Rank-Dependent Utility Theory

Overview of Theory

Rank-dependent utility theory does not rely on the assumption of independence found in the expected utility theory. Rather, the theory assumes comonotonic independence. Independence in expected utility theory requires that if different common outcomes that have equal value are used, the decision maker's preference between these two choices would not be changed. That is, the decision maker would choose the same kind of options again. However, in rank-dependent utility, independence requirements are not useful. This is because each decision maker ranks the choices in a different way, based on his or her preferences. The comonotonic independence assumption indicates that using different common outcomes or treatments should not change the rank ordering of the outcomes. As a result, the decision maker's weighting of the choice is also considered. Rank-dependent utility theory relies on decision makers deriving probability weights from the entire probability distribution, not a single probability. Decisions are made after considering the entire outcome set, not one outcome at a time. Rank-dependent utility theory is able to operate under the assumption of comonotonic independence because it assumes that people rank the possible outcomes and transform the probabilities accordingly. After the ranking is complete, the order of outcomes is used to make a decision, not the individual probabilities.

Examples

Let's first consider an example of expected utility theory. Suppose a patient has an infection in her liver and needs to choose between two treatments to protect her from further infection. Treatment A has a 30% chance of protecting her for 5 years and a 70% chance of protecting her for 3 years. Treatment B has a 40% chance of protecting her for 4 years and a 60% chance of protecting her for 2 years. If this patient uses the expected utility approach, she would choose the treatment option that provides the maximum protection in the future for her, which in this example is Treatment A. Imagine that further research regarding these treatment options indicate that the actual protection levels are as follows: Treatment A has a 30% chance of 5 years' protection, a 60% chance of 3 years' protection, and a 10% chance of no protection; and Treatment B has a 40% chance of 4 years' protection, a 50% chance of 2 years' protection, and a 10% chance of 6 years' protection. Even with these modifications, Treatment A would still provide more overall protection to the patient. The independence criteria in expected utility theory indicate that since the overall value of Treatment A is still higher than Treatment B, the patient would choose Treatment A. However, using only independence neglects the fact that Treatment A has a 10% chance of not curing the patient at all. It also neglects the fact that Treatment B has actually the highest year of protection (10% chance of 6-year protection), which may be preferred by some patients.

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