 We present here one such axiom system to derive expected utility theory, a simple set of axioms for the binary relation \(\succeq\), which represents the relation “is weakly preferred to”. The objects of comparison for this axiomatization are prospects, which associate probabilities to a fixed set of consequences, where both probabilities and consequences are known to the agent. To illustrate, the prospect (−€10, ½; €20, ½) concerns two consequences, losing 10 Euros and winning 20 Euros, each assigned the probability one-half. A rational agent will prefer this prospect to another with the same consequences but greater chance of losing than winning, such as (\(-\)€10, ⅔; €20, ⅓), assuming his aim is to maximize his financial welfare. More generally, suppose that \(X = \{x_1, x_2, \ldots, x_n\}\) is a mutually exclusive and exhaustive set of consequences and that \(p_i\) denotes the probability of \(x_i\), where each \(p_i \geq 0\) and \(\sum_{i}^{n} p_i = 1\). A prospect P is simply the set of consequence-probability pairs, \(P = (x_1, p_1; \ x_2, p_2; \ldots; \ x_n, p_n)\). By convention, a prospect’s consequence-probability pairs are ordered by the value of each consequence, from least favorable to most. When prospects P, Q, R are comparable under a specific preference relation, \(\succeq\), and the (ordered) set of consequences X is fixed, then prospects may be simply represented by a vector of probabilities.