A Resolution of the Regionalization Problem and Its Implications for Political Geography and Social Justice

Abstract

The purpose of this paper is to demonstrate that the set theoretic foundations of the usual formal representations of “region” and “boundary” do not lead to an adequate (or interesting) characterization of the nature of areal units and that by changing the underlying set theory (and formal language) it is possible to obtain richer descriptive and prescriptive models. In particular, it is argued that a shift from classical Boolean set theory to Zadeh's theory of fuzzy sets provides the basis for a subjective characterization of “region” in terms of a graded participation function. The argument is then extended to demonstrate that this alternative characterization of “region” leads directly to a form of weighted voting and that it therefore has important implications for the theory of political geography and social justice.

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