Arrow's Axioms and the Functional Structure of Democracy: A Reinterpretation Based on Feedback, Accountability, and Evolving Preference Spaces

This work offers a structural reinterpretation of Arrow’s impossibility theorem by demonstrating that the contradiction arises not from democracy itself but from Arrow’s assumption of a fixed and exogenous preference space. Building on the functional definition of democracy developed in Beyond Regulation and the measure-theoretic insights of Simpson’s Paradox Revisited, the paper shows that real democratic institutions operate as dynamic systems characterized by substantive negative feedback, genuine accountability, and the institutionalized creation of alternatives. These mechanisms imply evolving preference spaces, endogenous information structures, and iterative decision processes—features fundamentally incompatible with Arrow’s static axiomatic framework. By formalizing how preference spaces P_t change over time and explaining why IIA and fixed-preference assumptions cannot hold in systems with feedback and responsibility, the paper reframes Arrow’s theorem as a limitation of a particular formal model rather than a paradox of democratic governance. This reinterpretation provides a new foundation for understanding democracy as a dynamic, corrigible, and structurally adaptive institution.