Changes

Note that we have minimum winning coalitions, a value of the game <math>v_{i}=1/n</math> proposal power equal to <math>x_{i}^{i}\geq 1/2 \geq \delta/n</math>. We have fairness because the value of the game is equal across all players.

Comparitive statics around proposal power: <math>x_{i}^{i}=1-\frac{\delta(n-1)}{2n}</math>. Note that patience reduces proposal power: <math>\frac{\partial x_{i}^{i}}{\partial\delta}=-\frac{n-1}{2n}<0</math>. Larger legislatures reduce proposal power:<math>\frac{\partial x_{i}^{i}}{\partial n}=-\frac{\delta}{2}+\frac{\delta(n-1)}{2n^{2}}=\frac{-\delta(n^{2}-n-1}{2n^{2}}<0</math>.

Difference in equality between proposer and coalition members=<math>\Delta=1-\frac{\delta(n-1)}{2n}-\frac{\delta}{n}</math>. <math>\frac{\partial \Delta}{\partial n}=\frac{\delta}{n}>0</math>. Coalition members also worse off as legislature size gets bigger.