I’ve been meaning to do this for a while, but only now found the time. The following is a model of interest group lobbying as taken from “A Theory of Groups and Organizations”, the first chapter of “The Logic of Collective Action”, by Mancur Olson.
If economics is the field of inquiry (lest I say “science”) that studies how people apply scarce resources to satisfy their needs, and political science is the study of the determinants of how power and authority are deployed, then it must be that interest group theory fall within the prerogative of political economy.
Interest group theory is the specific line of enquiry considering the observed fact that groups organised a certain interest are able to deploy a substantial, and often dominant level of influence, not too seldomly decisive in the determination of political outcomes.
To my knowledge, while several considerations on this topic may have preceded those of Mancur Olson, his 1965 book is the seminal contribution of the field. Therefore, although I will also consider the contributions of Grossman and Helpman (here and here), Peltzman and Stigler, it is appropriate to begin at the beginning. Mancur Olson’s main contribution was to show that smaller, more cohesive groups, where a single individual will be able to shoulder a disproportionate share of the burden will be able to organise and cooperate more easily to provide a public good. The development of this model, described below, is significant to understand the power of interest groups in as much as the public good can be thought of as lobbying, or influencing, of decision makers on behalf of an entire sector. Among other things, it easily explains why employers, farmers and civil servants tend to be able to extract better political concessions than other workers .
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