Before revision:  Furthermore, we present an efficient post-computation which , when paired with an approximation algorithm for maximin support , returns a new solution that a) preserves the approximation guarantee, b) satisfies the PJRproperty , and c) can be efficiently verified to satisfy PJR by an untrusting third party. Besides being of independent theoretical interest, our results enable the network to run an efficient validator election protocol that simultaneously achieves the PJR property and a constant-factor approximation for maximin support, thus offering strong theoretical guarantees on decentralization and security .
After revision:  Furthermore, we present an efficient post-computation which , when paired with an approximation algorithm for maximin support , returns a new solution that a) preserves the approximation guarantee, b) satisfies the PJRproperty , and c) can be efficiently verified to satisfy PJR . Our work is motivated by an application on blockchains that implement Nominated Proof-of-Stake (NPoS), where the community must elect a committee of validators to participate in its consensus protocol, and where fighting overrepresentation protects the system against attacks by an adversarial minority. Our election rule enables a validator election protocol that simultaneously achieves the PJR property and a constant-factor approximation for maximin support, thus offering strong theoretical guarantees on decentralization and security .