Proportionality for Constrained Public Decisions

We study situations where a group of voters need to take a collective decision over a number of public issues, with the goal of getting a result that reflects the voters' opinions in a proportional manner. Our focus is on interconnected public decisions, where the outcome on one or more issues has repercussions on the acceptance or rejection of other issues in the agenda. We show that the adaptation of classical justified-representation axioms to this enriched setting are always satisfiable only for restricted classes of public agendas. We adapt well-known proportional decision rules to take the structure of the public agenda into account, and we show that they match justified-representation properties in approximation on a class of expressive constraints. We also identify another path to achieving proportionality on interconnected issues via an adaptation of the notion of priceability.