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 generalise 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 Phragm\'{e}n 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，在该模型中，需在特定可行性约束条件下选择若干候选人。该模型概括了委员会选举（仅对候选人数量有单一约束）、带有多样性约束的各种选举、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。投票的关键特性在于其公平性——不仅针对个体选民，也要公平对待在投票议题上持相似观点的选民群体；换言之，选举结果应成比例地反映选民的偏好。我们在该广义模型中制定了比例性公理。这些公理无需预定义选民群体；相反，我们确保每个偏好足够一致的选民子集的意见都能按其规模比例得到充分考虑。我们的公理推广了已知可满足的最强公理（针对更具体模型）。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序列规则，以及稳定价格性概念——适配至我们的广义模型。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。