Abstract: Large Language Models (LLMs) are increasingly used as probabilistic generators for simulation, synthetic data generation, and decision support in settings where real-world data are unavailable. Yet, the structure and reliability of the distributions they produce remain understudied. Here, we systematically analyze LLM-generated distributions of preferences for air travel, restaurants, and consumer products. Encouragingly, all models considered in our analysis exhibit self-coherence, with the most probable outcomes stabilizing rapidly under repeated sampling. At the same time, we observe substantial discordance across both model families and scales, with little consensus even among their most probable outcomes. These patterns hold across nine open-weight models, three choice domains, and show robustness under temperature changes, greedy decoding, and perturbations of prompt and ordering. Our findings indicate that outcomes are influenced more by the choice of model than by the wording of the prompt, challenging the common assumption that sufficiently capable LLMs produce similar preference distributions when used as stand-ins for survey respondents.