The bargain begins with the work of assembling the bargainers. Smoke can reach a thousand households before any two of them have spoken, and a promise to reduce it needs someone able to speak for those who breathe it. The households differ in their injuries, incomes and willingness to wait. Some will soon leave; some have nowhere else to go. The owner of the chimney can sign one agreement. The people downwind must decide who may sign theirs, who will pay for the negotiation and how today's promise will bind tomorrow's conduct. A gain from agreement can exist throughout this interval without an agreement existing. The multitude has to become a party before the theorem's bargain can begin.
The work of making an agreement can consume the gain that would justify it. Coase's account of transaction costs includes discovering whom to approach, communicating terms, negotiating, writing the agreement and inspecting performance. These are uses of scarce resources. An hour spent at the meeting is an hour unavailable for something else, even if no one submits a bill. Suppose a cleaner process provides benefits worth a hundred and costs eighty to install and operate. Twenty remains to cover the arrangement. If finding the parties, settling their shares and enforcing the promise consumes thirty, this route costs more than it creates. The environmental improvement remains valuable. Its net advantage depends on the means by which it can actually be secured.
A necessary signature creates a further obstacle even when signing itself is cheap. Imagine three adjoining plots, each worth thirty to its present owner, and a project that requires all three. The assembled site is worth a hundred and twenty after the project's other costs have been paid. There are thirty of possible gains from agreement. If each owner demands forty-five, the demands add to a hundred and thirty-five and cannot all be met. An owner asking for more may expect the others to accept less, since each knows that the project needs every plot. The value created by assembly becomes a prize to divide, and the attempt to divide it can prevent the assembly.
The incompatible demands identify a possibility of holdout, not a verdict on an owner's refusal. The figures assume that thirty is each owner's true reservation amount. A home may in fact be worth more to its occupant than a comparable sale would reveal; a refusal may protect an interest the project has failed to measure. Even under the stated valuations, the example does not prove that forty-five will be each owner's final demand. Thirty-five apiece would give each owner five above the reservation amount and leave the assembler fifteen. The joint gain permits agreement without dictating its terms. To call every refusal a holdout would convert the analyst's estimate into the very right to decide that the parties are contesting.
The free rider occupies a different position: the improvement can reach him without his permission or contribution. A household whose assent is unnecessary to a smoke-reduction agreement may still breathe the cleaner air after its neighbors have paid. This separates the benefit of the improvement from the benefit of joining the effort to obtain it. Samuelson's collective-consumption problem concerns this common enjoyment and the incentive to conceal how much it is worth. The holdout possesses a permission others require; the free rider can receive a benefit while declining to help provide it. A large negotiation can encounter both, but their remedies need not be the same. Buying a necessary permission and inducing a contribution purchase different things.
A conditional promise can sometimes turn waiting into assurance. Let a filter cost twelve and give each of three households a benefit worth five. Each can pledge a nonnegative amount; installation occurs if the pledges reach twelve, and all money is returned otherwise. Suppose the households care only about their own benefit and payment, know the terms and change their pledges separately. With no pledges, no household can profit by moving alone. Less than twelve buys nothing; twelve buys a benefit worth five. Yet a pledge of four by each is also stable. Each then gains one. Reducing its pledge would defeat installation and leave that household with zero, while increasing it would only raise its payment. The same benefits and costs admit both failure and provision.
The assurance changes the risk of contributing, but it does not choose the successful outcome by itself. A contribution that will be refunded if the others decline is easier to contemplate than one lost regardless, yet the all-zero outcome in the example remains an equilibrium. Coordination still has to supply a reason to expect the other pledges. A credible organizer, a visible sequence of commitments or a shared convention can change those expectations; each must be assessed in its particular setting. Nor can assurances manufacture a joint gain where none exists. If each household valued the filter at three, the total benefit would be nine against a cost of twelve. The obstacle would then be the stipulated value of the project, even if every participant trusted every other completely.
Representation can reduce the number of bargains while creating a new bargain inside the group. An association can gather contributions, appoint an expert and authorize one negotiator. Its members must still decide what that negotiator may concede. A resident facing serious harm may want an injunction; another may prefer a payment; a tenant may value protection now while an owner values the effect on the property later. A single signature can conceal these differences as easily as resolve them. The association's rules about membership, voting, disclosure and challenge therefore belong in the analysis of its cost. They determine whether the promise represents the people whose loss gives the negotiation its point.
Common control offers another route where separate bargains are costly. An owner of several adjoining uses can compare their combined returns without negotiating every adjustment among separate proprietors. Coase treated organization within the firm as one alternative to market transactions, while emphasizing that internal administration also has costs. Bringing activities under one authority can make an adjustment easier and information harder to obtain. The result depends on what that authority knows, what it can direct and what incentives govern its decisions. A boundary that is economical for one cluster of uses may be unwieldy for a whole city. The number of signatures is one part of the institutional problem, not its complete measure.
The state can reach participants whom a voluntary association cannot gather. A levy can finance a common measure; an emissions rule can bind sources that would decline a contract. That capacity matters, especially where benefits are dispersed and the decision must endure. It carries its own tasks of measurement, representation and enforcement, along with the possibility of mistakes and unequal influence. Coase's comparison consequently includes government without treating it as either a costless cure or an intrusion that must always fail. The relevant question is what a specified public arrangement can achieve, at what cost, compared with the arrangements actually available. A failed negotiation supplies evidence of an obstacle; it does not complete that comparison.
The initial allocation of rights acquires practical force when a bargain cannot revise it. It determines who must approach whom, whose permission is needed and which condition persists while everyone waits. Even where a monetary sum identifies a joint gain, the parties' ability to finance a payment can differ sharply. Distribution and legitimacy therefore survive the efficiency calculation. Counting the costs of agreement does not answer who should have been given the starting claim, or whether the terms of an eventual settlement respect those affected. The account becomes more useful when those questions remain visible instead of being folded into the unexplained assertion that bargaining is either free or impossible.
A possible gain must survive the work of making it common.
The question left by the multitude is therefore a question about institutions capable of acting for it. A contract, an association, common control and a public rule can each change what the parties can accomplish, while changing what they must spend and whom they must trust. Their comparison begins with the obstacle actually present: a missing contribution, a necessary permission, uncertain performance or disagreement about the division of a gain. Naming the obstacle makes the choice more concrete. The next plate asks what happens when the gain itself has no ready number—when the parties can be brought together, but the value they must compare is still in shadow. The argument remains open.