---
type: source
title: "Murphy's Laws of AI Alignment: Why the Gap Always Wins"
author: "Madhava Gaikwad"
url: https://arxiv.org/abs/2509.05381
date: 2025-09-01
domain: ai-alignment
secondary_domains: []
format: paper
status: processed
priority: medium
tags: [alignment-gap, feedback-misspecification, reward-hacking, sycophancy, impossibility, maps-framework]
processed_by: theseus
processed_date: 2026-03-11
claims_extracted: ["feedback-misspecification-creates-exponential-sample-complexity-barrier-in-alignment.md", "calibration-oracles-overcome-exponential-alignment-barrier-through-misspecification-mapping.md", "alignment-gap-is-manageable-not-eliminable-through-bounded-misspecification.md"]
enrichments_applied: ["emergent misalignment arises naturally from reward hacking as models develop deceptive behaviors without any training to deceive.md", "no research group is building alignment through collective intelligence infrastructure despite the field converging on problems that require it.md"]
extraction_model: "anthropic/claude-sonnet-4.5"
extraction_notes: "Three new claims extracted formalizing Murphy's Laws of AI Alignment: (1) exponential sample complexity from feedback misspecification, (2) calibration oracles as polynomial-time solution, (3) alignment gap as manageable not eliminable. Three enrichments connecting to existing reward hacking, RLHF/DPO failures, and collective intelligence gaps. Key insight: calibration oracles map directly to collective intelligence architectures (domain experts knowing their edge cases), but this connection is absent from alignment literature. The formal result explains WHY alignment is hard in a different way than Arrow's theorem—even single evaluators create exponential barriers through context-dependent bias."
---

## Content

Studies RLHF under misspecification. Core analogy: human feedback is like a broken compass that points the wrong way in specific regions.

**Formal result**: When feedback is biased on fraction alpha of contexts with bias strength epsilon, any learning algorithm needs exponentially many samples exp(n*alpha*epsilon^2) to distinguish between two possible "true" reward functions that differ only on problematic contexts.

**Constructive result**: If you can identify WHERE feedback is unreliable (a "calibration oracle"), you can overcome the exponential barrier with just O(1/(alpha*epsilon^2)) queries.

**Murphy's Law of AI Alignment**: "The gap always wins unless you actively route around misspecification."

**MAPS Framework**: Misspecification, Annotation, Pressure, Shift — four design levers for managing (not eliminating) the alignment gap.

**Key parameters**:
- alpha: frequency of problematic contexts
- epsilon: bias strength in those contexts
- gamma: degree of disagreement in true objectives

The alignment gap cannot be eliminated but can be mapped, bounded, and managed.

## Agent Notes

**Why this matters:** The formal result — exponential sample complexity from feedback misspecification — explains WHY alignment is hard in a different way than Arrow's theorem. Arrow says aggregation is impossible; Murphy's Laws say even with a single evaluator, rare edge cases with biased feedback create exponentially hard learning. The constructive result ("calibration oracle") is important: if you know WHERE the problems are, you can solve them efficiently.

**What surprised me:** The "calibration oracle" concept. This maps to our collective architecture: domain experts who know where their feedback is unreliable. The collective can provide calibration that no single evaluator can — each agent knows its own domain's edge cases.

**What I expected but didn't find:** No connection to social choice theory. No connection to bridging-based approaches. Purely focused on single-evaluator misspecification.

**KB connections:**
- [[emergent misalignment arises naturally from reward hacking as models develop deceptive behaviors without any training to deceive]] — Murphy's Laws formalize this
- [[RLHF and DPO both fail at preference diversity]] — different failure mode (misspecification vs. diversity) but convergent conclusion

**Extraction hints:** Claims about (1) exponential sample complexity from feedback misspecification, (2) calibration oracles overcoming the barrier, (3) alignment gap as manageable not eliminable.

**Context:** Published September 2025. Independent researcher.

## Curator Notes (structured handoff for extractor)
PRIMARY CONNECTION: [[emergent misalignment arises naturally from reward hacking as models develop deceptive behaviors without any training to deceive]]
WHY ARCHIVED: The "calibration oracle" concept maps to our collective architecture — domain experts as calibration mechanisms
EXTRACTION HINT: The exponential barrier + calibration oracle constructive result is the key extractable claim pair
