Reaching Consensus Under a Deadline
Marina Bannikova, Lihi Dery, Svetlana Obraztsova, Zinovi Rabinovich, Jeffrey S. Rosenschein
TL;DR
This paper addresses reaching a group-wide consensus under a fixed deadline in settings where a default outcome is costly if no consensus is reached. It introduces Consensus Under a Deadline (CUD), a time-bounded iterative voting framework built on plurality with a threshold, supplemented by a default option and a deadline $\\tau$. The authors prove termination guarantees, derive additive Price of Anarchy bounds $PoA^+$, and provide extensive simulations that compare lazy and proactive voters, plus a CUD-based user study examining human vs. bot behavior. The findings show rapid convergence under realistic deadlines, generally small $PoA^+$, and notable benefits from using bots to reach higher-quality consensus, suggesting practical utility for deadline-driven organizational decisions and guiding extensions to broader scoring rules and agent delegation.
Abstract
Committee decisions are complicated by a deadline, e.g., the next start of a budget, or the beginning of a semester. In committee hiring decisions, it may be that if no candidate is supported by a strong majority, the default is to hire no one - an option that may cost dearly. As a result, committee members might prefer to agree on a reasonable, if not necessarily the best, candidate, to avoid unfilled positions. In this paper, we propose a model for the above scenario - Consensus Under a Deadline (CUD)- based on a time-bounded iterative voting process. We provide convergence guarantees and an analysis of the quality of the final decision. An extensive experimental study demonstrates more subtle features of CUDs, e.g., the difference between two simple types of committee member behavior, lazy vs.~proactive voters. Finally, a user study examines the differences between the behavior of rational voting bots and real voters, concluding that it may often be best to have bots play on the voters' behalf.