Bounds for Preference Function Assessment

It is well known that when an individual assesses a preference (utility) function, the set of assessed gambles and certainty equivalents is often inconsistent and, if consistent, many preference functions may satisfy the assessments. Mathematical programming is employed to examine properties that might be useful in a sequential determination of the individual's preference function. Specifically, given a consistent set of assessments, if an additional gamble were to be assessed, upper and lower bounds can be found for the probability of the better consequence of the gamble when the certainty equivalent is specified and also bounds for the certainty equivalent of the gamble when the probabilities are specified such that the augmented set of specifications remains consistent. The results are given for general, as well as risk averse preference functions.