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The property of proportional representation in approval-based committeeelections has appeared in the social choice literature for over a century, andis typically understood as avoiding the underrepresentation of minorities.However, we argue that the security of some distributed systems is directlylinked to the opposite goal of avoiding the overrepresentation of any minority,a goal not previously formalized that leads us to an optimization objectiveknown as maximin support. After providing a thorough analysis of thecomputational complexity of this objective, we propose a new efficient electionrule that simultaneously achieves a) a constant-factor approximation guaranteefor it, and b) the property of proportional justified representation (PJR) -one of the strongest forms of proportional representation. However, the moststriking feature of the new rule is that one can verify in linear time that thewinning committee satisfies the two aforementioned guarantees, even when thealgorithm is executed by an untrusted party who only communicates the output.As a result, the rule can be adapted into a verifiable computing scheme.Moreover, its verification procedure easily admits parallel processing forfurther efficiency.  Our work is motivated by an application on blockchain networks that implementNominated Proof-of-Stake, where the community elects a committee of validatorsto participate in the consensus protocol, and where preventingoverrepresentation protects the network against attacks by an adversarialminority. Our election rule enables a validator selection protocol with formalguarantees on security and proportionality, and its adaptation as a verifiablecomputing scheme with a parallelized verification proves to be key for itssuccessful implementation given the computationally limited nature of theblockchain architecture.

A verifiably secure and proportional committee election rule