This appendix derives the results of the legislative bargaining model presented in Chapter 2. I deal first with the general case, before then finding equilibria for specific configurations of parameters (Examples 1 to 4). In any subgame perfect equilibrium of the legislative bargaining game, each player will maximize his or her utility subject to the constraint of offering another player at least his or her continuation value, which is the expected utility from voting against a proposal and continuing to the next round. In an equilibrium where player A offers to player B, player C offers to player B, and player B offers to player A, the three continuation constraints A1A3 would need to be satisfied. These equations represent the continuation constraints for player A’s offer to B, player C’s offer to B, and player B’s offer to A, respectively. For each of the examples considered in this paper, there is a subgame perfect equilibrium with this pattern of offers. In many cases there is also a subgame perfect equilibrium with the following sequence of offers: A→B, C→B, B→C, but as described in the text, in most cases the proposals in this equilibrium are identical to those where C offers to A. Player B makes the same proposal regardless of whether he or she offers to player A or player C, and so I do not consider this possibility here.