Fully Proportional Representation as Resource Allocation:   Approximability Results
  We model Monroe's and Chamberlin and Courant's multiwinner voting systems as a certain resource allocation problem. We show that for many restricted variants of this problem, under standard complexity-theoretic assumptions, there are no constant-factor approximation algorithms. Yet, we also show cases where good approximation algorithms exist (briefly put, these variants correspond to optimizing total voter satisfaction under Borda scores, within Monroe's and Chamberlin and Courant's voting systems). 
Piotr Skowron, Piotr Faliszewski, Arkadii Slinko
cs.GT cs.MA