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I would like to find a function on events in a probability space satisfying two conditions. The function is with respect to an event Q.
.
for any A and B. So shrinking a set increases f.
I had originally thought was an example, but alas I discovered that it doesn't satisfy condition 2.
The motivation is this: Think of Q as a "goal", and E as your "belief state". Obviously, you want to act so that be high. But it's possible that you will gain new evidence that reduces , but you want a utility function that seeks out that information anyway (and doesn't throw it away, because that would be irrational). Condition 2 ensures that gaining new evidence never harms you, even if it reduces P(Q|E). So maximize instead. -- 49.184.160.10 ( talk) 10:19, 27 March 2018 (UTC)
Q is realized on the whole probability space or nowhere at all, but which is a bit different. So technically, events that happen almost surely or almost never are not covered by the demo, but it should be easy enough to carve a proper subset of E such that the demonstration holds. Tigraan Click here to contact me 14:53, 27 March 2018 (UTC)
Mathematics desk | ||
---|---|---|
< March 26 | << Feb | March | Apr >> | March 28 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
I would like to find a function on events in a probability space satisfying two conditions. The function is with respect to an event Q.
.
for any A and B. So shrinking a set increases f.
I had originally thought was an example, but alas I discovered that it doesn't satisfy condition 2.
The motivation is this: Think of Q as a "goal", and E as your "belief state". Obviously, you want to act so that be high. But it's possible that you will gain new evidence that reduces , but you want a utility function that seeks out that information anyway (and doesn't throw it away, because that would be irrational). Condition 2 ensures that gaining new evidence never harms you, even if it reduces P(Q|E). So maximize instead. -- 49.184.160.10 ( talk) 10:19, 27 March 2018 (UTC)
Q is realized on the whole probability space or nowhere at all, but which is a bit different. So technically, events that happen almost surely or almost never are not covered by the demo, but it should be easy enough to carve a proper subset of E such that the demonstration holds. Tigraan Click here to contact me 14:53, 27 March 2018 (UTC)