Consider a mechanism for the binary public good provision problem that is dominant

strategy incentive compatible (DSIC), ex-post individually rational (EPIR), and ex-post

budget balanced (EPBB). Suppose this mechanism has the additional property that the

utility from participating in the mechanism to the lowest types is zero for all agents.

Such a mechanism must be of a threshold form, in which there is a fixed threshold for

each agent such that the public good is not provided if there is an agent with a value

below her threshold and is provided if all agents’ values exceed their respective threshold.

There are mechanism that are DSIC, EPIR, and EPBB that are not of the threshold

form. Mechanisms that maximize welfare subject to DSIC, EPIR, and EPBB must again

have the threshold form. Finally, mechanisms that are DSIC, EPIR, EPBB and that

furthermore satisfy the condition that there is at least one type profile in which all agents

can block the provision of the public good, also must be of the threshold form. As we

allow individuals’ values for the public good to be negative and positive, our results cover

examples including bilateral trade, bilateral wage negotiations, a seller selling to a group

of individuals (who then have joint ownership rights), and rezoning the use of land.