teleo-codex/inbox/archive/2024-10-00-qiu-representative-social-choice-alignment.md

type	title	author	url	date	domain	secondary_domains	format	status	priority	tags	flagged_for_rio
source	Representative Social Choice: From Learning Theory to AI Alignment	Tianyi Qiu (Peking University & CHAI, UC Berkeley)	https://arxiv.org/abs/2410.23953	2024-10-01	ai-alignment	collective-intelligence mechanisms	paper	unprocessed	high	social-choice representative-alignment arrows-theorem privilege-graphs learning-theory generalization	Social choice mechanisms as prediction market analogues — preference aggregation parallels

Content

Accepted at NeurIPS 2024 Pluralistic Alignment Workshop. From CHAI (Center for Human-Compatible AI) at UC Berkeley.

Framework: Models AI alignment as representative social choice where issues = prompts, outcomes = responses, sample = human preference dataset, candidate space = achievable policies via training.

Arrow-like impossibility theorems (new results):

• Weak Representative Impossibility (Theorem 3): When candidate space permits structural independence, no mechanism simultaneously satisfies Probabilistic Pareto Efficiency, Weak Independence of Irrelevant Alternatives, and Weak Convergence.
• Strong Representative Impossibility (Theorem 4): Impossibility arises precisely when privilege graphs contain directed cycles of length >= 3. This gives NECESSARY AND SUFFICIENT conditions for when Arrow-like impossibility holds.

Constructive alternatives:

1. Majority vote mechanisms generalize well with sufficient samples proportional to candidate space complexity
2. Scoring mechanisms work for non-binary outcomes
3. Acyclic privilege graphs enable feasibility — Theorem 4 guarantees mechanisms satisfying all axioms exist when privilege graphs are cycle-free

Machine learning tools: VC dimension, Rademacher complexity, generalization bounds, concentration inequalities.

Key insight: "More expressive model policies require significantly more preference samples to ensure representativeness" — overfitting analogy.

Agent Notes

Why this matters: This is the most formally rigorous connection between social choice theory and AI alignment I've found. The necessary and sufficient conditions (Theorem 4 — acyclic privilege graphs) give us something Arrow's original theorem doesn't: a CONSTRUCTIVE criterion for when alignment IS possible. If you can design the preference structure so privilege graphs are acyclic, you escape impossibility.

What surprised me: The constructive result. Arrow's theorem is usually presented as pure impossibility. Qiu shows WHEN impossibility holds AND when it doesn't. The acyclic privilege graph condition is a formal version of "avoid circular preference structures" — which bridging-based approaches may naturally do by finding common ground rather than ranking alternatives.

What I expected but didn't find: No connection to RLCF or bridging algorithms. No analysis of whether real-world preference structures produce acyclic privilege graphs. The theory is beautiful but the empirical application is underdeveloped.

KB connections:

• universal alignment is mathematically impossible because Arrows impossibility theorem applies to aggregating diverse human preferences into a single coherent objective — this paper REFINES our claim: impossibility holds when privilege graphs are cyclic, but alignment IS possible when they're acyclic
• RLHF and DPO both fail at preference diversity — because they don't check privilege graph structure
• pluralistic alignment must accommodate irreducibly diverse values simultaneously — this paper shows when accommodation is formally possible

Extraction hints: Claims about (1) necessary and sufficient conditions for alignment impossibility via privilege graph cycles, (2) constructive alignment possible with acyclic preference structures, (3) model expressiveness requires proportionally more preference data.

Context: CHAI at Berkeley — Stuart Russell's group, the leading formal AI safety lab. NeurIPS venue.

Curator Notes (structured handoff for extractor)

PRIMARY CONNECTION: universal alignment is mathematically impossible because Arrows impossibility theorem applies to aggregating diverse human preferences into a single coherent objective WHY ARCHIVED: Gives NECESSARY AND SUFFICIENT conditions for impossibility — refines Arrow's from blanket impossibility to conditional impossibility, which is a major upgrade EXTRACTION HINT: The acyclic privilege graph condition is the key novel result — it tells us WHEN alignment is possible, not just when it isn't