  We study an axiomatic framework for anonymized risk sharing. In contrast to
traditional risk sharing settings, our framework requires no information on
preferences, identities, private operations and realized losses from the
individual agents, and thereby it is useful for modeling risk sharing in
decentralized systems. Four axioms natural in such a framework -- actuarial
fairness, risk fairness, risk anonymity, and operational anonymity -- are put
forward and discussed. We establish the remarkable fact that the four axioms
characterizes the conditional mean risk sharing rule, revealing the unique and
prominent role of this popular risk sharing rule among all others in relevant
applications of anonymized risk sharing. Several other properties and their
relations to the four axioms are studied, as well as their implications in
rationalizing the design of some sharing mechanisms in practice.
