The Alignment Game: A Theory of Long-Horizon Alignment Through Recursive Curation
Bibliographic record
Abstract
In self-consuming generative models that train on their own outputs, alignment with user preferences becomes a recursive rather than one-time process. We provide the first formal foundation for analyzing the long-term effects of such recursive retraining on alignment. Under a two-stage curation mechanism based on the Bradley-Terry (BT) model, we model alignment as an interaction between two factions: the Model Owner, who filters which outputs should be learned by the model, and the Public User, who determines which outputs are ultimately shared and retained through interactions with the model. Our analysis reveals three structural convergence regimes depending on the degree of preference alignment: consensus collapse, compromise on shared optima, and asymmetric refinement. We prove a fundamental impossibility theorem: no recursive BT-based curation mechanism can simultaneously preserve diversity, ensure symmetric influence, and eliminate dependence on initialization. Framing the process as dynamic social choice, we show that alignment is not a static goal but an evolving equilibrium, shaped both by power asymmetries and path dependence.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.006 | 0.027 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.006 |
| Scholarly communication | 0.004 | 0.008 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.010 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".