The impact of an event on you is the difference between the expected value of your utility function given certainty that the event will happen, and the current expected value of your utility function.
More formally, we say that the expected value of your utility function is the sum, over all possible worldstates X, of P(X)U(X), while the expected value of your utility function given certainty that a statement E about the world is true is the sum over all possible worldstates X of P(X|E)U(X). The impact of E being true, then, is the absolute value of the difference of those two quantities.
We’re talking about the impact of an event though. The very question is only asking about worlds where the event actually happens.
If I don’t know whether an event is going to happen and I want to know the impact it will have on me, I compare futures where the event happens to my current idea of the future, based on observation(which also includes some probability mass for the event in question, but not certainty).
In summary, I’m not updating to “X happened with certainty” rather I am estimating the utility in that counterfactual case.
Translation to normal spoiler text:
The impact of an event on you is the difference between the expected value of your utility function given certainty that the event will happen, and the current expected value of your utility function.
More formally, we say that the expected value of your utility function is the sum, over all possible worldstates X, of P(X)U(X), while the expected value of your utility function given certainty that a statement E about the world is true is the sum over all possible worldstates X of P(X|E)U(X). The impact of E being true, then, is the absolute value of the difference of those two quantities.
Nitpick: one should update based on observations, as opposed to “X has occurred with certainty”.
We’re talking about the impact of an event though. The very question is only asking about worlds where the event actually happens.
If I don’t know whether an event is going to happen and I want to know the impact it will have on me, I compare futures where the event happens to my current idea of the future, based on observation(which also includes some probability mass for the event in question, but not certainty).
In summary, I’m not updating to “X happened with certainty” rather I am estimating the utility in that counterfactual case.