Changes

We now have an application of Baron & Ferejohn (1989) - [http://www.edegan.com/wiki/index.php/Baron_Ferejohn_%281989%29_-_Bargaining_In_Legislatures#Closed_Rule_-_Infinite_Sessions Closed Rule, Infinite Session]

From Proposition 2 in the paper, if: <math>1 > \delta > \frac{(n+2)}{2(n-1)} \mbox{ and } n \ge 5\,</math> then: Any distribution of benefits (<math>x\,</math>) may be supported.

This is accomplished through use of punishment strategies for any voter who attempts to deviate from the allocation (<math>x\,</math>), as discussed at length on pp1189-1191. Such punishment strategies suffer from being at times only weakly credible, in that punishers may be indifferent to carrying out their threats, leading voters to anticipate that enforcement may occur with less than probability 1, and thus unraveling the equilibrium. Baron and Ferejohn propose a refinement called Stationary Equilibrium, where members take the same actions in structurally equivalent subgames. Note that two sub-games are structurally equivalent iff: (i) the agenda is identical, (ii) set members who may be recognized (at the next node) are identical, (iii) the strategy sets of the members are identical.

*A recognized member proposes to give <math>\frac{\delta}{n}\,</math> to <math>\frac{(n-1)}{2}\,</math> randomly chosen other members, and to keep <math>1-\frac{\delta (n-1)}{2n}\,</math> for himself.

*Each member votes for any proposal that gives him at least <math>\frac{\delta}{n}\,</math>.

*The first vote receives a majority, so the legislature completes in one session.