HARRY MARKOWITZ will buy more than one lottery ticket. This persons desiring large symmetric bets and contradicts observation, It the implausibility of the one(moderately <6. One might hypothesize that the utility of rich)man insurance company.Perhaps the ame, to be added to the utility of the only evidence of mine which could, so to outcomes, is a function of the possible loss speak, "stand up in court""is the testimony W,or the difference between gain and of the Mosteller- Nogee experiment. But this loss(W,-W2) Neither of these hypotheses does not fully suit our needs, since only a explains why people prefer small chances of narrow range of wealth positions were sam- gains with large chances of small losses realize that i have not demon- rather than vice versa In "beyond a shadow of a doubt? the why people play more conservatively when of the hypothesis introduced. 2 I losing than when winning have tried to present, motivate, and, to a In short, the classical hypothesis may be certain extent, justify and make plausible a consistent with the existence of chance-tak- hypothesis which should be kept in mind ing, but it does not explain the particular when explaining phenomena or designing chances which are taken. To explain such experiments concerning behavior under risk choices, while maintaining simple hypothe- or uncertainty ses concerning " fun of participation, "we 1 Even now we are of one class of com- must postulate a utility function as in Fig- monly observed phenomena which seems to be in ure 5 consistent with the hypothesis introduced in this I. It may be objected that the argu- pas intended to supersede. The existence of multiple as well as the hypotheses which this one ments in this paper are based on flimsy evi- lottery prizes with various sized prizes may con dence. It is true that many arguments are tradict the theory presented. If we are forced to based on"a priori"evidence. Like most"a concede that the individual (lottery-ticket buyer) priori, evidence, these are presumptions of fair lotteries, then my hypothesis cannot explain this the writer which he presumes are also held fact. Nor can any other hypothesis the reader. Such a priori evidence in- this paper explain a preference for dife. idered in udes bility of middle-income lotter or can hypothesis which sumes that people maximize expected utility. Ever vG, The statement that millionaires"ought"to now we must seek hypotheses which explain what for pennies is irrelevant. We seek a hypothesis our present hypotheses explain, avoid the con- o explain behavior, not a moral principle by which tradictions with observation to which they are to judge beh subject, and perhaps explain still other phenomena