Democracy as a Process: A Dynamic Arrow/GS with Endogenous Preference Revision

Kellogg (2023) argues that Arrow’s static setup misses Dewey’s insight: democratic preferences are habit-laden and change through conflict and problem-solving. We formalize an iterative model where (i) a mechanism selects outcomes each round, (ii) voters update preferences via social learning, deliberation signals, or outcome feedback, and (iii) the process converges (or not). We propose dynamic axioms—e.g., dynamic IIA (irrelevant alternatives don’t alter long-run limits), dynamic monotonicity, and convergence fairness. Leveraging Livson & Prokopenko’s (2025) equivalence between Arrow and contradictory preference cycles, we model cycles as transient phenomena in the induced preference dynamics and seek conditions (e.g., contractive updates, bounded confidence) under which cycles die out and a non-dictatorial limit ranking emerges. We further incorporate epistemic accuracy via Jury Theorem insights (Dietrich & Spiekermann, 2021), studying when information aggregation improves over time. This reframes impossibility: Arrow/GS bite at the snapshot level, but at the process level we can prove possibility theorems for mechanisms that guide societies to stable, non-dictatorial equilibria. The contribution is a rigorous dynamic theory that unites deliberation, conflict, and aggregation—making precise a long-standing philosophical critique with mathematical results.

References:

1. Democracy and Conflict: Kenneth Arrow’s Impossibility Theorem and John Dewey’s Pragmatism. F. Kellogg (2023). Social Science Research Network.
2. Arrow's Impossibility Theorem as a Generalisation of Condorcet's Paradox. Ori Livson, M. Prokopenko (2025).
3. Jury Theorems May 2021 forthcoming in : Stanford Encyclopedia of Philosophy. Franz Dietrich Kai Spiekermann (2021).