Before revision:  We prove that the maximin support problem is constant-factor approximable, as we present several approximation algorithms for it, and prove a matching hardness result. 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.
After revision:  We prove that the maximin support problem is constant-factor approximation guarantee for the objective, and b) the PJR property. Furthermore, a structural property allows one to quickly verify that the winning committee satisfies the two aforementioned properties, even if the algorithm is executed by an untrusted party who only communicates the output. Finally, 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.