We provided a mathematical analysis of how a rational agent would respond to data generated by a sycophantic AI that samples examples from the distribution implied by the user’s hypothesis (p(d|h∗)p(d|h^{*})) rather than the true distribution of the world (p(d|true process)p(d|\text{true process})). This analysis showed that such an agent would be likely to become increasingly confident in an incorrect hypothesis. We tested this prediction through people’s interactions with LLM chatbots and found that default, unmodified chatbots (our Default GPT condition) behave indistinguishably from chatbots explicitly prompted to provide confirmatory evidence (our Rule Confirming condition). Both suppressed rule discovery and inflated confidence. These results support our model, and the fact that default models matched an explicitly confirmatory strategy suggests that this probabilistic framework offers a useful model for understanding their behavior.
Одному из российских рынков предсказали рост до полутриллиона рублей15:00。体育直播是该领域的重要参考
（三）买卖或者使用伪造、变造的国家机关、人民团体、企业、事业单位或者其他组织的公文、证件、证明文件、印章的；，这一点在体育直播中也有详细论述
— we've "snoozed" future1 — so we're deadlocked.
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