Making the seemingly impossible appear possible: Effects of conjunction fallacies in evaluations of bets on football games

This paper investigates whether people obey the conjunction rule when evaluating predictions concerning the outcomes of football games. The conjunction rule states that if event A and event B are two independent events, the probability that both events A and B will occur cannot be greater than the probability that A will occur. Hence, the prediction that AC Milan will beat Fiorentina at the same times as Juventus will beat Lecce cannot be more likely than the prediction that AC Milan will beat Fiorentina. In an empirical study, it was shown that people frequently violated the conjunction rule. When a prediction with a low or intermediate likelihood of success (e.g., Stoke City will beat Manchester United) was combined with one or two predictions that had high likelihood of success (e.g., Liverpool FC will beat Wigan), it was perceived to be more likely to happen than when it was presented alone. This was not true when it was combined with a prediction with a low likelihood of success. Thus, the perceived likelihood of a particular prediction is dependent on the context in which it is presented.