Before revision:  The second objective, called maximin support, is to maximize the minimum amount of vote support assigned to any elected validator. We argue that the former objective aligns with the notion of decentralization, while the latter aligns with the security level of the consensus protocol. 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.
After revision:  We provide an inapproximability result for this objective, and propose a new election rule inspired in Phragmen's methods that achieves a) a constant-factor approximable, as we present several approximation algorithms for it, and prove a matching hardness result.