### AN EXPLANATION OF OPTIMAL EACH-WAY BETS BASED ON NON-EXPECTED UTILITY THEORY

#### Abstract

The purpose in this paper is to demonstrate how the non-expected utility models of Markowitz and Kahneman and Tversky can explain why an agent, chooses to bet each way on a horse.

We also show that that appeal to moments of return, such as a preference for skewness of return, ceteris paribus, to explain the choice of the each way gamble over the single win gamble is , in general, invalid.

#### Keywords

#### Full Text:

PDF#### References

Ali, M. M. (1977) ‘Probability and Utility Estimates for Racetrack Bettors,’ Journal of Political Economy, 85, 803-15.

Andersen, S., G. W. Harrison, M. I Lau and E. Rutström (2005) ‘Preference Heterogeneity in Experiments: Comparing the Field and Lab’, mimeo University of Durham

Battalio, R. C., J. C Kagel and K. Jiranyakul (1990) ‘Testing Between Alternative Models of Choice Under Uncertainty: Some Initial Results’, Journal of Risk and Uncertainty, 3, 25-50.

Bernstein, L. M., G. Chapman, C. Christensen and A.S. Elstein (1997) ‘Models of Choice Between Multioutcome Lotteries’, Journal of Behavioral Decision Making, 10, 93-115.

Binswanger, H. P. (1980) ‘Attitude Toward Risk: Experimental Measurement in Rural India’, Journal of Agricultural Economics, 62, 395-407.

Brockett, P.L. and Kahane, Y.(1992) “Risk, Return, Skewness and Preference”Management Science, Vol. 38,6, 851-866.

Brockett, P. L. and J. R. Garven (1998) ‘A Re-examination of the Relationship between Preference and Moment Orderings by Rational Risk Averse Investors’, Geneva Papers on Risk and Insurance Theory, 23, pp. 127-37.

Bruce, A. C. and J. E. V Johnson (1992) ‘ Toward an Explanation of Betting as a Leisure Pursuit’, Leisure Studies, 11, 201-18.

Cain, M. and D. Peel, (2004) ‘Utility and the Skewness of Return in Gambling’, The Geneva Papers on Risk and Insurance Theory, 29 (2), 145-63.

Cain, M., D. Law and D.A. Peel (2008) ‘Bounded Cumulative Prospect Theory: Some Implications for Gambling Outcomes’, Applied Economics. 40(1), 5-15.

Chamberlain, G.(1983) ‘A Characterihzation of the Distributions That Imply Mean-Variance Utility Functions,’. Journal of Economic Theory, 29, 185-201.

Conlisk, J. (1979) ‘Three Variants on the Allais Example’, The American Economic Review, 79 (3), 392-407.

Conlisk, J. (1993) ‘The Utility of Gambling." Journal of Risk and Uncertainty 6(3):255--275.

Clotfelter, C. T. and P. J. Cook, Selling Hope: State Lotteries in America (Cambridge, MA: Harvard University Press).

Farrell, L and I. Walker (1999) ‘The Welfare Effects of Lotto: Evidence from the UK’, Journal of Public Economics, 72, 99-120.

Friedman, M and L. Savage (1948) ‘The Utility Analysis of Choices involving Risk’, Journal of Political Economy, Vol. 56, 279-304.

Forrest, D. Simmos, R. and N.Chetsers (2000) ‘Buying a Dream: Alternative Models of Demand for Lotto.’ Economic Inquiry,40, 485-496.

David Forrest: Centre for the Study of Gambling and Commercial Gaming, University of Salford, Salford, M5 4WT, UK.

Robert Simmons: Centre for the Study of Gambling and Commercial Gaming, University of Salford, M5 4WT, UK.

Neil Chesters: Dresdner Kleinwort Wasserstein, Riverbank House, 2 Swan Lane, London EC4R 3UX, UK.

Golec, J. and M. Tamarkin, (1998) ‘Bettors Love Skewness, Not Risk, at the Horse Track’, Journal of Political Economy, 106, 205-25.

Harrison, G. W., J. List and C. Towe, (2007) ‘Naturally Occurring Preferences and Exogenous Laboratory Experiments: A Case Study of Risk Aversion,’ Econometrica, Vol. 75, No. 2, March, 433-58.

Hartog, J., A, F, I, Carbonell, and N. Jonker (2002) ‘Linking Measured Risk Aversion to Individual Characteristics’, Kyklos 55 (1), 3-26.

Harville, D. A. (1973) ‘Assigning probabilities to the outcomes of multi-entry competitions’, Journal of the American Statistical Association, 68, 312- 16.

Harinck, F.,Van Dijk, E. Van Beest, I. and Mersmann, P. (2007)

‘When Gains Loom Larger Than Losses Reversed Loss Aversion for Small Amounts of Money,’ Psychological Science,18,12 1099-1105.

Holt, C.A. and S. K. Laury (2002) ‘Risk Aversion and Incentive Effects’, American Economic Review, 97, 1644-55.

Kahneman, D. and A. Tversky (1979) ‘Prospect Theory: An Analysis of Decision under Risk,’ Econometrica, 47, 2, 263-91.

Köbberling, V. and P. Wakker (2005) ‘An Index of Loss Aversion,’ Journal of Economic Theory, 122, 119-31.

Law, D. and Peel, D.A. (2009) “Skewness as an explanation of gambling in cumulative prospect theory” Applied Economics,41, 685-689.

Le Roy, S. (2003), "Expected Utility: a Defense", Economics Bulletin, Vol. 7, No. 7, 1−3.

List, John A,. and Haigh, Michael.2005. "A Simple Test of Expected Utility Theory Using Professional Traders," Proceedings of the National Academy of Science , 102(3): 945-948.

Markowitz, H. M. 1952 ‘The Utility of Wealth’, Journal of Political Economy, 56, 151-54.

Meyer, J. (1987): “Two-Moment Decision Models and Expected Utility Maximization,” American Economic Review, 77(3), 421-430.

Prelec, D. (1998), “The Probability Weighting Function,” Econometrica, 66, 497-527.

Peel, D.A, Law,D. and Cain, M.(2000) ‘Product bundling and a rule of thumb versus the Harville formulae: can each way bets with UK bookmakers generate abnormal returns.’ Applied Economics, 32, 1737- 1744.

Peel, D.A. and Law, D. (2007) “Betting on odds on Favourites as an Optimal Choice in Cumulative Prospect Theory “Economic Bulletin 4, 1-10.

Peel, D.A., Zhang, Jie and D.Law (2007) ‘The Markowitz Model of Utility supplemented with a small degree of Probability Distortion as an explanation of Outcomes of Allais Experiments over Large and Small Payoffs and Gambling on Unlikely Outcomes‘.Applied Economics, 40, 17 – 26.

Peel, D.A. and Law, D. (2008) “A More General Non-Expected Utility Model as an Explanation of Gambling Outcomes for Individuals and Markets” Economica, 76, 251 – 263.

Rabin, M (2000), "Risk Aversion and Expected-Utility Theory: A Calibration Theorem", Econometrica 68, 5, 1281-1292.

Saha, A. (1993) ‘Expo-Power Utility: A Flexible Form for Absolute and Relative Risk Aversion’, American Journal of Agricultural Economics, (75), 905-13.

Scott, H.P. (2006) ‘Cumulative Prospect Theory’s Functional Menagerie’, Journal of Risk and Uncertainty.32, 101-130.

Starmer, C. (2000) ‘Developments in Non-Expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk,’ Journal of Economic Literature, Vol. XXXV111, 332-82.

Strumpf, K.S. (2002) ‘Illegal Sports Bookmakers’ mimeo University of North Carolina at Chapel Hill.

Tversky, A. and Kahneman, D. (1992) ‘Advances in Prospect Theory: Cumulative Representation of Uncertainty’, Journal of Risk and Uncertainty, 5, 4, 297-323

The Wager (2000), ‘Stress, Anxiety, and Why Gamblers Gamble’, 5, 27, Massachusetts Council on Compulsive Gambling.

Weitzman, M. (1965) ‘Utility Analysis and Groups Behavior: An Empirical Study’, Journal of Political Economy, 73, 18-26.

Vaughan Williams, L. (1999) ‘Information Efficiency in Betting Markets: A Survey’, Bulletin of Economic Research, 5l, pp. 307-37

DOI: http://dx.doi.org/10.5750/jgbe.v3i2.584

### Refbacks

- There are currently no refbacks.