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theseus: enrich Arrow's impossibility claim with Yamamoto (2026) formal proof

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- What: Added Yamamoto (PLOS One, 2026-02) as evidence to the existing
  Arrow's impossibility claim in foundations/collective-intelligence/.
  Enriched body with paragraph on formal proof calculus representation
  and its implications. Updated source field and last_evaluated date.
  Marked archive source as processed.
- Why: Yamamoto provides the first full formal representation of Arrow's
  theorem in proof calculus (complementing AAAI 2008 computer-aided
  proof), revealing the global structure of the social welfare function.
  This upgrades the claim's evidentiary basis from mathematical argument
  to formally derivable result, strengthening the alignment impossibility
  implication.
- Connections: Enrichment only — no standalone claim warranted per
  curator notes. Relates to formal verification theme in
  domains/ai-alignment/ (machine-checked correctness).

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foundations/collective-intelligence/universal alignment is mathematically impossible because Arrows impossibility theorem applies to aggregating diverse human preferences into a single coherent objective.md
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@ -3,9 +3,10 @@ description: Social choice theory formally proves that no voting rule can simult
type: claim type: claim
domain: collective-intelligence domain: collective-intelligence
created: 2026-02-17 created: 2026-02-17
source: "Conitzer et al, Social Choice for AI Alignment (arXiv 2404.10271, ICML 2024); Mishra, AI Alignment and Social Choice (arXiv 2310.16048, October 2023)" source: "Conitzer et al, Social Choice for AI Alignment (arXiv 2404.10271, ICML 2024); Mishra, AI Alignment and Social Choice (arXiv 2310.16048, October 2023); Yamamoto, A Full Formal Representation of Arrow's Impossibility Theorem (PLOS One, 2026-02)"
confidence: likely confidence: likely
tradition: "social choice theory, formal methods" tradition: "social choice theory, formal methods"
last_evaluated: 2026-03-11
--- ---
# universal alignment is mathematically impossible because Arrows impossibility theorem applies to aggregating diverse human preferences into a single coherent objective # universal alignment is mathematically impossible because Arrows impossibility theorem applies to aggregating diverse human preferences into a single coherent objective
@ -16,6 +17,8 @@ Mishra (2023) applies Arrow's and Sen's impossibility theorems directly, proving
This has devastating implications for the "align once, deploy everywhere" paradigm. Since [[RLHF and DPO both fail at preference diversity because they assume a single reward function can capture context-dependent human values]], Arrow's theorem provides the formal mathematical proof for why that assumption cannot work in principle. It is not a limitation of current techniques but an impossibility result about the structure of the problem itself. This has devastating implications for the "align once, deploy everywhere" paradigm. Since [[RLHF and DPO both fail at preference diversity because they assume a single reward function can capture context-dependent human values]], Arrow's theorem provides the formal mathematical proof for why that assumption cannot work in principle. It is not a limitation of current techniques but an impossibility result about the structure of the problem itself.
Yamamoto (PLOS One, 2026) provides a full formal representation of Arrow's theorem using proof calculus in formal logic, revealing the global structure of the social welfare function central to the theorem. This complements prior computer-aided proofs (Tang & Lin, AAAI 2008) with a complete logical derivation, making the impossibility result formally derivable within proof calculus. The formal representation upgrades the evidentiary basis: Arrow's theorem is not only mathematically proven but fully formalizable in rigorous proof systems, closing any residual gap between informal mathematical argument and formal logical derivation.
The way out is not better aggregation but a different architecture entirely. Since [[the alignment problem dissolves when human values are continuously woven into the system rather than specified in advance]], continuous context-sensitive alignment sidesteps the impossibility by never attempting a single universal aggregation. Since [[collective intelligence requires diversity as a structural precondition not a moral preference]], collective architectures can preserve preference diversity structurally rather than trying to compress it into one objective function. The way out is not better aggregation but a different architecture entirely. Since [[the alignment problem dissolves when human values are continuously woven into the system rather than specified in advance]], continuous context-sensitive alignment sidesteps the impossibility by never attempting a single universal aggregation. Since [[collective intelligence requires diversity as a structural precondition not a moral preference]], collective architectures can preserve preference diversity structurally rather than trying to compress it into one objective function.
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inbox/archive/2026-02-00-yamamoto-full-formal-arrow-impossibility.md
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@ -7,7 +7,11 @@ date: 2026-02-01
domain: ai-alignment domain: ai-alignment
secondary_domains: [critical-systems] secondary_domains: [critical-systems]
format: paper format: paper
status: unprocessed status: processed
processed_by: theseus
processed_date: 2026-03-11
claims_extracted: 0
enrichments: "foundations/collective-intelligence/universal alignment is mathematically impossible because Arrows impossibility theorem applies to aggregating diverse human preferences into a single coherent objective.md — added Yamamoto (2026) as evidence for formal proof calculus representation of Arrow's theorem; added to source field and body"
priority: medium priority: medium
tags: [arrows-theorem, formal-proof, proof-calculus, social-choice] tags: [arrows-theorem, formal-proof, proof-calculus, social-choice]
--- ---