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114 Decision making under uncertainty
Figure 5.10
Figure 5.11
Figure 5.12
Lottery 1:
Lottery 3:
1.0
Lottery 1: B Lottery 2:
1.0
Lottery 1: X Lottery 2:
1.0
0.6
0.4
$30000
$30000
(a)
Lottery 2:
Lottery 4:
0.85
0.15
0.6
p
1 − p
p
1 − p
A
C
Y
Z
$60000
−$10000
0.85
0.15
$11000
0.4
$11000
(b)
$60000
−$10000
appears as a reward in another lottery it can always be substituted by
lottery 2 because the decision maker regards X and lottery 2 as being
equally preferable. For example, the conference organizer indicated that
she was indifferent between the lotteries shown in Figure 5.12(a). If the
substitution axiom applies, she will also be indifferent between lotteries 3
and 4, which are shown in Figure 5.12(b). Note that these lotteries are
identical, except that in lottery 4 we have substituted lottery 2 for the
$30 000. Lottery 4 offers a 0.6 chance of winning a ticket in another lottery
and is therefore referred to as a compound lottery.
Axiom 5: Unequal probability axiom
Suppose that a decision maker prefers reward A to reward B. Then,
according to this axiom, if he is offered two lotteries which only offer
rewards A and B as possible outcomes he will prefer the lottery offering