options to either option individually). And even if they do, whoever loses the coin toss will have a strong incentive to renege on the deal.
We could see these issues merely as the type of frictions that plague any idealized theory. But we could also seem them as hints about what EUM is getting wrong on a more fundamental level. Intuitively speaking, the problem here is that there’s no mechanism for separately respecting the interests of Alice and Bob after they’ve aggregated into a single agent. For example, they might want the EUM they form to value fairness between their two original sets of interests. But adding this new value is not possible if they’re limited to (a probability distribution over) weighted averages of their utilities. This makes aggregation very risky when Alice and Bob can’t consider all possibilities in advance (i.e. in all realistic settings).
Based on similar reasoning, Scott Garrabrant rejects the independence axiom. He argues that the axiom is unjustified because rational agents should be able to lock in values like fairness based on prior agreements (or even hypothetical agreements).
I’ve now edited that section. Old version and new version here for posterity.
Old version:
None of these is very satisfactory! Intuitively speaking, Alice and Bob want to come to an agreement where respect for both of their interests is built in. For example, they might want the EUM they form to value fairness between their two original sets of interests. But adding this new value is not possible if they’re limited to weighted averages. The best they can do is to agree on a probabilistic mixture of EUMs—e.g. tossing a coin to decide between option 1 and option 2—which is still very inflexible, since it locks in one of them having priority indefinitely.
Based on similar reasoning, Scott Garrabrant rejects the independence axiom. He argues that the axiom is unjustified because rational agents should be able to follow through on commitments they made about which decision procedure to follow (or even hypothetical commitments).
New version:
These are all very unsatisfactory. Bob wouldn’t want #1, Alice wouldn’t want #2, and #3 is extremely non-robust. Alice and Bob could toss a coin to decide between options #1 and #2, but then they wouldn’t be acting as an EUM (since EUMs can’t prefer a probabilistic mixture of two options to either option individually). And even if they do, whoever loses the coin toss will have a strong incentive to renege on the deal.
We could see these issues merely as the type of frictions that plague any idealized theory. But we could also seem them as hints about what EUM is getting wrong on a more fundamental level. Intuitively speaking, the problem here is that there’s no mechanism for separately respecting the interests of Alice and Bob after they’ve aggregated into a single agent. For example, they might want the EUM they form to value fairness between their two original sets of interests. But adding this new value is not possible if they’re limited to (a probability distribution over) weighted averages of their utilities. This makes aggregation very risky when Alice and Bob can’t consider all possibilities in advance (i.e. in all realistic settings).
Based on similar reasoning, Scott Garrabrant rejects the independence axiom. He argues that the axiom is unjustified because rational agents should be able to lock in values like fairness based on prior agreements (or even hypothetical agreements).