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I begin learn PRM , Someone help me understand Four Basic Axioms of Maximising Expected Utility most intuitive way .Thank you very much enter image description here

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Here's a try/start:

Let $A,B$, and $C$ be three possible events, and let $U(event)$ be the utility derived from each event. For example, if event $A$ corresponds to the event of winning the lottery, then $U(A)$ will presumably be a very large value. By contrast, if event $C$ corresponds to the event of falling off a ladder and breaking an arm, $U(C)$ will likely be a very small value.

  1. Transitivity: if $U(A)>U(B)$ and $U(B)>U(C)$, then $U(A)>U(C)$
  2. Continuity: if $U(A)>U(B)>U(C)$, then $\exists p \in [0,1]$ such that $$U(B) = pU(A) + (1-p)U(C)$$ i.e. the utility function $U(event)$ is a continuous function
  3. Independence of Choice: (?)
  4. Stochastic Dominance: if $U(A) = U(B)$, then if we must choose between $A$ and $B$, we ought to choose the one that is more likely to occur
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