Inequity aversion in subjective evaluations: evidence from referees' decisions in soccer

Subjective evaluations in many contexts can be influenced by decision-makers' social preferences. We investigate this phenomenon using data from soccer referees' decisions. Referees are expected to evaluate each episode independently, regardless of prior calls. However, if referees dislike creating inequities between teams, they might compensate for earlier decisions. For instance, after awarding a penalty to the home team, they may apply a higher threshold when awarding a second penalty to the same team while lowering the threshold for the away team. Using play-byplay data from 21,400 matches in major European leagues, we find that referees exhibit a strong preference for equality: they increase the probability of awarding a penalty or issuing a red or yellow card against a team if the opposing team was previously subject to a similar decision, and reduce that probability if the team itself was previously subject to one. Finally, focusing on injury time, we show that referees tend to extend it when either the home or the away team is behind, further suggesting that referees have a preference for treating both teams equally.