Difference between revisions of "Baron, D. (1991), Bargaining Majoritarian Incentives, Pork Barrel Programs and Procedural Control"
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imported>Bo (New page: Note similarity to Baron and Ferejohn (1989): * Multi-lateral, * Bargaining * Divide the "pie" (not the dollar) * Non-cooperative * Use of stationary equilibrium * Divisibility and trans...) |
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+ | {{Article | ||
+ | |Has page=Baron, D. (1991), Bargaining Majoritarian Incentives, Pork Barrel Programs and Procedural Control | ||
+ | |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= | ||
+ | }} | ||
+ | [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): | Note similarity to Baron and Ferejohn (1989): | ||
* Multi-lateral, | * Multi-lateral, | ||
Line 10: | Line 24: | ||
Programs are characterized by B, T (total benefits and total taxes). P (programs) are characterized by <math>B/T, P\in[0,\inf]</math>. | 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>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>. | * 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>. | * 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)< | + | * 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. |
Latest revision as of 19:14, 29 September 2020
Article | |
---|---|
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 | |
© edegan.com, 2016 |
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.