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The role of 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. ===Open Rule: Infinite session===<i>Editor: What about open rule finite session? Doesn't seem to be in the majority paper anywhere</i>. Open rule : Member is recognized and makes a proposal. Another member is recognized and can either move the previous question to a vote agains the status quo (rather than say unaminitywhich is zero for everyone) , or offer an alterative proposal to be voted against the previous proposal. If first proposal ends: Game over. If amendment wins -- another recognition round to offer proposal. The equilibrium strategy is covered in as follows: * If recognized, keep <math>\hat{y}^{a}</math> for yourself and distribute the paperremainder 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 case 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 stationary 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 an openself 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-rule\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.
Baron Ferejohn (1989) - Bargaining In Legislatures (view source)
Revision as of 19:14, 29 September 2020
, 19:14, 29 September 2020no edit summary
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|Has article title=Bargaining In Legislatures
|Has author=Baron Ferejohn
|Has year=1989
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*This page is referenced in [[BPP Field Exam Papers]]
However, this is unsatisfactory as it requires a complete history at all points (which is unrealistic if <math>\delta\,</math> is a reelection probability and new members can't know the history), and if a member were indifferent between enforcing and not, it is only weakly credible.
====Equilibrium RestrictionWith equilibrium restriction: Stationary Equilibrium Exactly the same as Closed Rule +Finite Horizon ====
To restrict the equilibrium space the paper considers '''Stationary Equilibrium'''.
<b>This is the same as closed-rule, finite session.</b>
Note that we have minimum winning coalitions, a value of the game <math>v_{i}===In 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 Paper===game is equal across all players.
