|Working Paper #29-99|
|Inductive Inference: An Axiomatic Approach|
|Itzhak Gilboa and David Schmeidler|
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 repetitions of 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. A memory is identified with a vector, counting the number of repetitions of each case. Multiplication of the matrix by a memory vector yields a numerical representation of the ordinal plausibility ranking given that memory. Interpreting this result for the ranking of theories or hypotheses, rather than of specific eventualities, it is shown that one may ascribe to the predictor subjective conditional probabilities of cases given theories, such that her rankings of theories agree with their likelihood functions.
|Published in: Forthcoming - Econometrica|
|Jel Nos.: D8. D60.|
|Keywords: Learning. Inductive Inference. Maximum Likelihood.|
|PAPER in PDF|