By and large, the implications of the model hold even when we relax the simplifying assumptions. Nonetheless, in this appendix, we consider some small changes in outcomes that follow from relaxing two of our assumptions: that (1) k (and c) < ∣M – Mi∣ and (2) M and Mi are equidistant from F.

Expanding k and c

First, as k grows beyond ∣M – Mi∣ (i.e., as the minority's consideration cost becomes larger than the distance between the majority and minority ideal points), more status quos to the left of M become part of the minority no-offer zone, meaning that the majority party does not have to “defend” them with preemptive offers that reduce majority utility. Figure A.1 shows an example of this result. Here, k has grown, pushing the edges of the minority no-offer zone well beyond M and Mi. Under our normal assumptions, the status quo in this example – which is to the extreme side of M – would have been moved right by M, leapfrogging his ideal point with a proposal at NOL (see Figure 3.6a). However, with the expansion of k, the status quo in Figure A.1 will remain unchanged, as Mi can no longer make a proposal that will improve her policy utility enough to offset the consideration cost. Thus, M can simply leave the status quo where it is, avoiding paying a consideration cost himself to keep policy from leaving his side of the space.