Two-Envelope Problems in Lithic Moral-Weight Estimation.

Abstract

When credences about per-entity moral weight are themselves probability distributions, the "expected" welfare comparison across populations becomes sensitive to framing in ways that resemble the classical two-envelope paradox. We document the structure of this dependence in the lithic case, show that different framings yield estimates that differ by many orders of magnitude, and propose three partial mitigations. We do not claim to resolve the paradox.

Key claims

• The choice of unit (per-kg, per-rock, per-mole-of-mineral) materially changes which population dominates in expected value. None of these choices is privileged on first-principles grounds.
• Our headline RAPD figure is reported under one such framing, made explicit in this paper. Under at least two alternative framings, the figure is unbounded; under at least one, it is modest.
• The honest reading is that the case for lithic welfare research is robust under most framings, but the magnitude of the cost-effectiveness claim is not.

Proposed mitigations

1. Report results under multiple framings simultaneously, with the framing-dependence visible to readers.
2. Treat large divergences across framings as evidence of model fragility, not of cause-area dominance.
3. Apply a framing-sensitivity discount when communicating headline figures to non-specialist audiences.

We do not consider these mitigations adequate. We consider them the best that can presently be said. The full derivation behind the 4.2-million-rocks-per-dollar figure, and how it shifts under each alternative framing, appears in the body of the paper.

Pre-print available on request via contact. Peer review pending. See also our 2 May 2026 release note.