Emulate or Estimate? The Divergent Strengths of Base and Post-Trained Language Models for Opinion Simulation

Large language models are increasingly used to simulate human opinions, but prior work reports conflicting results: some studies find promising alignment with human survey data, while others find persona collapse and weak demographic sensitivity. We show that much of this conflict stems from conflating two distinct tasks. We call the first task emulation, in which models generate individual responses that aggregate into a population distribution. We call the second task estimation, in which models directly predict the population distribution. Evaluating six matched base and post-trained models on the Pew American Trends Panel, we find that base models are stronger emulators: they produce response distributions closer to human ground truth and better preserve demographic structure. Post-trained models are stronger estimators, producing more accurate distributional predictions when asked directly. We propose that model selection for human simulation should be guided by whether the task requires generating text or predicting distributions.

Grounded Chess Reasoning in Language Models via Master Distillation

Language models often lack grounded reasoning capabilities in specialized domains where training data is scarce but bespoke systems excel. We introduce a general framework for distilling expert system reasoning into natural language chain-of-thought explanations, enabling compact models to acquire domain expertise and the ability to generate faithful, grounded explanations. Rather than distilling only final outputs, we capture the full reasoning process, transforming opaque expert computations into transparent, step-by-step explanations. We demonstrate this approach in chess, a canonical reasoning domain where language models continue to underperform. Our 4B parameter model, C1, advances from a near-zero baseline to 48.1% accuracy, outperforming all open-source models and most frontier proprietary systems. Notably, C1 surpasses its distillation teacher and generates solutions in two orders of magnitude fewer tokens than baselines. Unlike prior neural chess approaches that predict only best moves, C1 generates explainable solutions revealing strategic reasoning. Our pipeline combines supervised fine-tuning and reinforcement learning with theme-balanced data sampling for comprehensive tactical coverage. Master Distillation demonstrates how to inject expert-level knowledge into compact models for under-optimized domains, offering a recipe for unlocking RLVR where LLMs lack sufficient base capabilities.