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solution

Assign a utility of 0 to A (the lowest outcome) and a utility of 1 to B (the highest outcome).

Determine the utility associated with any intermediate value by the following process:

 i. Present the individual with two alternatives. The first alternative consists of the intermediate value X, the utility of which is to be determined. The second alternative consists of a lottery which has two possible outcomes, A and B, with probabilities p1 and p2 attached to them (p1 + p2 = 1).

ii. Ask the individual to choose one of the alternatives presented in (i) above.

 iii. If the individual chooses the first alternative, revise the second alternative such that it becomes more attractive. This means the value of p2 should be increased and the value of p1 should be decreased. If the individual chooses the second alternative, revise it such that it becomes less attractive. This means the value of p2 should be decreased and the value of p1 should be increased.

iv. Ask the individual to choose after the revision of lottery as per step (iii). Continue this till the individual becomes indifferent to both the alternatives.

v. When the individual becomes indifferent to both the alternatives, the utility of X is simply the value of p2

 

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