Algorithms for Generating Sets of Gambles for Decision Making with Lower Previsions

Abstract

© 2020, Springer Nature Switzerland AG. (Formula Presented)-maximin, (Formula Presented)-maximax, maximality and interval dominance are well-known criteria for decision making using lower previsions when precise probabilities are not available. This study proposes algorithms for generating a set of gambles that has a precise number of (Formula Presented)-maximin (or (Formula Presented)-maximax) gambles that can be used to generate random decision problems for benchmarking algorithms for finding (Formula Presented)-maximin (or (Formula Presented)-maximax) gambles. Since (Formula Presented)-maximin and (Formula Presented)-maximax imply maximality and interval dominance, the algorithms can also be used as an alternative algorithm for generating random decision problems with pre-determined numbers of maximal and interval dominant gambles.