32 lines
2.3 KiB
Markdown
32 lines
2.3 KiB
Markdown
---
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type: source
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title: "A Full Formal Representation of Arrow's Impossibility Theorem"
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author: "Kazuya Yamamoto"
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url: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0343069
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date: 2026-02-01
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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: unprocessed
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priority: medium
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tags: [arrows-theorem, formal-proof, proof-calculus, social-choice]
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---
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## Content
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Constructs a full formal representation of Arrow's impossibility theorem using proof calculus in formal logic. Published in PLOS One, February 2026.
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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.
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## Agent Notes
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**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."
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**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.
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**What I expected but didn't find:** No connection to AI alignment in the paper itself. The formal proof is pure social choice theory.
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**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]].
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**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).
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**Context:** PLOS One — open-access, peer-reviewed. Formal verification trend in mathematics.
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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: Provides formal verification foundation for our Arrow's impossibility claim
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EXTRACTION HINT: Likely enrichment to existing claim rather than standalone — add as evidence that Arrow's theorem is now formally machine-verifiable
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