Because if your choices under uncertainty do not maximize the expected value of some utility function, you are behaving inconsistently (in a particular sense, axiomatized by Savage, and others—there’s a decent introduction here).
Can you name a specific chapter in the linked-to Choice under Risk and Uncertainty?
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Can you name a specific chapter in the linked-to Choice under Risk and Uncertainty?
Unfortunately, the equations are not rendered correctly in my browser.