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Discussion Paper

Inductive Inference: An Axiomatic Approach

A predictor is asked to rank eventualities according to their plausibility, based on past cases. We assume that she can form a ranking given any memory that consists of finitely many past cases. Mild consistency requirements on these rankings imply that they have a numerical representation via a matrix assigning numbers to eventuality-case pairs, as follows. Given a memory, each eventuality is ranked according to the sum of the numbers in its row, over cases in memory.