Online (Budgeted) Social Choice

We consider a classic social choice problem in an online setting. In each round, a decision maker observes a single agent’s preferences over a set of m candidates, and must choose whether to irrevocably add a candidate to a selection set of limited cardinality k. Each agent’s (positional) score depends on the candidates in the set when he arrives, and the decisionmaker’s goal is to maximize average (over all agents) score.