Connecting Common Ratio and Common Consequence Preferences

Many models of decision-making under uncertainty are motivated by two prominent deviations from
expected utility (EU): the common consequence effect (CCE) and the common ratio effect (CRE). Both
decision problems were originally proposed as thought experiments by Allais (1953), and later popu-
larized by Kahneman & Tversky (1979). The apparent deviations from EU predictions in each problem
have motivated a wide body of decision theories in risky choice.
Although the CRE and CCE both represent violations of the EU axiom of independence, they have been
studied mostly independently, and using quite different experimental parameters. In fact, however, the
two decision problems are closely related: If conducted at a common set of experimental parameters,
the two problems would share three out of four possible options. Moreover, the connections between
the two problems are relevant for assessing various non-EU models—i.e., different models predict
specific patterns.
In this paper, we extend existing empirical tests by (i) explicitly recognizing the connection between
the two decision problems; (ii) conducting a large number of experiments covering connected CRE
and CCE problems at different experimental parameters; and (iii) implementing experiments using
both paired choice tasks (for comparison to the prior literature) and paired valuation tasks (our pre-
ferred approach given the inferential challenges outlined in McGranaghan et al (2024)).
Our results provide important insights on the shape of risk preferences. We find small but significant
CR preferences, but systematic reverse CC preferences. Through their connection, this pattern implies
that individuals violate betweenness by preferring mixtures. These results are inconsistent with lead-
ing non-EU models, and we propose a model to rationalize these findings.