  Proportional representation (PR) is often discussed in voting settings as a
major desideratum. For the past century or so, it is common both in practice
and in the academic literature to jump to single transferable vote (STV) as the
solution for achieving PR. Some of the most prominent electoral reform
movements around the globe are pushing for the adoption of STV. It has been
termed a major open problem to design a voting rule that satisfies the same PR
properties as STV and better monotonicity properties. In this paper, we first
present a taxonomy of proportional representation axioms for general weak order
preferences, some of which generalise and strengthen previously introduced
concepts. We then present a rule called Expanding Approvals Rule (EAR) that
satisfies properties stronger than the central PR axiom satisfied by STV, can
handle indifferences in a convenient and computationally efficient manner, and
also satisfies better candidate monotonicity properties. In view of this, our
proposed rule seems to be a compelling solution for achieving proportional
representation in voting settings.
