Empirically identify whether model-level and cross-model curvature coincide

Determine empirically whether real decision-makers' curvature parameters for model-level robustness and cross-model aggregation coincide, by separately identifying these two forms of ambiguity response in choice data.

Background

The theoretical results show that exact reduction to a single-layer entropic value requires matched curvature, \lambda=\xi, and that mismatched curvature cannot be repaired by changing the target curvature or baseline. However, the theorems do not establish whether actual decision-makers exhibit this equality.

The proposed unresolved empirical problem is to design choice data that separately identify responses to misspecification of a single model and responses to enlargement or contraction of the model set, allowing the matching restriction to be tested rather than imposed.

References

Theorem \ref{thm:mismatch-impossibility} settles the theory --- $\lambda\ne\xi$ admits no single-layer entropic value at any target curvature --- but is silent on whether real decision-makers' $\lambda$ and $\xi$ coincide.

— The Uniqueness of Exponential Second-Order Expected Utility  (2609.26552 - Hashidate, 22 Sep 2026) in Section 5, Concluding Remarks