diff --git a/foundations/collective-intelligence/universal alignment is mathematically impossible because Arrows impossibility theorem applies to aggregating diverse human preferences into a single coherent objective.md b/foundations/collective-intelligence/universal alignment is mathematically impossible because Arrows impossibility theorem applies to aggregating diverse human preferences into a single coherent objective.md index 18719c31..67dd6344 100644 --- a/foundations/collective-intelligence/universal alignment is mathematically impossible because Arrows impossibility theorem applies to aggregating diverse human preferences into a single coherent objective.md +++ b/foundations/collective-intelligence/universal alignment is mathematically impossible because Arrows impossibility theorem applies to aggregating diverse human preferences into a single coherent objective.md @@ -3,9 +3,10 @@ description: Social choice theory formally proves that no voting rule can simult type: claim domain: collective-intelligence 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 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 @@ -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. +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. --- diff --git a/inbox/archive/2026-02-00-yamamoto-full-formal-arrow-impossibility.md b/inbox/archive/2026-02-00-yamamoto-full-formal-arrow-impossibility.md index fe5851b6..7e4155e7 100644 --- a/inbox/archive/2026-02-00-yamamoto-full-formal-arrow-impossibility.md +++ b/inbox/archive/2026-02-00-yamamoto-full-formal-arrow-impossibility.md @@ -7,7 +7,11 @@ date: 2026-02-01 domain: ai-alignment secondary_domains: [critical-systems] 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 tags: [arrows-theorem, formal-proof, proof-calculus, social-choice] ---