Don't ask an LLM for a confidence score

It's obvious to me that writing "Give me a confidence score from 1-5" in your prompt will have disappointing results if you use that score directly. If you want self-reported confidence scores that are at all useful, you need to think about statistics and score calibration regardless of whether those scores are produced by an LLM or a human.

Take a corpus of problems you know the answers to, but the AI sometimes gets wrong [1]. Have the AI try to solve each problem and give you a 1-5 integer confidence score. The known proportion of correct answers in each bucket gives you a mapping from scores to probabilities [2].

[1] One possible corpus creation strategy might be math problems that you really need to run a program to solve. You can run the program to generate the correct answer key, but disallow tool calling for the AI.

[2] I'm pretty sure there's some stats wizardry that will let you put error bars on each bucket's probability based on the number of problems that end up in each bucket.

Dang, my bad. Thought I cleaned that up. To be clear, I use AI to help clean up scattered thoughts, and then I edit it further but sometimes I miss the AI-isms that it inserts.

Agreed. However my research is showing that saturation of the rubric occurs in unique configuration that drive the transfer curve to near binary. Effectively turning a 1-10 rating system into yes/no.

Slop with the stop!

In human memory, we often use a sense of familiarity to guide our memory decision, in the absence of explicit recollection of details. There is a whole memory literature about "recollection and familiarity" that dissociates the two cognitive processes, recollection which involves retrieval of specific details of an experience, and familiarity, which is a sense of memory strength, but absent of any qualitative detail. Familiarity is a faster process, and can often spur subsequent retrieval attempts that can lead to actual recollection..e.g. you see someone that seems familiar, but can't place where...and after a few moments, you remember who they were and where you had met them.

When measuring these processes, one approach has been to ask participants to provide confidence ratings. Recollection tends to lead to threshold-like, very high confident responses. Familiarity is more graded and continuous. Many then use a dual-process ROC model to identify the recollection and familiarity components, on average, of a person's memory of a memory test (see work by Andy Yonelinas).

This kind of work goes beyond memory, but applied to the general problem of how people judge their confidence in answers.

Its likely been applied to LLMs. A familiarity signal would probably be pretty easy to generate... The recollection kind of component might take some of those introspection type of approaches. For example, these papers, which I have not read, [1] https://arxiv.org/html/2603.17839v1 [2]https://arxiv.org/abs/2603.09250 might be getting at these ideas.

This might be relevant