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In the stylized models to be used further throughout the book, positions on the matrix diagonals embody symmetry or generality in the collectively imposed behavioral adjustments among the interacting parties; positions off the diagonal embody asymmetry or differential adjustments along the separate dimensions, thereby a violation of the generality criterion. Section A relates the matrix construction to the more familiar analyses of majority voting in conventional public choice theory. In Section B we extend the model to three parties, and we specify more carefully the elements of the matrix construction.

At this juncture, the ideal theory of politics as exchange may seem to offer little or no understanding or guidance for the institutional realities of collective action. The unanimity requirement may be dismissed, even as a benchmark criterion, once the difficulties of reaching agreement on the distribution of cost shares are fully acknowledged. And, even if these difficulties are deemed somehow surmountable, in some idealized sense, for collective action aimed at supplying commonly shared goods, they emerge in exacerbated form when welfare transfers are considered.

The extension of the analysis to allow for differences in the evaluation of the commonly shared good is clearly indicated. How many of the generalized results depend critically on the presumed identity in the separate evaluations? 4 suggests, the introduction of differences in orderings modifies the earlier result of neutrality of the decision rule even when constitutional restrictions allow for solutions only on the diagonal. Similarly, even within such constraints, the identity of the majority matters, along with the decision rule.