P 5 RACTITIONERS and political scientists alike have long recognized that legislative decisions are often determined by the strategic behavior of legislators and the procedures of a legislature. Almost every text on the American legislative process discusses how the voting order, the voting procedures, and other legislative procedures can affect the final nature of legislation. While offering insight into the importance of the voting process and the process of strategic behavior, much of the early writing on these topics was primarily descriptive. In recent years a new body of literature on voting processes and strategic behavior in legislatures has developed which is based upon social choice theory.' This literature has addressed a number of topics: coalition formation and stability, vote trading, and legislative procedures such as the voting process. That portion which deals with voting procedures primarily derives from the work of Black (1971) and Farquharson (1969). Black examined how any voting body would select a single proposal out of a series of alternatives for a given voting procedure. Farquharson demonstrated how, for the threevoter three-alternative case, the selection of one final alternative would depend upon the voting process, the voting order, and whether voters were employing sincere or sophisticated strategies. In a recent work, Miller (1977) used a graph-theoretic approach to extend Farquharson's analysis to the general case in which a voting decision must be reached out of a set of n proposals. While a number of legislative voting procedures have been discussed in the literature, such analyses have not taken into account one central characteristic of the American legislative process: bicameralism. The literature has emphasized that the so-called amendment procedure most closely approximates the voting procedure in American legislatures. Under the amendment procedure two proposals are paired for a majority vote, the defeated proposal is eliminated with the winning proposal now being paired against a third proposal. This process continues until one proposal remains. Since the votes are being taken in one chamber, the sincere and sophisticated outcomes as determined by Farquharson and Miller are dependent upon the legislators' preferences among the alternatives presented in the one chamber, the voting order, and the willingness of voters to vote strategically. Actions or anticipated actions outside of the chamber are assumed to have no impact upon the votes or outcome within the chamber.