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.