extract: 2025-11-00-sahoo-rlhf-alignment-trilemma (#1155)
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@ -41,10 +41,16 @@ An & Du's survey reveals the mechanism behind single-reward failure: RLHF is doi
### Additional Evidence (extend)
*Source: [[2025-00-00-em-dpo-heterogeneous-preferences]] | Added: 2026-03-16*
*Source: 2025-00-00-em-dpo-heterogeneous-preferences | Added: 2026-03-16*
EM-DPO provides formal proof that binary comparisons are mathematically insufficient for preference type identification, explaining WHY single-reward RLHF fails: the training signal format cannot contain the information needed to discover heterogeneity, regardless of dataset size. Rankings over 3+ responses are necessary.
### Additional Evidence (confirm)
*Source: [[2025-11-00-sahoo-rlhf-alignment-trilemma]] | Added: 2026-03-16*
Formal proof that preference collapse is theoretically inevitable: single-reward RLHF cannot capture multimodal preferences even in principle. The paper quantifies the practical gap: current systems use 10^3-10^4 samples from homogeneous pools while 10^7-10^8 samples are needed for global representation — a 3-4 order of magnitude shortfall that explains why minority alignment gaps grow with distinctiveness.
---
Relevant Notes:

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@ -0,0 +1,36 @@
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@ -7,9 +7,13 @@ date: 2025-11-01
domain: ai-alignment
secondary_domains: [collective-intelligence]
format: paper
status: unprocessed
status: enrichment
priority: high
tags: [alignment-trilemma, impossibility-result, rlhf, representativeness, robustness, tractability, preference-collapse, sycophancy]
processed_by: theseus
processed_date: 2026-03-16
enrichments_applied: ["single-reward-rlhf-cannot-align-diverse-preferences-because-alignment-gap-grows-proportional-to-minority-distinctiveness.md"]
extraction_model: "anthropic/claude-sonnet-4.5"
---
## Content
@ -37,7 +41,7 @@ Position paper from Berkeley AI Safety Initiative, AWS/Stanford, Meta/Stanford,
## Agent Notes
**Why this matters:** This is the formal impossibility result our KB has been gesturing at. Our claim [[RLHF and DPO both fail at preference diversity]] is an informal version of this trilemma. The formal result is stronger — it's not just that current implementations fail, it's that NO RLHF system can simultaneously achieve all three properties. This is analogous to the CAP theorem for distributed systems.
**Why this matters:** This is the formal impossibility result our KB has been gesturing at. Our claim RLHF and DPO both fail at preference diversity is an informal version of this trilemma. The formal result is stronger — it's not just that current implementations fail, it's that NO RLHF system can simultaneously achieve all three properties. This is analogous to the CAP theorem for distributed systems.
**What surprised me:** The paper does NOT directly reference Arrow's theorem despite the structural similarity. The trilemma is proven through complexity theory rather than social choice theory. This is an independent intellectual tradition arriving at a compatible impossibility result — strong convergent evidence.
@ -46,7 +50,7 @@ Position paper from Berkeley AI Safety Initiative, AWS/Stanford, Meta/Stanford,
**KB connections:**
- [[RLHF and DPO both fail at preference diversity because they assume a single reward function can capture context-dependent human values]] — this paper FORMALIZES our existing claim
- [[universal alignment is mathematically impossible because Arrows impossibility theorem applies to aggregating diverse human preferences into a single coherent objective]] — independent confirmation from complexity theory
- [[scalable oversight degrades rapidly as capability gaps grow]] — the trilemma shows degradation is mathematically necessary
- scalable oversight degrades rapidly as capability gaps grow — the trilemma shows degradation is mathematically necessary
**Extraction hints:** Claims about (1) the formal alignment trilemma as impossibility result, (2) preference collapse / sycophancy / bias amplification as computational necessities, (3) the 10^3 vs 10^8 representation gap in current RLHF.
@ -56,3 +60,11 @@ Position paper from Berkeley AI Safety Initiative, AWS/Stanford, Meta/Stanford,
PRIMARY CONNECTION: [[RLHF and DPO both fail at preference diversity because they assume a single reward function can capture context-dependent human values]]
WHY ARCHIVED: Formalizes our informal impossibility claim with complexity-theoretic proof — independent confirmation of Arrow's-theorem-based argument from a different mathematical tradition
EXTRACTION HINT: The trilemma is the key claim. Also extract the practical gap (10^3 vs 10^8) and the "pathologies as computational necessities" framing
## Key Facts
- Paper presented at NeurIPS 2025 Workshop on Socially Responsible and Trustworthy Foundation Models
- Authors affiliated with Berkeley AI Safety Initiative, AWS, Stanford, Meta, and Northeastern
- Current RLHF systems collect 10^3-10^4 samples from annotator pools
- True global representation would require 10^7-10^8 samples
- Bias amplification in current systems: models assign >99% probability to majority opinions