LLM-SAA: LLM-persona Generated Distributions for Decision-making

LLMs can generate a wealth of data, from simulated personas imitating human valuations to demand forecasts based on world knowledge. But how well do such LLM-generated distributions support downstream decision-making? We study LLM-SAA, where an LLM constructs an estimated distribution and the decision is optimized under it, and we propose decision-aware metrics to evaluate it. Across three canonical problems—assortment optimization, pricing, and newsvendor—we find that LLM-generated distributions are practically useful, especially in low-data regimes, and that decision-agnostic metrics such as Wasserstein distance can be misleading for evaluating distributions intended for decision-making.