The Multiple-Volunteers Principle for Assigning Unpleasant and Pleasant Tasks

We present a class of simple transfer-free rules that are very effective tools for assigning an unpleasant task among a group of agents: agents decide simultaneously whether or not to “volunteer”; if the number of volunteers exceeds a threshold number, the task is assigned to a volunteer; if the number is below the threshold, the task is assigned to a non-volunteer. In a setting in which agents have non-trivial preferences over who performs the task, such a threshold rule is utilitarian optimal across all binary-action rules. In a large group, the first best is reached approximately via a threshold rule with a large threshold. Threshold rules have a robust-improvement property: any rule with a non-extreme threshold always has an equilibrium that yields a strict interim Pareto improvement over a random task assignment. We show that assigning the task to a non-volunteer rather than randomly among all agents if the threshold is not reached is crucial for this result. Such a uniformly-random default, however, is utilitarian optimal if ex-post participation constraints are imposed, and is still good enough to approximate the first best in a large population. The results can be adapted to the problem of assigning a pleasant task.