The Expected Utility Model: Its Variants, Purposes, Evidence and ...

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Schoemaker: The Expected Utility Model 543 + .5U(O), whereas the latter preference implies the reverse inequality. To see why this preference pattern violates the third EU axiom, note the following relationship between situations A and B: In prospect theory, Kahneman and Tversky (1979) provide several additional examples of this certainty effect, which they explain as the result of probability distortions. A related experiment on the effect of certainty vs. uncertainty was performed by Ellsberg (1961); however, his focus was on the probability dimension. He showed that people dislike ambiguity as to the exact level of the probability of winning (pi). The essential finding was that subjects look at more than the expected value of such a probability, when given some prior distribution as to its levels. This sensitivity to other moments is contrary to EU theory for which only E(f5i) matters.9 The Allais and Ellsberg paradoxes can both be shown to entail a violation of an alternative type of EU axiom, called Savage's independence or sure-thing principle (1954). This axiom holds that if two lotteries have an identical probability and payoff branch, the levels of this payoff and probability should not affect people's choice between the lotteries. The above violations particularly raise questions about the fifth EU axiom, i.e., the assessment of compound lotteries. Direct evidence of its violation was offered A normative reply to the Ellsberg paradox can be found in RaifFa (1961), Harry Roberts (1963), and Jacques Dreze (1974). Other discussions of the Ellsberg experiment and related paradoxes (e.g., Allais) are contained in William Fellner (1961), Selwyn Becker and Fred Brownson (1964), Karl Borch (1968), Kenneth MacCrimmon (1968), Frank Yates and Lisa Zukowski (1976), MacCrimrnon and Stig Larsson (1979), and Soo-Hong Chew and MacCrirnmon (1979b). by Maya Bar-Hillel (1973) who found that people tend to overestimate the probability of conjunctive events and underestimate the probability of disjunctive events. In her experiment subjects were presented with three events on which they could bet: 1. A simple event: drawing a red marble from a bag containing 50 percent red and 50 percent white marbles. 2. A conjunctive event: drawing a red marble 7 times in succession, with replacement, from a bag containing 90 percent red marbles and 10 percent white marbles. 3. A disjunctive event: drawing a red marble at least once in 7 successive tries, with replacement, from a bag containing 10 percent red marbles and 90 percent white marbles. The majority preferred bet 2 to bet 1.Subjects also preferred bet 1 to bet 3. The probabilities of the three events, however, are .50, .48 and .52 respectively. These biases can be explained as effects of anchoring: i.e., the stated probability of the elementary event (.l in the disjunctive case) provides a natural starting point from which insufficient adjustment is made to arrive at the final answer. A sixth postulate, not formally part of NM utility theory, is the traditional riskaversion assumption in economics and finance, particularly for losses (Friedman and Savage, 1948; Arrow, 1971; Isaac Ehrlich and Becker, 1972; J. Marshall, 1974; Martin Bailey et al., 1980). Recent laboratory studies, however, seriously question this pervasive assumption (also see, Harry Markowitz, 1952). For instance, John Hershey and Schoemaker (1980) found that less than 40 percent of their subjects would pay $100 to protect against a .O1 chance of losing $10,000. Similar refusals to accept actuarially fair insurance were uncovered by Paul Slovic et al. (1977), Kahneman and Tversky (1979), Schoemaker and Howard Kunreuther (1979), and Fishburn and Gary Kochenberger (1979). Dan Laughhunn et al. (1981) found
544 Journal of Economic Literature, Vol. XX (June 1982) executives to be risk-seeking when presented with gambles having outcomes below target return levels (e.g., breakeven returns on investments). However, when the gambles involved ruinous losses, the executives were often risk-averse. b. Field Studies From a positivistic viewpoint the above evidence may be of limited interest. For instance, economists might argue that although subjects may behave non-optimally in hypothetical and unrepresentative experiments, in the real world, where decisions do matter, people will in fact maximize expected utility. Real-world data on insurance against flood and earthquake insurance, however, suggest a different conclusion (Dan Anderson, 1974). In spite of Federal subsidies of up to 90 percent for flood insurance (this past decade), Kunreuther et al. (1978) found that the majority of eligible homeowners in flood plains were uninsured. One obvious reason could be that people's perceptions of the probability and magnitude of loss, or their perceptions as to the cost of insurance, differed from the actuarial figures used by the government. To test whether homeowners were subjectively rational, Kunreuther et al. interviewed 2,000 homeowners in flood plains and 1,000 homeowners in earthquake areas to obtain subjective estimates of these figures. Many respondents, over one-half, were ill-informed on the availability of insurance against these hazards. Of those who were aware, however, many acted contrary to subjective EU maximization (around 40 percent for flood and 30 percent for earthquake insurance), assuming a marginal tax rate of 30 percent and plausible degrees of risk aversion. The study for expecting postdisaster relief aid from federal, state or local agencies. Results found by Kunreuther et (1978) thus seriously quest-on people's ability to process information On low probability, high loss events. (See also Kunreuther, 1976). A similar conclusion emerges from the low demand for crime insurance (Federal Insurance Administration, 1974), and people's general reluctance to wear seat belts in automobiles (L. Robertson, 1974).1° Although the above results imply riskseeking for losses (within the EU model), in other domains of insurance people appear highly risk-averse. As mentioned earlier, Pashigian et al. uncovered a strong preference for expensive low deductible automobile insurance. Similarly, Robert Eisner and Strotz (1961) showed that although flight-insurance is considerably more expensive than regular life-insurance, there exists a strong demand for the former. Indeed, flight insurance is one of the few coverages which is actually "bought" (i.e., the consumer rather than insurance agent initiates the purchase). The above examples suggest that people sometimes ignore low probability events, whereas at other times they focus on the loss dimension. They question whether people are as coherent and consistent as EU maximization implies, highlighting the importance of psychological factors in economic behavior (George Katona, 1975). An interesting illustration of the need to include psychological factors was offered by Katona (1965). He examined whether working people who expect retirement income from pension plans placed more or less funds into private savings (e.g., deposits with banks and savings institutions, bonds or stocks) than working people who are not covered by such pension plans. Private pension plans, which were relatively unimportant in 1945, ex- lo An intriguing economic explanation for this was offered by Sam Peltzman (1975).His data show that the effects of legally mandated installation of various automobile safety devices are offset by increased Tisk-taking by drivers (e.g., not wearing seatbelts), supporting the notion that drivers determine their om, individually optimal, risk exposure.
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