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This never seems to appear in real life: Winning coalitions are often much larger than 50%. The paper's goal is to develop a formal model to explain these larger margins. The author achieves this by modeling the "informal rules" seen in Congress within the formal game theoretic setup. The author shows how legislative rules that lead to large majorities are better for legislators than rules that lead to smaller majorities -- thus suggesting how such rules could come about endogenously.

<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 district is equal to <math>a(b-ac)+(1-a)(-ac)=a(b-c)</math> </blockquote>

<blockquote>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(b-c)</math> since <math>1<a</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> From here the author studies the relaxation of the <math>b>c</math> assumption. * First he shows the conditions under which legislators will propose their project --assuming that all other legislators are proposing theirs. * Then the author discusses the notion that <math>b/c</math> is decreasing over time -- so that the "worthwhile" projects are used early in the game, and the bad ones will continue later. The author notes that at some point, pork is no longer rational for the legislators and voters. However, this happens sooner in the majority rule than the universal rule.