Proportional Rankings

We extend the principle of proportional representation to rankings: given approval preferences, we aim to generate aggregate rankings so that cohesive groups of voters are represented proportionally in each initial segment of the ranking. Such rankings are desirable in situations where initial segments of different lengths may be relevant, e.g., in recommender systems, for hiring decisions, or for the presentation of competing proposals on a liquid democracy platform. We define what it means for rankings to be proportional, provide bounds for well-known aggregation rules, and experimentally evaluate the performance of these rules.