Assigning an unpleasant task without payment

How should a group of people decide to allocate a task that has to be done but is not adequately rewarded? This paper finds an optimal mechanism for the private provision of a public service in an environment without monetary transfers. All members of the group have the same cost of providing the service, but some individuals are better suited for the task than others. The optimal mechanism is a threshold rule that assigns the task randomly among volunteers if enough volunteers come forward, and otherwise assigns the task among the non-volunteers.