timtyler comments on Utility is unintuitive - Less Wrong
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That's the issue of the usefulness of the Axiom of Independence - I believe.
You can drop that - though you are still usually left with expected utility maximisation.
Then you become a money pump.
It is the most commonly dropped axiom. Dropping it has the advantage of allowing you use the framework to model a wider range of intelligent agents - increasing the scope of the model.
What is the issue? Where, in my account, does AoI come into play? And why do you suggest that AoI only sometimes makes a difference?
My comments about independence were triggered by:
The independence axiom says "no" - I think - though it is "just" an axiom.
For the last question, if you drop axioms you are still usually left with expected utility maximisation - though it depends on exactly how much you drop at once. Maybe it will just be utility maximisation that is left - for example.