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In this short note, we describe an approval-based committee selection rule that admits a polynomial-time algorithm and satisfies the Extended Justified Representation (EJR) axiom. This rule is based on approximately maximizing the PAV score, by means of local search. Our proof strategy is to show that this rule provides almost optimal average satisfaction to all cohesive groups of voters, and that high average satisfaction for cohesive groups implies extended justified representation.
The goal of multi-winner elections is to choose a fixed-size committee based on voters preferences. An important concern in this setting is representation: large groups of voters with cohesive preferences should be adequately represented by the elect
We investigate issues related to two hard problems related to voting, the optimal weighted lobbying problem and the winner problem for Dodgson elections. Regarding the former, Christian et al. [CFRS06] showed that optimal lobbying is intractable in t
In the late 19th century, Swedish mathematician Lars Edvard Phragm{e}n proposed a load-balancing approach for selecting committees based on approval ballots. We consider three committee voting rules resulting from this approach: two optimization vari
An average-time game is played on the infinite graph of configurations of a finite timed automaton. The two players, Min and Max, construct an infinite run of the automaton by taking turns to perform a timed transition. Player Min wants to minimise t
We describe the practical implementation of an average polynomial-time algorithm for counting points on superelliptic curves defined over $mathbb Q$ that is substantially faster than previous approaches. Our algorithm takes as input a superelliptic c