Combine and conquer: A joint application of conjoint and functional approaches to the problem of risk measurement.

Abstract

Functional measurement and conjoint measurement techniques were combined in a study of subjective risk designed as a partial check of the risk measures suggested by-Luce (1980, 1981). The effect of multiplying all outcomes of a gamble by a constant (i.e., a change of scale) on subjective risk was of interest for this purpose. Ten Harvard undergraduates repeatedly rated the riskiness of two sets of gambles. Both sets of gambles allowed independent assessment of the effect of a gamble's expected payoff (mean), its skewness, and its scalefactor. Each of the 20 data sets was treated as a separate experiment. Employing both functional measurement and polynomial conjoint measurement techniques, we obtained the following results: All three variables showed significant main effects. For 6 of the 18 data sets analyzed, a combination rule that was multiplicative for the variables mean and skewness and additive for scale could be fit. Six additional data sets could be fit by a combination rule multiplicative in all three factors (or, equivalently, additive in all three factors for some monotonic transformation of risk, because there was no sign dependence). In the remaining six data sets simple independence was violated for skewness and/or scale, indicating that more complex combinations of these variables than were considered here might have been applied. Thus, for two-thirds of the data sets the effect of a change of scale on perceived risk was additive. Comparison of the effectiveness of conjoint and functional techniques suggests that the two methods should be used in a complementary way.