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

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Has bibtex key
Has article title Bargaining Majoritarian Incentives, Pork Barrel Programs and Procedural Control
Has author Baron, D.
Has year 1991
In journal
In volume
In number
Has pages
Has publisher
©, 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.