• WMKn) < 0, which is enough to imply CnK < 0 and dK/df < 0, but is insufficient to predict the sign of CnT. If buying off a more concentrated opposition is sufficiently important to render MTn ' 0, then dT/df < 0. 2. A parametric shift in the opposition function, h. This yields precisely the same result as a shift in support (the vector of the relevant cross-partials is the same as the right-hand side of equation (19)), and this symmetry between the effects of support and opposition is perhaps one of the chief insights of Stigler's model. If a more effective political support technology (a rise in f) induces a more numerous winning group, a more effective opposition technology must lead the regulator to permit a larger group to escape taxation as well. Some losers will then be made winners when there is a rise in opposition. This is better stated in the reverse. The difficulty of translating a tax into political opposition ( a low h) induces the regulator to tax the many and thus to concentrate his favors on a few. Hence the filtering of information through the noise of a political process that forces consideration of many programs simultaneously acts unambiguously, as Stigler intuited, to restrict the size of the winning group. This filtering must be done by both winners and losers, and this makes it simultaneously unattractive to spread the benefits and attractive to spread the losses over large numbers. 3. A parametric shift in the cost of organizing a group for political support. Stigler argues that the cost of organizing support (for example, the cost of overcoming the "free rider" problem) also restricts n. However, on closer inspection, this is not obvious. Consider a rise in the C(n) of (3) which, for simplicity, leaves marginal cost unchanged. Then, focusing only on dn/dC, we obtain
This will be ambiguous for reasons apart from ambiguity about CTn. Stigler's argument focuses essentially on Mnc, which is indeed negative and induces a smaller n. However, because of diminishing returns to per capita gains, a rise in C will lead to an offsetting decrease in K (Mc < 0). On balance, this fall in K requires a rise in n (CnK < 0). That is, if K is reduced, restoring optimum effectiveness of lobbying and education efforts requires concentration of these efforts on a smaller group of losers. To obtain Stigler's result, one must conjecture that this sort of secondary effect is outweighed by the initial impulse to concentrate gains to offset the effect of increased organization costs. It is well to summarize the results of this formalization of Stigler's model: 1. With a few ambiguities, the thrust of imperfect information about both the gains and losses of regulatory decisions and of costs of organizing for political favors is to restrict the size of the winning group. 2. But this winning group will not obtain even a gross gain through political action as great as is within the power of the political process to grant it.