I’m not sure that the proof can be summarised in a comment, but the theorem can:
Suppose you are an agent that knows that you are living in an Everettian universe. You have a choice between unitary transformations (the only type of evolution that the world is allowed to undergo in MWI), that will in general cause your ‘world’ to split and give you various rewards or punishments in the various resulting branches. Your preferences between unitary transformations satisfy a few constraints:
Some technical ones about which unitary transformations are available.
Your preferences should be a total ordering on the set of the available unitary transformations.
If you currently have unitary transformation U available, and after performing U you will have unitary transformations V and V’ available, and you know that you will later prefer V to V’, then you should currently prefer (U and then V) to (U and then V’).
If there are two microstates that give rise to the same macrostate, you don’t care about which one you end up in.
You don’t care about branching in and of itself: if I offer to flip a quantum coin and give you reward R whether it lands heads or tails, you should be indifferent between me doing that and just giving you reward R.
You only care about which state the universe ends up in.
If you prefer U to V, then changing U and V by some sufficiently small amount does not change this preference.
Then, you act exactly as if you have a utility function on the set of rewards, and you are evaluating each unitary transformation based on the weighted sum of the utility of the reward you get in each resulting branch, where you weight by the Born ‘probability’ of each branch.
Thanks! The list of assumptions seems longer than in the De Raedt et al. paper and you need to first postulate branching and unitarity (let’s set aside how reasonable/justified this postulate is) in addition to rational reasoning. But it looks like you can get there eventually.
I’m not sure that the proof can be summarised in a comment, but the theorem can:
Suppose you are an agent that knows that you are living in an Everettian universe. You have a choice between unitary transformations (the only type of evolution that the world is allowed to undergo in MWI), that will in general cause your ‘world’ to split and give you various rewards or punishments in the various resulting branches. Your preferences between unitary transformations satisfy a few constraints:
Some technical ones about which unitary transformations are available.
Your preferences should be a total ordering on the set of the available unitary transformations.
If you currently have unitary transformation U available, and after performing U you will have unitary transformations V and V’ available, and you know that you will later prefer V to V’, then you should currently prefer (U and then V) to (U and then V’).
If there are two microstates that give rise to the same macrostate, you don’t care about which one you end up in.
You don’t care about branching in and of itself: if I offer to flip a quantum coin and give you reward R whether it lands heads or tails, you should be indifferent between me doing that and just giving you reward R.
You only care about which state the universe ends up in.
If you prefer U to V, then changing U and V by some sufficiently small amount does not change this preference.
Then, you act exactly as if you have a utility function on the set of rewards, and you are evaluating each unitary transformation based on the weighted sum of the utility of the reward you get in each resulting branch, where you weight by the Born ‘probability’ of each branch.
Thanks! The list of assumptions seems longer than in the De Raedt et al. paper and you need to first postulate branching and unitarity (let’s set aside how reasonable/justified this postulate is) in addition to rational reasoning. But it looks like you can get there eventually.