REWARD VERSUS RISK IN UNCERTAIN INFERENCE: THEOREMS AND SIMULATIONS

Abstract

AbstractSystems oflogico-probabilistic(LP) reasoning characterize inference from conditional assertions that express high conditional probabilities. In this paper we investigate four prominent LP systems, the systemsO, P,Z, andQC. These systems differ in the number of inferences they licence (O⊂ P ⊂Z⊂QC). LP systems that license more inferences enjoy the possiblerewardof deriving more true and informative conclusions, but with this possible reward comes theriskof drawing more false or uninformative conclusions. In the first part of the paper, we present the four systems and extend each of them by theorems that allow one to compute almost-tight lower-probability-bounds for the conclusion of an inference, given lower-probability-bounds for its premises. In the second part of the paper, we investigate by means of computer simulations which of the four systems provides the best balance ofrewardversusrisk. Our results suggest that systemZoffers the best balance.