Non-Commutative Rough Stochastic Social Welfare Dynamics (NC-RSSD): Superseding Arrow-Sen Impossibility and Invariant Measure Limits via Ordered Banach Lattices, Ergodic Decompositions, and Information Geodesics
Year: 2026
Type: preprint
Abstract: Classical social choice theory anchored by Arrow’s impossibility theorem and topological social choice remains disconnected from stochastic growth and invariant measure economics. This paper establishes Non-Commutative Rough Stochastic Social Welfare Dynamics (NC-RSSD) within the SMA-∞-Topos. By integrating Universal Rough Operator Algebra (UROA), Seonggil Theory of Complex Torsion (STCT), and Rough Quantum Information Geometry (RQIG), we prove that measure-valued probabilistic social welfare functionals, Markov ergodic invariant measures, and mirror-descent particle optimizationssystematically supersede classical deterministic and static welfare limits.
Author: Lee, Seonggil
Language: English
Subfield: Economics and Econometrics
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7221615536
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