Inequity Aversion in Subjective Evaluations: Evidence from Referees' Decisions in Soccer

Subjective evaluations in many contexts might be affected by decision-makers' social preferences. To explore this phenomenon, we use data from soccer referees' decisions. According to soccer rules, referees are expected to evaluate each episode independently, without taking into account previous decisions. However, if referees are averse to creating inequities between teams, they might seek to balance their decisions and, for example, after awarding a penalty to the home team, they may raise the evidence threshold for awarding a second penalty to the same team, while lowering it for awarding a penalty to the away team. First, we offer a simple theoretical model to explain these insights. Then, using detailed minute-by-minute commentary data from approximately 21,400 matches in major European leagues, we show a strong preference by referees to treat teams fairly: they reduce the probability of awarding a penalty (or a red or yellow card) to a team if it has already been awarded to that team, while increasing the probability if it has been awarded to the opposing team. In the final part, focusing on injury time, we show that referees tend to lengthen injury time both when the home team is behind and when the away team is behind, suggesting that referees may have a preference for treating both teams fairly.