 The Allais paradox, discussed in  Section 2.3  above, is a classic example where the aforementioned separability seems to fail. For ease of reference, the options that generate the paradox are reproduced as Table 3. Recall from  Section 2.3  that people tend to prefer \(L_2\) over \(L_1\) and \(L_3\) over \(L_4\)—an attitude that has been called Allais’ preferences—in violation of expected utility theory. The violation occurs precisely because the contributions that some of these outcomes make towards the overall value of an option is not independent of the other outcomes that the option can have. Compare the extra chance of outcome $0 that \(L_1\) has over \(L_2\) with the same extra chance of $0 that \(L_3\) has over \(L_4\). Many people think that this extra chance counts more heavily in the first comparison than the latter, i.e., that an extra 0.01 chance of $0 contributes a greater negative value to \(L_1\) than to \(L_3\). Some explain this by pointing out that the regret one would experience by winning nothing when one could have had $2400 for sure—i.e., when choosing \(L_1\) over \(L_2\) and the first ticket is drawn—is much greater than the regret one would experience by winning nothing when the option one turned down also had a high chance of resulting in $0—such as when choosing \(L_3\) over \(L_4\) (see, e.g., Loomes and Sugden 1982). But whether or not the preference in question should be explained by the potential for regret, it would seem that the desirability of the $0-outcome depends on what could (or would) otherwise have been; in violation of the aforementioned assumption of separability. (See Thoma 2020a for a recent extensive discussion of this assumption.) 