Rawls (1971) argued that individuals choosing institutions from behind the veil of ignorance would unanimously agree on institutions that maximized the imputations of the least advantaged persons in the post‐choice social outcome. Critics have argued that the Rawlsian contract requires risk averse individuals. Our paper focuses on the contractual element inherent in constitutional choice when individuals have differing subjective estimates of the working properties of different institutions. We show that in genuinely Rawlsian contractual settings there may exist a general bias toward the selection of institutions that embody maximin solutions without the assumption of risk aversio