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

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© edegan.com, 2016

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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}\gt 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}\gt \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.