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| Auteur principal: | |
|---|---|
| Format: | Recurso digital |
| Langue: | anglais |
| Publié: |
Zenodo
2026
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| Sujets: | |
| Accès en ligne: | https://doi.org/10.5281/zenodo.18156054 |
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Table des matières:
- <p>Classical social choice theory is organized around “no-go” results: Arrow’s impossibility<br>theorem and Condorcet cycles show that no ordinal aggregation rule can universally convert<br>individual rankings into a coherent transitive social ordering while satisfying minimal fairness<br>axioms. This paper pivots from the static existence question to a dynamic stability question.<br>We treat paradoxes as regimes of a stochastic dynamical system.<br><br>Our first contribution is a measurement layer that replaces an often-undefined social ranking<br>with an observable state variable: the ordinal-profile distribution p over ballot types or joint<br>ordinal profiles. Majorization (equivalently Lorenz order) supplies a label-free concentration<br>order on p, and Shannon ordinal majorization entropy (OME) supplies a scalar potential that is<br>ordinally invariant and exactly decomposable across subgroups. We provide full proofs of Lorenz<br>consistency, decomposability, and a characterization theorem identifying Shannon entropy as the<br>unique continuous Lorenz-monotone refinement-decomposable index (up to positive scale).<br><br>Our second contribution is a dynamical layer based on Dynamic Inequality Equilibrium (DIE):<br>we map political dynamics into a two-dimensional phase space Φ = (M, D) where D is Lorenz<br>drift (an inequality-velocity statistic) and M is rank mobility (a micro-turbulence statistic). We<br>prove that a persistent Condorcet cycle is a churning equilibrium: macro-stationary (D = 0) but<br>micro-volatile (M is order one).<br><br>Our third contribution is a mechanism design result. We formalize a constitutional circuit<br>breaker as an affine reinjection (restart) update pt+1 = (1 − ε)Ppt + εs, which is exactly the<br>PageRank/random-walk-with-restart operator. A contraction theorem guarantees convergence<br>to a unique stationary distribution for any ε > 0, damping persistent cycling without pretending<br>to “solve” Arrow.</p>