How to Be IncoherentandSeductive: Bookmakers' Odds and Support Theory☆☆☆

Abstract Support theory (Tversky and Koehler, 1994) implies that different descriptions of the same event can prompt different subjective probabilities. More explicit descriptions are assumed to enable retrieval of stronger evidence prompting a higher subjective likelihood. In this paper bookmakers' odds are examined in relation to this hypothesis. British bookmakers quote odds for victory, draw, or loss for football teams and also for more specific components such as the actual score of the game. Consistent with support theory, bookmakers' odds for general hypotheses are subadditive; they are smaller than the sum of the odds given to an explicitly unpacked, but extensionally equivalent, disjunction of events subsumed by the general hypothesis. The extent of the subadditivity increases for hypotheses unpacked into a larger number of components. However, although support theory implies that probabilities for explicitly presented disjunctions of events should be additive, the sum of the odds given to race horses increases with the number of horses in the race. These findings are discussed in relation to other evidence for non-additivity.

[1]  A. Tversky,et al.  Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment , 1983 .

[2]  Yaacov Schul,et al.  Elimination and inclusion procedures in judgment. , 1997 .

[3]  David L. Ronis,et al.  Probability judgment accuracy: China, Japan, and the United States , 1989 .

[4]  J. Edward Russo,et al.  An availability bias in professional judgment. , 1988 .

[5]  Eric J. Johnson,et al.  Framing, probability distortions, and insurance decisions , 1993 .

[6]  Bernt P. Stigum,et al.  Foundations of utility and risk theory with applications , 1983 .

[7]  Rami Zwick,et al.  Comparing the calibration and coherence of numerical and verbal probability judgments , 1993 .

[8]  F. Alberoni,et al.  Contribution to the study of subjective probability. I. , 1962, The Journal of general psychology.

[9]  L. Macchi.  Pragmatic Aspects of the Base-rate Fallacy , 1995 .

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

[11]  Arthur E. Hoerl,et al.  Reliability of Subjective Evaluations in a High Incentive Situation , 1974 .

[12]  J. K. Clarkson,et al.  An explanation of conservatism in the bookbag-and-pokerchips situation , 1972 .

[13]  Nigel Harvey,et al.  Judging the probability that the next point in an observed time series will be below, or above, a given value , 1995 .

[14]  B. Fischhoff,et al.  Fault trees: Sensitivity of estimated failure probabilities to problem representation. , 1978 .

[15]  C. C. Chandler,et al.  Studying related pictures can reduce accuracy, but increase confidence, in a modified recognition test , 1994, Memory & cognition.

[16]  A. Tversky,et al.  Support theory: A nonextensional representation of subjective probability. , 1994 .

[17]  J. Frank Yates,et al.  Subjective probability accuracy analysis. , 1994 .

[18]  Peter Whalley,et al.  The Supra-Additivity of Subjective Probability , 1983 .

[19]  Index betting on sports , 1994 .

[20]  M. Watkins,et al.  Recall of a twice-presented item without recall of either presentation: generic memory for events , 1985 .

[21]  K. Busche,et al.  An Exception to the Risk Preference Anomaly , 1988 .

[22]  E. J. Dearnaley,et al.  The addition of subjective probabilities:The summation of estimates of success and failure , 1956 .

[23]  Ward Edwards,et al.  Conservatism in Complex Probabilistic Inference , 1966 .

[24]  Peter Ayton,et al.  Assessing and improving judgemental probability forecasts , 1987 .

[25]  Lawrence D. Phillips,et al.  CULTURAL VARIATION IN PROBABILISTIC THINKING: ALTERNATIVE WAYS OF DEALING WITH UNCERTAINTY* , 1980 .

[26]  G. Gigerenzer,et al.  Probabilistic mental models: a Brunswikian theory of confidence. , 1991, Psychological review.