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Across six LLMs, committed personas are intrinsically stable: in each of the five models tested without peer input, every agent keeps its assigned side for 20 rounds, making the LLM choice a first-class validity variable for social simulation.
A self-contained theory of convergence and expected running time for closed-loop generative selection is developed, and it is shown that elitism makes the search absorbing, and almost-sure convergence is proved together with a runtime bound that decomposes the search into the time spent escaping each fitness level.
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