The operation of betting markets is straightforward, which helps in the analysis of decision-making behavior. Specifically, in a betting market individuals are able to place bets on a set of outcomes of a particular event. For instance, in the simplest of markets for betting on a horse race with n runners, n different bets are available, one for each horse to win the race. After the market has closed and the race has taken place, each bet pays a return, £ri, for each £1 staked if horse i wins the race but pays nothing 492 motivation, behavior, and decision-making in betting markets otherwise.
While the returns,ri (usually referred to as the“odds”against each outcome), are determined differently according to the type of market and event, generally they depend on the relative amounts bet on each outcome by all the market participants. Consequently, bettors have an incentive to continue to place money on each outcome until the returns reflect the market’s best estimate of that outcome’s probability of occurring (Figlewski 1979).
Therefore, a typical approach to assessing decisions in betting markets is summarized (with reference to horse race betting) by R. M. Griffith (1949, 290) as follows: the odds on the various horses in any race are a functioning of the proportion of the total money that is bet on each and hence are socially determined. On the other hand, the objective probability for winners from any group of horses is given a posteriori by the percentage of winners.
Thus the odds express (reciprocally) a psychological probability while the percentage of winners at any odds group measures the true probability; any consistent discrepancy between the two may cast light not only on the specific topics of horse-race betting and gambling but on the more general field of the psychology of probabilities. So, the “socially determined” prices in betting markets reflect the “subjective probabilities” assigned to each possible outcome by the bettors, in aggregate. The results of the event then determine the “objective probabilities.”
A comparison of subjective and objective probabilities thus allows an evaluation of any biases in bettors’ decisions. If the betting is such that the relative volumes of betting on each outcome introduce a systematic bias, this can be detected by researchers. A drawback of most betting market research is that, for ethical and/or practical reasons, it is usually not possible to obtain information relating to the decisions of individual bettors.
Instead, subjective probabilities are an aggregation of opinions of all bettors. Hence it is possible that “certain biases present in an individual bettor’s decisions are being counterbalanced by opposite biases in other bettors’ decisions” (Johnson and Bruce 2001, 280). Colin Camerer (1987, 982) noted that a common argument for the rationality of market participants is that “random mistakes of individuals will cancel out” but also offered the counterargument that “biases found by psychologists are generally systematic—most people err in the same direction.” Thus the best we can hope for in betting market research is evidence of systematic bias.