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We consider a committee voting setting in which each voter approves of asubset of candidates and based on the approvals, a target number of candidatesare to be selected. In particular we focus on the axiomatic property calledextended justified representation (EJR). Although a committee satisfying EJR isguaranteed to exist, the computational complexity of finding such a committeehas been an open problem and explicitly mentioned in multiple recent papers. Wesettle the complexity of finding a committee satisfying EJR by presenting apolynomial-time algorithm for the problem. Our algorithmic approach may beuseful for constructing other voting rules in multi-winner voting.

A Polynomial-time Algorithm to Achieve Extended Justified Representation