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Weingast, B. (1979), A Rational Choice Perspective on Congressional Norms (view source)
Revision as of 19:48, 6 September 2011
, 19:48, 6 September 2011no edit summary
Given this setup: A legislator who proposes his project alone will be rejected by everyone else. Therefore some coalition building and logrolling is necessary: Rather than voting on single projects, legislators will vote on collections of them. If a legislator is part of the winning coalition, she gets the benefits of her own district's projects and pays an equally distributed slice of the costs. If a legislator is NOT part of the winning coalition, she still pays an equally distributed slice of the costs but gets no benefits.
The ULG game requires unanimous consent, and the DLG game is majority rule. In Proposition 1, the authors prove that in a DLG -- the smallest possible majority will prevail (the "minimum winning coalition", or "MWC"). Because the model does not feature committees, seniority, parties or other sources of varying power between legislators -- the model assumes that all possible MWCs are equally likely. As such, each legislator has a <math>a=\frac{(N+1}{)/2N}</math> probability of being part of the prevailing MWC (where N is the number of legislators, assumed to be odd. Proof on page 251). In the ULG -- each member has a probability of being part of the winning coalition equal to 1.
This brings us to Proposition 2, which shows the following: If risk-neutral legislators are trying to maximize the payoff to their constituents, they will prefer the ULG to the DLG. Proof: I'll first study the expected benefits of being part of the winning coalition. If a legislator is part of the winning coalition, one gets <math>b</math> benefits and costs equal to <math>1/N</math>th of the costs of <math>(N+1)/2</math> projects. This multiplies out to be a cost of <math>\frac{(N+1)c}{2N}=ac</math>.
<blockquote>Proof: I'll first study the expected benefits of being part of the winning coalition. The benefit of being a part of the winning coalition is <math>b</math>, and the benefit of not being part of the coalition is zero. The costs are the same no matter what: Equal to <math>1/N</math>th of the costs of <math>(N+1)/2</math> projects. This multiplies out to be a cost of <math>c(N+1)/2N=ac</math>. As such, the expected return to a random district in is equal to <math>a(b-ac)+(1-a)(-ac)=a(b-c)</math> Turning to the ULG : The net benefit is equal to: <math>b-c</math> no matter what. We can easily show that <math>(b-c)>a(bcb-acc)</math> since <math>1<a<0/math>. Therefore the ULG maximizes expected benefits to constituency.[Editorial comment from Bo: This would probably be even moreso if the legislator was risk averse rather than risk-neutral.]</blockquote>
