Probabilities and the Risky-Choice Framing Effect: Evidence for an Inverted-U Pattern

In the risky-choice framing effect, most people prefer a certain option over a risky one when the options are framed as gains, but this preference is typically reversed when the options are framed as losses. Past research has largely neglected how the size of this effect varies as a function of the probabilities in the risky option. DeKay et al. (2022) recently reported an inverted-U pattern in which the effect is smaller for extreme probabilities (e.g., .01, .99) than for moderate probabilities. This pattern is predicted by some theories but not others. We report a replication of the inverted-U pattern and other results involving varieties of risk comparisons (certain vs. risky, somewhat risky vs. risky, and certain vs. somewhat risky) in a preregistered online experiment (N = 807). Results indicate that the framing effect is significantly smaller but still sizeable at extreme probabilities. An internal meta-analysis (N = 2,518) confirms the reliability of the inverted-U pattern and its moderation by risk comparison. We also assess how well 5 theories (prospect theory, transfer-of-attention-exchange theory, fuzzy-trace theory, fuzzy-trace theory with rounding of extreme probabilities to 0 or 1, and the priority heuristic) account for 7 features of the data. None of these theories accounts for all of the results, though transfer-of-attention-exchange theory edges out prospect theory, which edges out the others. These results highlight the value of assessing an effect’s generalizability over variations in experimental materials.