Evidence Collection and Inductive Inference

We study a two-period model where the decision in the second period is based on the ex ante test choice. Individuals are assumed to rank pairs of an option and a trial, where an option is a finite subset of alternatives that represents second period possible choices, and a trial is a finite subset of tests that renders the information of alternatives. Several axioms yield a numerical representation through a credence function as follows. The credence function assigns numbers to alternative-test pairs. The credence number attached to an alternative-test pair can be interpreted as the degree of support that the test renders to the plausibility of the alternative. Given a trial, each alternative is assessed according to the sum of credence numbers over tests in the trial. A pair of an option and a trial is therefore ranked according to the maximum sum of credence numbers among the option with respect to the trial.