From weakest-link to best-shot: The voluntary provision of public goods

Abstract

It has traditionally been assumed that the socially available amount X of a public good is the simple sum of the separate amounts x _i produced by the i = 1, ..., I members of the community. But there are many other possibilities of practical importance. Among them are: (i) Weakest-link rule, where the socially available amount is the minimum of the quantities individually provided, and (ii) Best-shot rule, where the socially available amount is the maximum of the individual quantities. The former tends to arise in linear situations, where each individual has a veto on the total to be provided (e.g., if each is responsible for one link of a chain); the latter tends to arise when there is a single prize of overwhelming importance for the community, with any individual's effort having a chance of securing the prize.

In comparison with the standard Summation formula of ordinary public-good theory, it is shown that underprovision of the public good tends to considerably moderated when the Weakest-link function is applicable, but aggravated when the Best-shot function is applicable. In time of disaster, where the survival of the community may depend upon each person's doing his duty, the conditions for applicability of the Weakest-link rule are approximated. This circumstance explains the historical observation that disaster conditions tend to elicit an extraordinary amount of unselfish behavior.