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REWARD VERSUS RISK IN UNCERTAIN INFERENCE: THEOREMS AND SIMULATIONS

Published online by Cambridge University Press:  04 July 2012

GERHARD SCHURZ
Affiliation:
Department of Philosophy, University of Duesseldorf
PAUL D. THORN
Affiliation:
Department of Philosophy, University of Duesseldorf

Abstract

Systems of logico-probabilistic (LP) reasoning characterize inference from conditional assertions that express high conditional probabilities. In this paper we investigate four prominent LP systems, the systems O, P, Z, and QC. These systems differ in the number of inferences they licence (O ⊂ P ⊂ ZQC). LP systems that license more inferences enjoy the possible reward of deriving more true and informative conclusions, but with this possible reward comes the risk of 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 of reward versus risk. Our results suggest that system Z offers the best balance.

Type
Research Articles
Copyright
Copyright © Association for Symbolic Logic 2012

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