 Most people (strictly) prefer \(L_1\) to \(L_2,\) and (strictly) prefer \(L_4\) to \(L_3,\) but there are no values \(u(\$0),\) \(u(\$1\rM),\) and \(u(\$5\rM)\) such that \(\EU(L_1) \gt \EU(L_2)\) and \(\EU(L_4) \gt \EU(L_3).\) The Allais preferences violate the Independence Axiom; when the lotteries are suitably reframed as acts (e.g., defined over events such as the drawing of a 100-ticket lottery), they violate the Sure-thing Principle or related separability principles.