Triple bisection algorithms for 1-D utility elicitation in the case of monotonic preference
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Abstract
The paper focuses on four techniques for elicitation of utilities over 1-D sets of prizes probability, certainty, lottery, and uncertain equivalence methods. The preferential equation of each method results from a general theoretic scheme. Since real decision makers disobey some of the rationality principles of preferences, they are referred as fuzzy rational, and elicit utilities in the form of uncertainty intervals. The elicitation of those is presented in an algorithm that uses triple bisection. Algorithms account for the type of preferences of the fuzzy rational decision maker, i.e. whether those are monotonically increasing or decreasing over the prize set. An example is presented, where preferences are elicited both by the uncertain equivalence and the lottery equivalence methods.
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