Expanding Common-Ratio and Common-Consequence Comparisons

The Common Ratio (CR) and Common Consequence (CC) problems have been extremely widely studied as examples of non-Expected Utility risk preferences. Blavatskyy et al. (2022, 2023) document a total of 224 experimental studies of these problems. Interestingly, other tests of EU's parallelism have not been systematically pursued. One notable shortcoming is that while CR and CC problems investigate the geometry of preferences in the lower right (southeast) portion of the probability simplex, there has not been commensurate interest in the upper left (northwest) portion of the simplex. Indeed, our investigation of the literature identified far fewer studies investigating that region of the simplex. The lack of exploration is critical because a range of behavioral decision theories predict specific forms of non-parallelism in the equivalent of CR and CC problems conducted on the upper left portion of the simplex, and sometimes predict distinct (or sometimes notably similar) patterns between upper left and lower right. Prominent examples include Prospect Theory (Kahneman and Tversky, 1979; Tversky and Kahneman, 1992) as well as other models of “fanning-out”, “fanning-in”, and “mixed-fanning” of indifference curves. The objective of this project is to provide an expanded exploration of the geometry of preferences throughout the probability simplex in order to provide a more complete foundation for assessing EU and non-EU theories.