This paper introduces inductive randomness predictors, which form a superset of inductive conformal predictors. Its focus is on a very simple special case, binary inductive randomness predictors. It is interesting that binary inductive randomness predictors have an advantage over inductive conformal predictors, although they also have a serious disadvantage. This advantage will allow us to reach the surprising conclusion that non-trivial inductive conformal predictors are inadmissible in the sense of statistical decision theory.

Conformal prediction is usually presented as a method of set prediction [10, Part I], i.e., as a way of producing prediction sets (rather than pointpredictions). Another way to look at a conformal predictor is as a way of producin g a p-value function (discussed, in a slightly different context, in, e.g., [4]), which is a function mapping each possible label y of a test object to the corresponding conformal p-value. In analogy with "prediction sets", we will call su ch p-value functions "prediction functions".