Question

Briefly explain the role the independence axiom plays in the expected utility theorem.

Answer 1

Expected utility refers to an average utility value that is obtained by taking an average of all tge expected results once the naturw of the outcome is out of the context of prediction and thus an average is considered as a result for predicting the outcome. Expected utility theorem is used in such cases where the individuals are expected to take decisions without knowing the result or outcome of such decisions. Thus, it represents a decision making under uncertainity and hence would take the role of other agents and the utility of all possible functions would be taken in to consideration along with the risk aversion of the individual who is taking the decision.

The independent axiom in such a theory would mean that the preference made by the decision maker in deciding between two outcomes is not affected by the mixing of the two possible outcomes. The probabilistic independent axiom extends this particular decision making to probabilistic decision making where the act of making decsions would vary with each predictions. Accordibg to probability axiom, the decsion making does not vary with the mixing of more pribability decisions that happens while choosing the outcome. Thus, we can see that independent axioms plays a good role in decision making and determination of the manner of decision making in expected utilitites.