i'm a little bit confused about the utility calculation. In the attachment i have constructed two simple scenarios with a utility node U1 and two chance nodes as parents (S1,S2). I thought, that the Utility is an expected value, calculated by the parent's propagated evidence. So let's say we have only one chance node weather with states rainy, and sunny and it is a parent node of U, it is calculating
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U(weather=rainy)=-10; U(weather=sunny)=20 -> Expected Value: P(weather=rainy)*-10 + P(weather=sunny)*20
This approach worked fine, also with more than one parent node. But since i have connected these parents like in the scenarios (S1->S2), this approach is not working anymore. It is only working for case 1. In case 2 i have only changed one utility-table-entry from 10 to 100. So i think i have done a mistake in this approach. Can someone tell me, what is wrong in my calculation approach?
I would be really grateful, if you could help me. Thanks a lot!