Proportionality in General Social Choice Models

We consider a model where a number of candidates need to be selected subject to certain feasibility constraints. The model generalises committee elections (where there is a single constraint on the number of candidates that need to be selected), various elections with diversity constraints, the model of public decisions (where there is a set of independent issues, and the constraints say that we need to pick a single decision for each issue) and the model of collective scheduling. The voters express their preferences over the candidates through voting, and the goal is to select the outcome that would be arguable fair. We mainly focus on group fairness understood as proportionality. We formulate axioms of proportionality in this general model. Our axioms are always satisfiable, and generalise the strongest known satisfiable axioms for the more specific models. This is a working paper.