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Theorems and Models in Political Theory: An Application to Pettit on Popular Control

Sean Ingham

2014
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Social Science Research Network
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particular those who see themselves as occupying the more "analytical" wing of the discipline, consider the careful de nition of terms and the construction of deductive arguments as an important part of their craft. It would be surprising if mathematics never had a useful role to play in political theory, given this understanding of the enterprise. This essay presents an example of how political theory can bene t from mathematics, i.e., formal de nitions and deductive reasoning. I begin in the
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... ng. I begin in the next section with observations on Phillip Pettit's recent account of popular control. These observations are the stu of "conventional" political theory-I claim he con ates two distinct conditions in his conception of popular control-and they neither require nor bene t (much) from formal constructions. But they raise questions that would be all but impossible to answer without formal de nitions and arguments. In section 3, I present formal de nitions that facilitate this inquiry. In section 4, the inquiry proceeds through increasingly denser thickets of logical complexity, culminating in a theorem that is similar in its underlying logical structure to theorems on preference-aggregation, like the famous theorems of Arrow or Gibbard and Satterthwaite: popular control, as Pettit models it, implies that either the government is sometimes perversely responsive to citizens' normative attitudes or there is a single citizen whose normative attitudes unilaterally x-in the manner of a "dictator"-government policy. The argument requires only elementary mathematical concepts, like that of a set and a function, so it is not a display of "sophisticated" mathematics per se. But with this quali cation, I hope it will illustrate the plausibility of Rawls's 2 suggestion. 2. Pettit (2013) o ers a novel republican theory and model of democracy. The theory consists of an account of popular control over government, which Pettit argues is necessary for non-domination and legitimacy. The model is meant to show how a certain kind of deliberative democracy could establish popular control. But the theory and model seem to operate with distinct interpretations of popular control. The theory sets up an ideal of popular control that is more stringent and demanding than the form of popular control that the model describes as feasible, or so I will argue.

doi:10.2139/ssrn.2536030
fatcat:jdcrqp46obdb7ai4sj2lo6k6me