Driven by an ever-growing number of studies that explore the effectiveness of institutional mechanisms meant to mitigate cooperation problems, recent years have seen an increasing interest in the endogenous implementation of these institutions. In this paper, we test within a unified framework how the process of institution formation is affected by three key aspects of natural environments: i) heterogeneity among players in the benefits of cooperation, ii) (a)symmetry in players' institutional obligations, and iii) potential trade-offs between efficiency and equality in payoff allocations. We observe social preferences to be limiting the scope for institution formation. Inequality-averse players frequently object to institutions that fail to address differences in players' benefits from cooperation – even if rejecting the institution causes monetary losses to all players. Relating our findings to previous studies on institution formation, we discuss potential advantages and drawbacks of stipulating unanimous support for implementing institutions that foster cooperation.