Changes

* If recognized, keep <math>\hat{y}^{a}</math> for yourself and distribute the remainder to <math>m(\delta,n) </math> other members, where <math>1-n\geq m \geq (n-1)</math>. <math>1>m/2\geq 1/2</math>. * If recognized as an amender who is part of the aforementioned group of <math>m</math>: Move to a vote. * If recognized as an amender who is NOT part of the aforementioned group of <math>m</math>: Make a proposal to keep <math>\hat{y}^{a}</math> for yourself and distribute the remainder to <math>m(\delta,n)</math> other members -- including all those who are not in the first proposer's majority. Recognizer is never included because he is too expensive to pay off. * If you're a voter: Same rules as above. Vote for whichever pays you higher, and for the amendement if you're indifferent.  In equilibrium, the game procedes sequentially until nature randomly selects an amender who is in the coalition of the original proposer, when the proposal is approved. ====Proof ==== Let <math>y^{a}</math> be what proposer (j) keeps for self m members have continuation values offered to <math>V_{j}^{m}(y^{j})</math> be the value of the game to <math>j</math> when <math>y^{j}</math> is on the floor.  Note: Stationarity implies that <math>y^{j\ast}</math> will be the same in all recognized rounds. Note: N members, member 1 is recognized, member j is excluded member recognized, member  A: <math>\frac{1-\hat{y}^{a}}{m}\geq \delta V_{i}(y^{i})</math>. This means that the amendment <math>\max V_{i}^{m\ast}(y_{i}). </math> ==== Substantive conclusions ====* Possibility of delay. * Size of winning coalition can be larger than the minimum winning coalition. * <math>\frac{\partial m}{\partial \delta}<0</math>, and (separately) <math>\frac{\partial m}{\partial n}<0</math>(Rui says this latter one needs to be checked). * More equal because proposer spreads wealth more broadly.