Budgeted Social Choice: A Framework for Multiple Recommendations in Consensus Decision Making

We develop a new framework for social choice problems, budgeted social choice, in which a limited number of alternatives can be recommended/prescribed to a population of agents. This limit is determined by some form of budget. Such problems naturally arise in a variety of contexts. Our model is general, spanning the continuum from pure consensus decisions (i.e., standard social choice) to fully personalized recommendation. Our results show that standard rank aggregation rules are not appropriate for such tasks and that good solutions typically involve picking diverse alternatives tailored to different agent types. The corresponding optimization problems are shown to be NP-complete, but we develop fast greedy algorithms with some theoretical guarantees. Experimental results on real-world datasets (APA election and sushi) show some interesting patterns and the prove the effectiveness of our greedy algorithms.