A key solution for public good provision is the voluntary formation of institutions that commit players to cooperate. Such institutions generate inequality if some players decide not to participate but cannot be excluded from cooperation benefits. Prior research with small groups emphasizes the role of fairness concerns with positive effects on cooperation. We show that effects do not generalize to larger groups: if group size increases, groups are less willing to form institutions generating inequality. In contrast to smaller groups, however, this does not increase the number of participating players, thereby limiting the positive impact of institution formation on cooperation.