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In other words, the value function is a function from monetary gains and losses to a measure of subjective utility. The major difference between this value function and 47 conventional subjective utility is that it is applied to changes – that is gains and losses – rather than to final states. A typical value function is shown in diagram 3. As will be seen, it is concave for gains and convex for losses, and it is steeper for losses than for gains. Since the value function is different for different reference points (amounts of present wealth), it should in principle be treated as a function of two arguments, v(w, x), where w is the present state of wealth.

Variations of expected utility A large number of models for decision-making under risk have been developed, most of which are variations or generalizations of EU theory. 1 Process utilities and regret theory In EU, an option is evaluated according to the utility that each outcome has irrespectively of what the other possible outcomes are. However, these are not the only values that may influence decision-makers. A decision-maker may also be influenced by a wish to avoid uncertainty, by a wish to gamble or by other wishes that are related to expectations or to the relations between the actual outcome and other possible outcomes, rather than to the actual outcomes as such.

Under the broader interpretation of the consequences, which incorporates non-monetary considerations such as regret utility theory remains intact... In the absence of any constraints, the consequences can always be interpreted so as to satisfy the axioms. In this case, however, the theory becomes empty from both descriptive and normative standpoints. " (Tversky 1975, p. 171) This line of criticism may be valid against GEU in its most general form, with no limits to the numbers and types of process utilities.

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