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five axioms of choice under uncertainty

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Please explain utility theory----five axioms of choice under uncertainty (axioms of cardinal utility)

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Summarize five axioms of choice under uncertainty.

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to develop a theory of rational decision making in the face of uncertainty, it is necessary to make precise assumptions about an individual's behavior----known as axioms of cardinal utility.

Axiom 1 Completeness
For the entire set S of uncertain alternatives either
X is preferred to y: (x>y)*
Y is preferred to x: (y>x)
Individual is indifferent to x and y (x~y)
*> or < is not mathematical inequality, ...

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