In this reply, I will focus on the implications of Montero and Vidal-Puga's finding, acknowledging that their result is correct. Thus, what follows should not be interpreted as a defense of the Proposition 2 of Morelli 1999, but as a clarification of the impact of this correction for the demand bargaining research agenda as a whole.
AGENDA SETTING AND POLICY COMPROMISE
The main motivation for my 1999 paper was to provide a simple model of legislators' strategic interaction when they derive utility from both private goods and common policy decisions. The previous literature had focused either on the divide-the-dollar purely distributive bargaining problem or on policy bargaining when legislators care exclusively about a one-dimensional policy space. Moreover, no one had explored whether the identity of the agenda setter and the order of play have similar or different effects on the various possible dimensions on which legislators bargain. The simple result obtained for the case of symmetric players (one vote per legislator) is that the identity of the agenda setter matters exclusively for the distributive dimension, whereas the policy outcome is not affected. This insight obviously does not depend on whether the proportionality result of Proposition 2 extends to weighted voting, because in any committee in which pork barrel projects and policies are negotiated in Congress, each voter has just one vote. In a nutshell, the case of β > 0 and one vote per legislator is the most realistic case for legislative bargaining applications, and the counterexample provided in the note does not refer to this relevant case.
BARGAINING AMONG LEGISLATORS VERSUS BARGAINING AMONG PARTIES
In American politics many scholars would agree that the relevant negotiating unit is the individual legislator, because party loyalty is not often relevant in the crafting of bills that include both resource distribution and law and policy reforms. The counterexample provided by Montero and Vidal-Puga has implications only for the cases in which it is reasonable to believe that the relevant negotiating unit is the party, which is more often the case in the negotiation of a government coalition in a parliamentary system. The proportionality result does extend to homogeneous games in which negotiating parties hold different voting weight, when the order of play is fixed and decreasing in the weights (a case supported by Diermeier and Merlo's [2004] empirical findings) and in the opposite extreme game form in which the next mover is always random from the perspective of the current mover, as in Frechette, Kagel, and Morelli (2005). Moreover, as Montero and Vidal-Puga recall, the proportionality result for weighted voting was also obtained in Morelli and Montero 2003 in its cooperative and noncooperative form. Hence, although the specific game form of my 1999 paper does not correctly extend the proportionality result to the case of negotiating parties, there are several modifications and variations on that game form that yield that result. So the demand bargaining approach in general should not receive a judgment in terms of its applicability to party politics on the basis of this counterexample.
THE DEMAND BARGAINING SET
When Montero and I wrote the axiomatic characterization of the Demand Bargaining Set (DBS) and established the proportionality outcome for weighted proper and strong games in that setting, we tried to establish a formal connection between Proposition 2 in my 1999 paper and the cooperative result of the DBS, but we realized that the proportional payoff division outcome was not unique. For this reason the noncooperative implementation of the DBS that we derived differed from the game form of my 1999 paper. The counterexample provided by Montero and Vidal-Puga clarifies nicely why that specific game form couldn't be used to implement the DBS.

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