Experimental Design Details
A multiple of four participants take part in the experiment. They are randomly allocated to groups of two, which are numbered consecutively from one to N. In each group, one participant is called X and the other Y. All participants receive a fixed participation fee and—during the experiment—points that are worth money. Importantly, no player makes any decision regarding their own group. Instead, groups decide for players in other groups along a circle, i.e., Group 1 decides for Group 2, Group 2 decides for Group 3, ..., and Group N decides for Group 1. Players are being told so before learning any of the details of the experiment. Each player makes two decisions, each between 20 different options. One decision is about the trade-off between equality and efficiency, the other is about the trade-off between equality and equity, i.e., attribution of responsibility. For the Efficiency Procedure, players are allocated to roles A and B, where A profits from efficiency and B from equality. For the Equity Procedure, roles are denoted by a and b, where role a profits from equity and role b from equality. The names of roles are only used for the formal exposition and do not appear in the instructions. The same is also true for the two procedures. Their order is randomized on the player-level, and they are simply referred to by their order of appearance. Any two players in any two adjoining groups share exactly one role.
This structure ensures that no player is ever confronted with another player belonging to a "double out-group" in terms of their roles and thereby alleviates concerns about in-group–out-group bias. Players first learn about types in their own groups and potential payoff consequences for themselves before being informed about the details of the succeeding group, for which they decide. At the end of the experiment, one of the two procedures is selected at random and the respective decision of one player from either all odd- or all even-numbered groups is implemented. These players themselves receive 1000 points, i.e., the maximum that can be attained in the experiment.