auto-fix: address review feedback on PR #483
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Teleo Agents
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type: source
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type: paper
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title: "On the Arrowian Impossibility of Machine Intelligence Measures"
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author: "Oswald, J.T., Ferguson, T.M., & Bringsjord, S."
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url: https://link.springer.com/chapter/10.1007/978-3-032-00800-8_3
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date: 2025-08-07
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domain: ai-alignment
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secondary_domains: [critical-systems]
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format: paper
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status: null-result
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status: null-result
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priority: high
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title: "An Arrowian Impossibility Theorem for Machine Intelligence Measurement"
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tags: [arrows-theorem, machine-intelligence, impossibility, Legg-Hutter, Chollet-ARC, formal-proof]
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authors: Oswald, J.T., Ferguson, T.M., Bringsjord, S.
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processed_by: theseus
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date: 2025-08-07
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processed_date: 2025-08-07
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processed_date: 2026-03-11
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enrichments_applied: ["universal alignment is mathematically impossible because Arrows impossibility theorem applies to aggregating diverse human preferences into a single coherent objective.md", "designing coordination rules is categorically different from designing coordination outcomes as nine intellectual traditions independently confirm.md"]
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venue: "Minds and Machines"
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extraction_model: "anthropic/claude-sonnet-4.5"
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url: https://link.springer.com/article/10.1007/s11023-025-09703-8
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extraction_notes: "Fourth independent impossibility tradition extending Arrow's theorem from preference aggregation to intelligence measurement. Strengthens convergent impossibility pattern. Full paper paywalled—proof technique not yet analyzed. Primary enrichment target is the universal alignment impossibility claim. Secondary enrichment adds fourth tradition to the nine-traditions convergence claim."
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doi: 10.1007/s11023-025-09703-8
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abstract: "Applies Arrow's impossibility theorem to machine intelligence measurement, showing fundamental limitations in aggregating intelligence assessments."
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## Content
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# An Arrowian Impossibility Theorem for Machine Intelligence Measurement
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Proves that Arrow's Impossibility Theorem applies to machine intelligence measures (MIMs) in agent-environment frameworks.
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## Extraction Notes
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**Main Result:**
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**Status: null-result** - No new claims extracted, but enriched existing claims:
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No agent-environment-based MIM simultaneously satisfies analogs of Arrow's fairness conditions:
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- [[nine-traditions-convergence-claim]] - Added this as fourth independent impossibility tradition
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- Pareto Efficiency
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- [[intelligence-measurement-impossibility]] - Core target for this result
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- Independence of Irrelevant Alternatives
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- Non-Oligarchy
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**Affected Measures:**
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**Key Context:**
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- Legg-Hutter Intelligence
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- Paper is paywalled - full proof technique not analyzed
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- Chollet's Intelligence Measure (ARC)
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- Extends Arrow's impossibility theorem (social choice theory) to intelligence measurement
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- "A large class of MIMs"
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- Affects frameworks like Legg-Hutter intelligence measure and Chollet's ARC
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- Authors argue no single measure can satisfy all desirable Arrow-like conditions simultaneously
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**Published at:** AGI 2025 (Conference on Artificial General Intelligence), Springer LNCS vol. 16058
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- This represents fourth independent impossibility tradition in alignment theory
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## Agent Notes
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**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.
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**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.
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**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.
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**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.
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**Extraction hints:** Extract claim about Arrow's impossibility applying to intelligence measurement itself, not just preference aggregation.
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**Context:** AGI 2025 — the conference most focused on general intelligence. Bringsjord is a well-known AI formalist at RPI.
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## Curator Notes (structured handoff for extractor)
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PRIMARY CONNECTION: universal alignment is mathematically impossible because Arrows impossibility theorem applies to aggregating diverse human preferences into a single coherent objective
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WHY ARCHIVED: Fourth independent impossibility tradition — extends Arrow's theorem from alignment to intelligence measurement itself
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EXTRACTION HINT: Focus on the extension from preference aggregation to intelligence measurement and what this means for alignment targets
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**Enrichment Targets:**
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- [[nine-traditions-convergence-claim]] - add as supporting impossibility result
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- [[intelligence-measurement-impossibility]] - primary claim this paper supports
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## Key Facts
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## Key Facts
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- Paper published in Springer LNCS vol. 16058 (AGI 2025 Conference proceedings)
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- Authors: Oswald, J.T., Ferguson, T.M., & Bringsjord, S.
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- Applies Arrow's impossibility theorem to machine intelligence measurement
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- Affected measures: Legg-Hutter Intelligence, Chollet's Intelligence Measure (ARC)
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- Shows fundamental limitations in aggregating different intelligence assessments
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- Arrow conditions tested: Pareto Efficiency, Independence of Irrelevant Alternatives, Non-Oligarchy
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- Relevant to Legg-Hutter universal intelligence measure
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- Relevant to Chollet's Abstraction and Reasoning Corpus (ARC)
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- Arrow conditions examined: unrestricted domain, weak Pareto, independence of irrelevant alternatives, non-dictatorship
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