Hearsay or Fact? How Framing and Elicitation Shape LLM Probability Updates

Large language models (LLMs) are increasingly used as judgment assistants and as stand-in participants in psychology experiments, yet little is known about how much their probability estimates move in response to a single new piece of information. We pair premise-hypothesis items from δ-SNLI with one strengthener and one weakener each, elicit the prior and the posteriors in separate calls, and measure the directional movement s: the mean posterior change signed by the annotated direction, so that the prior cancels out. We vary whether the update is stated ("Here is something else you learned") or reported ("Someone said that"), and whether the model gives one probability or five weighted estimates. We test seven configurations: two local models (Qwen3-8B, OLMo-2-7B; 240 pairs) and five configurations run through agent command-line harnesses (120 pairs), with hypotheses and analysis rules fixed before the formal runs (not publicly registered). Under stated, direct elicitation all seven move in the annotated direction (s = 18-28 percentage points). Reporting lowers s in all seven point estimates (significantly in six, by 2-5 points) and raises the share of reverse movements in all seven: the effect is consistent but small. Five weighted estimates lower the share of responses at leq5% or geq95% in all seven, but in the two local models they also reduce s by 43% and 68%, whereas in the harnessed configurations the point estimates of the change lie between -3.7 and +0.5 points. An elicitation format that reduces extreme values thus need not preserve sensitivity to evidence; the two should be tested separately. Because δ-NLI annotates only direction, we make no claim about how large an update should be. Code, data and the frozen plan: https://github.com/asj252/llm-judgment-studies