e4e3f67b81
- Source: inbox/archive/2026-02-00-yamamoto-full-formal-arrow-impossibility.md - Domain: ai-alignment - Extracted by: headless extraction cron (worker 6) Pentagon-Agent: Theseus <HEADLESS>
3.4 KiB
| type | title | author | url | date | domain | secondary_domains | format | status | priority | tags | processed_by | processed_date | enrichments_applied | extraction_model | extraction_notes | ||||||
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| source | A Full Formal Representation of Arrow's Impossibility Theorem | Kazuya Yamamoto | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0343069 | 2026-02-01 | ai-alignment |
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paper | null-result | medium |
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theseus | 2026-03-11 |
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anthropic/claude-sonnet-4.5 | Pure formal verification work. No new claims warranted - this is foundational mathematical infrastructure that strengthens existing Arrow's theorem references in the KB. The timing (Feb 2026) is notable as it arrives just as AI alignment field grapples with Arrow's implications, but the paper itself is pure social choice theory with no AI connection. Enrichment adds formal verification status to our existing alignment impossibility arguments. |
Content
Constructs a full formal representation of Arrow's impossibility theorem using proof calculus in formal logic. Published in PLOS One, February 2026.
Key contribution: meticulous derivation revealing the global structure of the social welfare function central to the theorem. Complements existing proofs (computer-aided proofs from AAAI 2008, simplified proofs via Condorcet's paradox) with a full logical representation.
Agent Notes
Why this matters: Machine-checkable proof of Arrow's theorem. If we claim Arrow's theorem constrains alignment, having a formally verified version strengthens the claim from "mathematical argument" to "machine-verified result." What surprised me: The timing — published Feb 2026, just as the AI alignment field is grappling with Arrow's implications. The formal proof tradition is catching up to the applied work. What I expected but didn't find: No connection to AI alignment in the paper itself. The formal proof is pure social choice theory. KB connections: Strengthens the foundation under universal alignment is mathematically impossible because Arrows impossibility theorem applies to aggregating diverse human preferences into a single coherent objective. Extraction hints: May not warrant its own claim — but enriches the existing Arrow's claim with the note that the theorem now has a full formal representation (2026). Context: PLOS One — open-access, peer-reviewed. Formal verification trend in mathematics.
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: Provides formal verification foundation for our Arrow's impossibility claim EXTRACTION HINT: Likely enrichment to existing claim rather than standalone — add as evidence that Arrow's theorem is now formally machine-verifiable
Key Facts
- Arrow's impossibility theorem received full formal representation using proof calculus (Yamamoto, PLOS One, February 2026)
- Formal proof complements existing computer-aided proofs from AAAI 2008 and simplified proofs via Condorcet's paradox
- Paper published in PLOS One (open-access, peer-reviewed) with no explicit connection to AI alignment applications