Since we know already that the model by Bolton and Ockenfels (2000) and the pure reciprocity models fail to capture third-party punishment, we concentrate on the other models. The model by Levine predicts no difference between secondand thirdparty punishment, because a given low transfer to the recipient reveals the dictator's selfish or spiteful preferences regardless of whether the recipient (i.e., the second party) or the third party can punish. Thus, Levine's model cannot explain the treatment differences. This contrasts with the Fehr–Schmidt and Falk–Fischbacher models, which predict that third parties will punish less than second parties.

XREF: Connects to the experimental approach of comparing second-party and third-party punishment treatments to discriminate between competing theoretical models.

Ernst Fehr, Third-Party Punishment and …, loc. 103