Many different functional forms have been suggested for both the value function and probability weighting function of Cumulative Prospect Theory (Tversky and Kahneman, 1992). There are also many stochastic choice functions available. Since these three components only make predictions when considered in combination, this paper examines the complete pattern of 256 model variants that can be constructed from twenty functions. All these variants are fit to experimental data and their explanatory power assessed. Significant interaction effects are observed. The best model has a power value function, a risky weighting function due to Prelec (1998), and a Logit function. Copyright Springer Science + Business Media, LLC 2006Cumulative prospect theory, Stochastic choice,

In many theories of decision under risk (e.g., expected utility theory, rank dependent utility theory, and prospect theory) the utility or value of a prospect is independent of other prospects or options in the choice set. The experiments presented here show a large effect of the available options set, suggesting instead that prospects are valued relative to one another.The judged certainty equivalent is strongly influenced by the options available. Similarly, the selection of a preferred option from a set of prospects is strongly influenced by the prospects available. Alternative theories of decision under risk (e.g., the stochastic difference model, multialternative decision field theory, and range frequency theory), where prospects themselves or prospect attributes are valued relative to one another, can provide an account of these context effects.

The efficiency of gambling markets has frequently been questioned. In order to investigate the rationality of bookmaker odds, we use an ordered probit model to generate predictions for English football matches and compare these predictions with the odds of UK bookmaker William Hill. Further, we develop a model that predicts bookmaker odds. Combining a predictive model based on results and a bookmaker model based on previous quoted odds allows us to compare directly William Hill opinion of various teams with the team ratings generated by the predictive model. We also compare the objective value of individual home advantage and distance travelled with the value attributed to these factors by bookmakers. We show that there are systematic biases in bookmaker odds, and that these biases cannot be explained by William Hill odds omitting valuable, or excluding extraneous, information.