View source for Baron, D. (1991), Bargaining Majoritarian Incentives, Pork Barrel Programs and Procedural Control

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[http://www.edegan.com/wiki/images/3/3f/Baron_%281991%29_-_Bargaining_Majoritarian_Incentives_Pork_Barrel_Programs_and_Procedural_Control.pdf Full-text PDF]

Note similarity to Baron and Ferejohn (1989): 
* Multi-lateral, 
* Bargaining
* Divide the "pie" (not the dollar)
* Non-cooperative
* Use of stationary equilibrium
* Divisibility and transferability of benefits. 

Looks at cases where B<T (benefits less than costs). 

Programs are characterized by B, T (total benefits and total taxes). P (programs) are characterized by <math>B/T, P\in[0,\inf]</math>. 
* <math>B: \{b|b_{i}>0, i=1,2,3,...,n, \sum b_{i}\leq B\}</math>
* T is always distributed equally among n districts so <math>t_{i}=T/n</math>. 
* Proposals are fully characterized by <math>b\in B</math> and net benefits are <math>z_{i}=b_{i}-T/n</math>. 
* Payoffs are discounted: <math>\delta^{\tau}z_{i}=U_{i}(z,\tau)</math>. Extensive form is the same as before for closed rule.

Structure of game: 
* P is drawn (which implies a ratio of B/T). 
* A random legislator is chosen to distribute B. Note that per the above, all T are distributed equally no matter what. 
* Legislators vote against the status quo, in which everyone gets nothing and is taxed nothing. 

Stationarity implies members are paid their continuation value in equilibrium in exchange for their votes. <math>\delta v(g,t), \forall t\in\Tau</math> 

Proposition 1: With closed rule the stationary EQM has the following properties: 
* (i) Inefficient pork barrel programs will be adopted. Inefficiency is increasing in <math>n</math>
* (ii) Possible set of programs is increasing in <math>\delta</math>. 
* (iiii) coalitions are minimum winning. 
* (iv) There is proposal power. 
* (v) 1st proposal is always selected.


Derivation of proposition 1: 
* <math>z_{i}>\delta\bar{V}</math>. <math> b_{i}-T/n\geq\bar{V} \implies b_{i}\geq T/n+\delta\bar{V}</math>. 
* Proposal will be accepted if <math>(n-1)/2</math> members vote yes, therefore proposals will be of the form of: Keep <math>B-\frac{n-1}{2}(\frac{T}{n+\delta\bar{V}}</math>. Give <math>T/n +\delta\bar{V}</math> to <math>(n-1)/2</math> others, and the rest zero. 
* <math>\bar{V}=P(selected)E[Value of being selected|p^{\ast})+P(not selected)(value of not being selected)</math>. 
* <math>\bar{V}=\frac{1}{n}(B-\frac{n-1}{2}(T/n+\delta\bar{V}))+\frac{n-1}{n}(\frac{1}{2}(T/n+\delta\bar{V}) +\frac{1}{2}(-T/n))</math>. Solve for <math>\bar{V}=\frac{B-T}{n}</math>. 
* Offer is <math>T/n+\frac{\delta(B-T)}{n}=\frac{\delta B-(1-\delta)T}{n}</math>. 

... unfinished. Sorry.

Open rule: 
* Never get universalism w/ inefficient program. 
* Inefficent program minimum winning coalition (MWC). 
* Amendments shift power to voters with inefficiency. 
* Set of proposals which are adopted is smaller.