We consider a voting 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 decisions needs to be taken on a number of independent issues), and the model of collective scheduling. A critical property of voting is that it should be fair -- not only to individuals but also to groups of voters with similar opinions on the subject of the vote; in other words, the outcome of an election should proportionally reflect the voters' preferences. We formulate axioms of proportionality in this general model. Our axioms do not require predefining groups of voters; to the contrary, we ensure that the opinion of every subset of voters whose preferences are cohesive-enough are taken into account to the extent that is proportional to the size of the subset. Our axioms are always satisfiable, and generalize the strongest known satisfiable axioms for the more specific models. We explain how to adapt two prominent committee election rules, Proportional Approval Voting (PAV) and Phragmen Sequential Rule, as well as the concept of stable-priceability to our general model. The two rules satisfy our proportionality axioms if and only if the feasibility constraints are matroids.

翻译：我们考虑一个投票模型，其中需要在满足特定可行性约束的条件下选择若干候选人。该模型概括了委员会选举（仅需对候选人数目施加单一约束）、各类具有多样性约束的选举、公共决策模型（需对多个独立议题做出决策）以及集体调度模型。投票的关键属性在于其公平性——不仅对个体选民公平，更要对在投票议题上持有相似观点的选民群体公平；换言之，选举结果应比例化地反映选民偏好。我们在此一般性模型中提出了比例性公理体系。这些公理无需预先定义选民群体；相反，我们确保每个偏好具有足够凝聚力的选民子集的意见，都能按其规模比例得到充分考虑。我们的公理始终可满足，且推广了现有特定模型中最强的可满足公理。我们阐释了如何将两种著名的委员会选举规则——比例批准投票（PAV）与Phragmén序贯规则，以及稳定可定价性概念——适配至该一般性模型。当且仅当可行性约束为拟阵时，这两种规则满足我们的比例性公理。