*crossposted on LessWrong*

I'm interested in questions of the form, "I have a bit of metadata/structure to the question, but I know very little about the content of the question (or alternatively, I'm too worried about biases/hacks to how I think about the problem or what pieces of information to pay attention to). In those situations, what prior should I start with?"

I'm not sure if there is a more technical term than "low-information prior."

Some examples of what I found useful recently:

1. Laplace's Rule of Succession, for when the underlying mechanism is unknown.

2. Percentage of binary questions that resolves as "yes" on Metaculus. It turns out that of all binary (Yes-No) questions asked on the prediction platform Metaculus, ~29% of them resolved yes. This means that even if you know *nothing* about the *content* of a Metaculus question, a reasonable starting point for answering a randomly selected binary Metaculus question is 29%.

In both cases, obviously there are reasons to override the prior in both practice and theory (for example, you can arbitrarily add a "not" to all questions on Metaculus such that your prior is now 71%). However (I claim), having a decent prior is nonetheless useful in practice, even if it's theoretically unprincipled.

I'd be interested in seeing something like 5-10 examples of low-information priors as useful as the rule of succession or the Metaculus binary prior.

The maximum entropy principle can give implausible results sometimes though. If you have a bag containing 100 balls which you know can only be coloured red or blue, and you adopt a maximum entropy prior over the possible ball colourings, then if you randomly drew 99 balls from the bag and they were all red, you'd conclude that the next ball is red with probability 50/50. This is because in the maximum entropy prior, the ball colourings are independent. But this feels wrong in this context. I'd want to put the probability on the 100th ball being red much higher.