Dictionary of Evidence-based Medicine.pdf

Dictionary of Evidence-based Medicine 159
forgo to regain complete health; (iii) standard gamble whereby patients are
asked to choose between living the rest of their lives in their current state
or a gamble which, if won, will mean perfect health and, if lost, will mean
death. The probability of winning the gamble is altered until the point of
indifference is reached.
Utility theory
Utility theory or expected utility theory is a formal model, first proposed
by von Neumann and Morgenstern to deal with choice in the presence of
risk. They described a set of axioms (see below) for characterizing rational
behaviour and proposed a strategy for choosing among alternatives under
such circumstances.
When measuring utilities, the person's risk preference is assumed to
follow the following five axioms:
• Completeness. When choosing between two outcomes (o v o 2 ) there are
three possibilities: o a is preferred to o 2 , neither is preferred or o 2 is
preferred to o r
• Transitivity. If o a is preferred to o 2 and o 2 is preferred to o 3 , then o l should
be preferred to o 3 . Likewise, if o 2 and o l are considered equivalent and
o 3 and o 2 are considered similarly, then o a and o 3 should be equivalent
too.
• Continuity. If o l is preferred to o 2 and o 2 to o 3/ then there exists a
probability p that the lottery shown in Figure 27 is preferred to the
certainty of receiving outcome o 2 .
• Independence (or substitution). If o l and o 2 are equally attractive under
conditions of certainty, then the lottery shown in Figure 27 and the
lottery shown in Figure 28 will be equally attractive for any value of p
oro 3 .
• Reduction of compound lotteries. A lottery whose initial outcomes are themselves
lotteries (i.e. a compound lottery) is as attractive as the simple
lottery that is obtained when multiplying through probabilities as
shown in Figures 29 and 30.
From those axioms, the expected utility (EU) theorem follows: a utility
function U can be defined on the outcomes with the property that a choice
with a higher expected utility is always preferred to one with a lower
expected utility (von Neumann J, Morgenstern O (1947) Theory of games and
economic behavior. 2nd edn. John Wiley, New York).