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Chapter 6 Legislative Bargaining Binary voting agendas are well-defined mechanisms, describing how a committee arrives at a collective choice from a given set of alternatives. And it is clear from Chapter 4, where we study the strategic implications of these mechanisms, that institutional details matter: even with a fixed preference profile, distinct collective choices can arise from small variations in the choice procedure. Not all committee decision-making, however, is governed by such well-defined procedures and it is implausible to look for an exhaustive description of how institutional variation maps into policy variation. While there are almost always rules and regulations covering some dimensions of any choice problem, for instance concerning who has the right to speak at any time or when final votes of legislative approval are required, there is much that is only loosely governed by formal procedure. Bargaining theory offers a quite general framework that plausibly captures at least some important aspects common to informal committee procedures. To the extent that this is the case, therefore, results derived from political bargaining models provide relatively institution-free insights into a wide class of collective choice processes. The chapter is concerned with developing a particular noncooperative theory of legislative bargaining. Although others can readily be imagined, the underlying structure of the theory below has a claim to being canonical : it is predicated on an intuitive and natural abstraction for any sort of noncooperative model of bargaining; it reflects fundamental tradeoffs across both time and participants; and it is extremely flexible, permitting considerable latitude in applying the basic framework to many distinct problems and environments. The key idea for the theory is perhaps most easily appreciated by first considering two-person bargaining, say between a buyer 193 194 CHAPTER 6. LEGISLATIVE BARGAINING and a seller of some indivisible good such as a car. A plausible approximation for how the bargaining might evolve is that the buyer first makes an offer of a purchase price to the seller who then either accepts or rejects the offer; if she accepts then the transaction is completed and the bargaining over; on the other hand, should she reject the opening offer, the seller has the opportunity to make a counter-offer which the buyer in turn is free to accept or reject, making a second offer, and so on until such time that a mutually agreeable price is reached. In general, individuals are impatient and so the later the bargaining reaches closure, the less the participants value the outcome; there is then a premium on obtaining an agreement earlier and such impatience endows the more patient individual with some strategic advantage . The objective of the theory is to explain the bargainers' optimal sequences of proposals, counter-proposals, acceptance criteria and so forth, so predicting the price at which the transaction is completed as a function of the parameters of the model (e.g. the seller's willingness to sell, the buyer's willingness to buy, the individuals' discount factors, etc). The legislative bargaining theory developed below amounts to an extension of the two-person sequential bargaining model to more general n-person bargaining over political decisions. The complication in making the extension is that typically not all n people are needed for a proposal to be accepted ; under majority rule with n odd, for instance, a proposer needs only (n - 1)/2 others to have his proposal accepted. The implications of this fact for legislative policy making are far-reaching and the subject of the chapter. 6.1 A basic framework In this section we sketch the abstract sequential bargaining procedure for committee decision-making, common to the various environments considered in the remainder of the chapter. A committee N = {I, ... , n} has to reach a collective choice from a nonempty compact, convex set of feasible alternatives, X C ~k, with status quo alternative xO E X. Every committee member i E N is assumed to have preferences over X, representable by a continuous concave utility function Ui : X --+ ~; that is, the underlying preference profile p lies in R~8 (section 1.1). Decision making takes place as follows. There is an infinite number of discrete periods, indexed t = 1,2, ..., each of which in principle includes a proposal stage and voting stage. At the start of the first period, some committee member is chosen randomly to offer a proposal x E X; once the proposal is made all committee members simultaneously vote over whether 6.1. A BASIC FRAMEWORK 195 to...

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