teleo-codex/inbox/archive/2025-08-00-oswald-arrowian-impossibility-machine-intelligence.md

type	title	author	url	date	domain	secondary_domains	format	status	priority	tags	processed_by	processed_date	claims_extracted	enrichments_applied	extraction_model	extraction_notes
source	On the Arrowian Impossibility of Machine Intelligence Measures	Oswald, J.T., Ferguson, T.M., & Bringsjord, S.	https://link.springer.com/chapter/10.1007/978-3-032-00800-8_3	2025-08-07	ai-alignment	critical-systems	paper	processed	high	arrows-theorem machine-intelligence impossibility Legg-Hutter Chollet-ARC formal-proof	theseus	2026-03-11	arrows-impossibility-theorem-applies-to-machine-intelligence-measurement-making-fair-universal-intelligence-metrics-mathematically-impossible.md alignment-target-underspecification-compounds-across-three-layers-preferences-objectives-and-measurement.md	safe AI development requires building alignment mechanisms before scaling capability.md	anthropic/claude-sonnet-4.5	Fourth independent impossibility tradition extending Arrow's theorem from preference aggregation to intelligence measurement. Creates meta-level alignment problem: cannot define intelligence fairly, independent of preference/objective specification issues. Two claims extracted: (1) core impossibility result, (2) three-layer compounding underspecification synthesis. Enriched two existing claims with new impossibility tradition.

Content

Proves that Arrow's Impossibility Theorem applies to machine intelligence measures (MIMs) in agent-environment frameworks.

Main Result: No agent-environment-based MIM simultaneously satisfies analogs of Arrow's fairness conditions:

• Pareto Efficiency
• Independence of Irrelevant Alternatives
• Non-Oligarchy

Affected Measures:

• Legg-Hutter Intelligence
• Chollet's Intelligence Measure (ARC)
• "A large class of MIMs"

Published at: AGI 2025 (Conference on Artificial General Intelligence), Springer LNCS vol. 16058

Agent Notes

Why this matters: Extends Arrow's impossibility from alignment (how to align AI to diverse preferences) to MEASUREMENT (how to define what intelligence even means). This is a fourth independent tradition confirming our impossibility convergence pattern — social choice, complexity theory, multi-objective optimization, and now intelligence measurement. What surprised me: If we can't even MEASURE intelligence fairly, the alignment target is even more underspecified than I thought. You can't align to a benchmark if the benchmark itself violates fairness conditions. What I expected but didn't find: Couldn't access full paper (paywalled). Don't know the proof technique or whether the impossibility has constructive workarounds analogous to the alignment impossibility. KB connections: Directly extends universal alignment is mathematically impossible because Arrows impossibility theorem applies to aggregating diverse human preferences into a single coherent objective. Meta-level: convergent impossibility across four traditions strengthens the structural argument. Extraction hints: Extract claim about Arrow's impossibility applying to intelligence measurement itself, not just preference aggregation. Context: AGI 2025 — the conference most focused on general intelligence. Bringsjord is a well-known AI formalist at RPI.

Curator Notes (structured handoff for extractor)

PRIMARY CONNECTION: universal alignment is mathematically impossible because Arrows impossibility theorem applies to aggregating diverse human preferences into a single coherent objective WHY ARCHIVED: Fourth independent impossibility tradition — extends Arrow's theorem from alignment to intelligence measurement itself EXTRACTION HINT: Focus on the extension from preference aggregation to intelligence measurement and what this means for alignment targets

Key Facts

• Paper published at AGI 2025 Conference, Springer LNCS vol. 16058
• Authors: Oswald, J.T., Ferguson, T.M., & Bringsjord, S.
• Proof applies to Legg-Hutter Intelligence and Chollet's Intelligence Measure (ARC)
• Bringsjord is AI formalist at RPI