How can small “special-interest groups” prevail over larger ones, as often seems to be the case?

An economics professor at Washington University with a specialty in game theory offers an economic model useful in analyzing situations in which two groups of different sizes vie over a particular policy outcome.

David K. Levine, writing in the European Journal of Political Economy, uses the case of farm subsidies, with the groups that favor subsidies (farmers) and those who typically oppose them (other taxpayers). The relative costs borne by individual participants in a struggle over subsidies — and the amounts they stand to gain or lose by the outcome — differ significantly.

I’m not going to waste a day lobbying to save a few bucks, but I would do so to get a few hundred thousand.

Individual farmers, obviously, have a great deal more at stake than the vastly greater numbers of taxpaying nonfarmers who pay for the subsidies. For that reason, the relative costs of participating in any lobbying activity are also disproportionate.

Levine explains it this way: “If it costs me the equivalent of a day [per year] of work to participate in a lobbying activity, then it is hardly worth it if I am not a farmer since my individual cost of farm subsidies is less than that. So why waste a day on lobbying that might save me half a day’s wages? It is quite different for a farmer who might have a third of a year’s income in farm subsidies. Then it is well worth a day spent lobbying. I’m not going to waste a day lobbying to save a few bucks, but I would do so to get a few hundred thousand. So many people each with a few bucks at stake don’t lobby, but the few with a few hundred thousand at stake do.”

The model, Levine suggests, is applicable to other situations, in which a small group for whom an outcome has a much larger impact can prevail over a larger one for whom an outcome has a smaller impact.

But there’s an interesting exception to this rule. When the policies being debated do not have clear financial and quantifiable implications for the adversaries — those involving civil rights, for example — the numerically larger groups tend to prevail.

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