The Topology of Quantum Theory and Social Choice

Based on the axioms of quantum theory, we identify a class topological singularities that encode fundamental difference between classic and probability, explain theory’s puzzles phenomena in simple mathematical terms so they are no longer ‘quantum paradoxes’. The provide also new experimental insights predictions presented this article establish surprising connection physical social sciences. key is topology spaces events frameworks postulated by these axioms. These quite different from their counterparts probability mathematically interference experiments existence several or ‘violation unicity’ characterizes physics. They entanglement, Heisenberg uncertainty principle, order dependence observations, conjunction fallacy geometric such as Pancharatnam–Berry phases. Somewhat surprisingly, find same impossibility selecting preference among individual preferences: which Arrow’s choice paradox: foundations theory therefore equivalent. We necessary sufficient conditions how to restrict avoid recover unicity, avoiding possible paradoxes; restriction shown resolution theorem Chichilnisky.