Ensuring fairness in social survey simulation is critical, as biased outputs can misrepresent underrepresented groups. This issue is growing as large language models (LLMs) are increasingly used for this task. However, standard fine-tuning based on Empirical Risk Minimization (ERM) often under-optimizes minority groups, causing substantial subgroup disparities. Distributionally robust Optimization (DRO) methods reduce worst-case errors, but their strict worst-case selection can lead to noisy and unstable optimization under demographic sparsity. These issues create intertwined challenges for fairness, convergence and stability. We propose SAFO, a dynamic utility–fairness optimization framework for LLM-based survey simulation that explicitly targets both fairness and training stability. SAFO combines (i) an Optimizer that preserves mean-loss utility, (ii) an Adversary that performs temperature-controlled, EMA-smoothed and loss-driven group reweighting, and (iii) a Nash-inspired Regulator that adaptively adjusts the utility–fairness trade-off by tracking weak-group gains and collateral utility damages. Experiments on three large-scale survey datasets from China, the U.S., and Europe show that SAFO consistently improves minority performance and social-welfare metrics. It reduces worst-group gaps by up to 12.7%, maintains overall accuracy with a mean change of less than 0.3% and lowers variance across random seeds. Our code is available at https://github.com/PiLab-ZJU/SAFO.

While large language models (LLMs) excel at understanding and generating plain text, they are not tailored to handle hierarchical text structures or directly predict task-specific properties such as text rating. In fact, selectively and repeatedly grasping the hierarchical structure of large-scale text is pivotal for deciphering its essence. To this end, we propose a novel framework for hierarchical text rating utilizing LLMs, which incorporates Recurrent Alignment with Hard Attention (RAHA). Particularly, hard attention mechanism prompts a frozen LLM to selectively focus on pertinent leaf texts associated with the root text and generate symbolic representations of their relationships. Inspired by the gradual stabilization of the Markov Chain, recurrent alignment strategy involves feeding predicted ratings iteratively back into the prompts of another trainable LLM, aligning it to progressively approximate the desired target. Experimental results demonstrate that RAHA outperforms existing state-of-the-art methods on three hierarchical text rating datasets. Theoretical and empirical analysis confirms RAHA’s ability to gradually converge towards the underlying target through multiple inferences. Additional experiments on plain text rating datasets verify the effectiveness of this Markov-like alignment. Our data and code can be available in https://github.com/ECNU-Text-Computing/Markov-LLM.