We both think you did wrong -- How agreement shapes and is shaped by indirect reciprocity

Humans judge each other's actions, which at least partly functions to detect and deter cheating and to enable helpfulness in an indirect reciprocity fashion. However, most forms of judging do not only concern the action itself, but also the moral status of the receiving individual (to deter cheating it must be morally acceptable to withhold help from cheaters). This is a problem, when not everybody agrees who is good and who is bad. Although it has been widely acknowledged that disagreement may exist and that it can be detrimental for indirect reciprocity, the details of this crucial feature of moral judgments have never been studied in depth. We show, that even when everybody assesses individually (aka privately), some moral judgement systems (aka norms) can lead to high levels of agreement. We give a detailed account of the mechanisms which cause it and we show how to predict agreement analytically without requiring agent-based simulations, and for any observation rate. Finally, we show that agreement may increase or decrease reputations and therefore how much helpfulness (aka cooperation) occurs.