ON THE OPTIMAL DESIGN OF LOTTERIES

In recent years, the expected utility model of choice under risk has been generalized to cope with phenomena such as probability weighting. In the present paper, one such generalized approach, the rank-dependent expected utility model, is applied to the problem of lottery gambling. The model is used to derive an optimal prize structure for lotteries, ivolving a few large prizes and a large number of small prizes. Other forms of gambling, such as racetrack betting, are discussed in the light of this result. Copyright 1991 by The London School of Economics and Political Science.

[1]  E. Rowland Theory of Games and Economic Behavior , 1946, Nature.

[2]  L. J. Savage,et al.  The Utility Analysis of Choices Involving Risk , 1948, Journal of Political Economy.

[3]  R. M. Griffith,et al.  Odds adjustments by American horse-race bettors. , 1949, The American journal of psychology.

[4]  A. Stuart,et al.  Portfolio Selection: Efficient Diversification of Investments , 1959 .

[5]  D. Ellsberg Decision, probability, and utility: Risk, ambiguity, and the Savage axioms , 1961 .

[6]  W. Edwards Subjective probabilities inferred from decisions. , 1962, Psychological review.

[7]  Ng Yew Kwang Why do People Buy Lottery Tickets? Choices Involving Risk and the Indivisibility of Expenditure , 1965, Journal of Political Economy.

[8]  Josef Hadar,et al.  Rules for Ordering Uncertain Prospects , 1969 .

[9]  J. Flemming The Utility of Wealth and the Utility of Windfalls , 1969 .

[10]  M. Rothschild,et al.  Increasing risk: I. A definition , 1970 .

[11]  M. Rothschild,et al.  Increasing risk II: Its economic consequences , 1971 .

[12]  Young Chin Kim Choice in the Lottery-Insurance Situation Augmented-Income Approach , 1973 .

[13]  Jagdish Handa,et al.  Risk, Probabilities, and a New Theory of Cardinal Utility , 1977, Journal of Political Economy.

[14]  Mukhtar M. Ali Probability and Utility Estimates for Racetrack Bettors , 1977, Journal of Political Economy.

[15]  Uday S. Karmarkar,et al.  Subjectively weighted utility: A descriptive extension of the expected utility model , 1978 .

[16]  Uday S. Karmarkar,et al.  Subjectively weighted utility and the Allais Paradox , 1979 .

[17]  A. Tversky,et al.  Prospect Theory : An Analysis of Decision under Risk Author ( s ) : , 2007 .

[18]  G. Shafer,et al.  Expected Utility Hypotheses and the Allais Paradox. , 1982 .

[19]  K. MacCrimmon,et al.  Utility Theory: Axioms Versus ‘Paradoxes’ , 1979 .

[20]  M. Machina "Expected Utility" Analysis without the Independence Axiom , 1982 .

[21]  J. Quiggin A theory of anticipated utility , 1982 .

[22]  A. F. M. Smith,et al.  Expected Utility Hypotheses and the Allais Paradox. , 1982 .

[23]  S. Chew A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox , 1983 .

[24]  M. Machina,et al.  ATTITUDES TOWARD RISK: FURTHER REMARKS* , 1984 .

[25]  G. Shafer,et al.  Expected Utility Hypotheses and the Allais Paradox. , 1982 .

[26]  Michael Carter,et al.  Expectations in Economics , 1984 .

[27]  B. Haig,et al.  Gambling in Australia. , 1985 .

[28]  Uzi Segal,et al.  SOME REMARKS ON QU|GGIN'S ANTICIPATED UTILITY* , 1986 .

[29]  M. Yaari The Dual Theory of Choice under Risk , 1987 .

[30]  Richard E. Quandt,et al.  Efficiency and Profitability in Exotic Bets , 1987 .

[31]  C. S. Hong,et al.  Risk aversion in the theory of expected utility with rank dependent probabilities , 1987 .

[32]  Edi Karni,et al.  Preference reversal and the observability of preferences by experimental methods , 1987 .

[33]  Uzi Segal,et al.  Non-expected utility risk premiums: The cases of probability ambiguity and outcome uncertainty , 1988 .