The highly stylized and abstract models of small-number interactions introduced at the end of Chapter 2 suggest the possible efficacy of constitutional constraints in reducing the size of the set of outcomes attainable under majority voting rules. By appropriate definition of the dimensions that describe the vector of outputs under collective action, the distinction between positions on and off the diagonals in the simple matrix illustrations facilitates precision in the classification of positions in accordance with the generality principle. 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. In the process we clarify the meaning of the distinction made between solutions on and off the diagonals. In this section we assume that all participants are identical in the sense that the public good is equally productive for all and that the supply of inputs to produce this good is equally costly. In Section C we examine the incentives for rent seeking under unconstrained and constrained majority rule. In Section D we drop the assumption of identical evaluation. Section E discusses the effect of the on-diagonal constraint on majority stability.