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The Informational Basis of Social Choice under Model Uncertainty: Reframing Arrow's Impossibility in the Presence of Strategic Obfuscation

Authors: Fathi, Kevin;

The Informational Basis of Social Choice under Model Uncertainty: Reframing Arrow's Impossibility in the Presence of Strategic Obfuscation

Abstract

Arrow's Impossibility Theorem is conventionally read as a logical conflict among appealing axioms given an ordinal preference profile.This paper studies an upstream fragility: when agents face uncertainty not merely about states of the world, but about the operative model (understood as an interpretive frame that changes payoff mappings), expressed preferences become endogenous and can be strategically shaped. We formalize \emph{spurious unanimity} on a target pair $(x,y)$: a public history that leaves posterior ambiguity over frames yet generates the same unanimous \emph{expressed} comparison on $(x,y)$ even though the unanimous \emph{informed} comparison reverses across frames. Our core contribution is an informational reframing of independence restrictions. We represent any restriction on what a procedure may use when ranking $(x,y)$ as an admissible information $\sigma$-field $\mathcal{G}_{xy}\subseteq\sigma(h,R^e)$. We then prove a sharp general Bayes-risk floor: among all rules measurable with respect to $\mathcal{G}_{xy}$, the minimal misranking probability equals the conditional Bayes error induced by the restricted posterior. Epistemic Independence of Irrelevant Alternatives becomes a special case. We close a standard criticism of wedge arguments by proving a genericity theorem: under spurious unanimity, any witness alternative whose comparisons have a frame-dependent distribution induces a diagnostic wedge with positive probability. Wedge exposure is therefore equivalent to the presence of frame-linked evidence outside $\{x,y\}$. We make witness alternatives operational by introducing canonical likelihood-ratio triangulation and its finite-sample error exponent: under conditional independence and identical distribution of witness evidence given the frame, the Bayes-optimal frame classifier based on witness likelihood ratios has error probability at most $\exp(-n C_z)$, where $C_z$ is the Chernoff information. We also connect geometric diagnostics to decision performance. The paper's original geometric diagnostic $\Delta_z$ is defined as an integrated generalized-Lorenz distance between \emph{truncated} witness scores and is preserved as a secondary visualization tool. For decision calibration we introduce a canonical nontruncated diagnostic $W_z$, the Wasserstein-1 distance between full log-likelihood ratio cross-sectional distributions. Under bounded log-likelihood ratios, we prove the conservative calibration bound $C_z\ge W_z^2/(8\kappa^2)$; since $\Delta_z\le W_z$, this yields $C_z\ge \Delta_z^2/(8\kappa^2)$. Finally, we formalize audit-augmented procedures and prove that the optimal audit trigger is a threshold rule: audit if and only if the expected loss from acting without audit exceeds the audit cost. We then add a minimal strategic obfuscation game and prove an equilibrium discipline result: a rational obfuscator moderates manipulation up to the audit boundary, making audits self-enforcing in equilibrium. This paper is positioned as the downstream aggregation and governance layer for upstream strategic-ambiguity environments.In particular, it complements the Bateson Game framework for strategic frame ambiguity in signaling games by translating frame uncertainty into axioms and risk bounds for social choice and mechanism design.

Keywords

strategic obfuscation, spurious unanimity, social choice under model uncertainty, boundary intercept test, Arrow's Impossibility Theorem, Epistemic IIA, Bayesian persuasion, audit-augmented social choice, diagnostic wedges

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average