Gur vzcnpg bs na rirag ba lbh vf gur qvssrerapr orgjrra gur rkcrpgrq inyhr bs lbhe hgvyvgl shapgvba tvira pregnvagl gung gur rirag jvyy unccra, naq gur pheerag rkcrpgrq inyhr bs lbhe hgvyvgl shapgvba.
Zber sbeznyyl, jr fnl gung gur rkcrpgrq inyhr bs lbhe hgvyvgl shapgvba vf gur fhz, bire nyy cbffvoyr jbeyqfgngrf K, bs C(K)*H(K), juvyr gur rkcrpgrq inyhr bs lbhe hgvyvgl shapgvba tvira pregnvagl gung n fgngrzrag R nobhg gur jbeyq vf gehr vf gur fhz bire nyy cbffvoyr jbeyqfgngrf K bs C(K|R)*H(K). Gur vzcnpg bs R orvat gehr, gura, vf gur nofbyhgr inyhr bs gur qvssrerapr bs gubfr gjb dhnagvgvrf.
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.
Rot13:
Gur vzcnpg bs na rirag ba lbh vf gur qvssrerapr orgjrra gur rkcrpgrq inyhr bs lbhe hgvyvgl shapgvba tvira pregnvagl gung gur rirag jvyy unccra, naq gur pheerag rkcrpgrq inyhr bs lbhe hgvyvgl shapgvba.
Zber sbeznyyl, jr fnl gung gur rkcrpgrq inyhr bs lbhe hgvyvgl shapgvba vf gur fhz, bire nyy cbffvoyr jbeyqfgngrf K, bs C(K)*H(K), juvyr gur rkcrpgrq inyhr bs lbhe hgvyvgl shapgvba tvira pregnvagl gung n fgngrzrag R nobhg gur jbeyq vf gehr vf gur fhz bire nyy cbffvoyr jbeyqfgngrf K bs C(K|R)*H(K). Gur vzcnpg bs R orvat gehr, gura, vf gur nofbyhgr inyhr bs gur qvssrerapr bs gubfr gjb dhnagvgvrf.
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.