  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.
