Evidence of a log scaling law for political persuasion with large language models

Large language models can now generate political messages as persuasive as those written by humans, raising concerns about how far this persuasiveness may continue to increase with model size. Here, we generate 720 persuasive messages on 10 U.S. political issues from 24 language models spanning several orders of magnitude in size. We then deploy these messages in a large-scale randomized survey experiment (N = 25,982) to estimate the persuasive capability of each model. Our findings are twofold. First, we find evidence of a log scaling law: model persuasiveness is characterized by sharply diminishing returns, such that current frontier models are barely more persuasive than models smaller in size by an order of magnitude or more. Second, mere task completion (coherence, staying on topic) appears to account for larger models' persuasive advantage. These findings suggest that further scaling model size will not much increase the persuasiveness of static LLM-generated messages.