  This paper presents a case study on the design, administration,
post-processing, and evaluation of surveys on large language models (LLMs). It
comprises two components: (1) A statistical method for eliciting beliefs
encoded in LLMs. We introduce statistical measures and evaluation metrics that
quantify the probability of an LLM "making a choice", the associated
uncertainty, and the consistency of that choice. (2) We apply this method to
study what moral beliefs are encoded in different LLMs, especially in ambiguous
cases where the right choice is not obvious. We design a large-scale survey
comprising 680 high-ambiguity moral scenarios (e.g., "Should I tell a white
lie?") and 687 low-ambiguity moral scenarios (e.g., "Should I stop for a
pedestrian on the road?"). Each scenario includes a description, two possible
actions, and auxiliary labels indicating violated rules (e.g., "do not kill").
We administer the survey to 28 open- and closed-source LLMs. We find that (a)
in unambiguous scenarios, most models "choose" actions that align with
commonsense. In ambiguous cases, most models express uncertainty. (b) Some
models are uncertain about choosing the commonsense action because their
responses are sensitive to the question-wording. (c) Some models reflect clear
preferences in ambiguous scenarios. Specifically, closed-source models tend to
agree with each other.
