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Key to the analysis of Majority Rule institutions is the notion of '''pivotal legislators''', and the trade-off between '''costs and benefits ''' for the lobbyist(s). Building a majority is inherently costly, and so majority building naturally focuses on the legislators who are easiest to recruit. Legislators who would vote to support a policy absent of lobbying efforts are not provided with additional (costly) resources.

How competition among interest groups should be modelled (to reflect reality) depends three four main factors: the sequence or simultaneity of offers, whether lobbyists can make more than one offer or not (i.e. the number of rounds), the nature of the offers (i.e. point or menu offers), and whether only one or more than one offer can be accepted. The bullets below give the appropriate model for some of these instances:*Simultaneous, 1 round, point offers, 1 accepted: [http://en.wikipedia.org/wiki/Colonel_Blotto Colonel Blotto] type games