 While the above reasoning may seem compelling, Allais’ preferences conflict with the  Independence axiom.  The following is true of both choice situations: whatever choice you make, you will get the same prize if one of the tickets in the last column is drawn. Therefore, Independence implies that both your preference between \(L_1\) and \(L_2\) and your preference between \(L_3\) and \(L_4\) should be independent of the prizes in that column. But when you ignore the last column, \(L_1\) becomes identical to \(L_3\) and \(L_2\) to \(L_4\). Hence, if you prefer \(L_2\) over \(L_1\) but \(L_3\) over \(L_4\), there seems to be an inconsistency in your preference ordering. And there is definitely a violation of Independence (given how the options have been described; an issue to which we return in  Section 5.1).  As a result, the pair of preferences under discussion cannot be represented as maximising expected utility. (Thus the “paradox”: many people think that Independence is a requirement of rationality, but nevertheless also want to claim that there is nothing irrational about Allais’ preferences.)