2 7 1D e c i s i o n s U n d e r I g n o r a n c eAnother problem is that the maximax and maximin rules do not take
probabilities into account at all. This makes sense when you know nothing
about the probabilities. But when some (even if limited) information about
probabilities is available, then it seems better to use as much information
as you have. Suppose, for example, that each of two options might lead to
disaster, and you do not know how likely a disaster is after either option, but
you do know that one option is more likely to lead to disaster than another.
In such situations, some decision theorists argue that you should choose the
option that minimizes the chance that any disaster will occur. This is called
the disaster avoidance rule.
To illustrate this rule, consider a different kind of case:
A forty-year-old man is diagnosed as having a rare disease and consults
the world’s leading expert on the disease. He is informed that the disease
is almost certainly not fatal but often causes serious paralysis that leaves its
victims bedridden for life. (In other cases it has no lasting effects.) The disease
is so rare that the expert can offer only a vague estimate of the probability of
paralysis: 20 to 60 percent. There is an experimental drug that, if administered
now, would almost certainly cure the disease. However, it kills a significant
but not accurately known percentage of those who take it. The expert guesses
that the probability of the drug being fatal is less than 20 percent, and the
patient thus assumes that he is definitely less likely to die if he takes the drug
than he is to be paralyzed if he lets the disease run its course. The patient
would regard bedridden life as preferable to death, but he considers both
outcomes as totally disastrous compared to continuing his life in good health.
Should he take the drug?^2
Since the worst outcome is death, and this outcome will not occur unless
he takes the drug, the maximin rule would tell him not to take the drug. In
contrast, the disaster avoidance rule would tell him to take the drug,
because both death and paralysis are disasters and taking the drug mini-
mizes his chances that any disaster will occur. Thus, although the disaster
avoidance rule opposes risk taking, it does so in a different way than the
maximin rule.
We are left, then, with a plethora of rules: dominance, insufficient rea-
son, maximax, maximin, and disaster avoidance. Other rules have been
proposed as well. With all of these rules in the offing, it is natural to ask
which is correct. Unfortunately, there is no consensus on this issue. Each
rule applies and seems plausible in some cases but not in others. Many peo-
ple conclude that each rule is appropriate to different kinds of situations. It
is still not clear, however, which rule should govern decisions in which cir-
cumstances. The important problem of decision under ignorance remains
unsolved.97364_ch12_ptg01_263-272.indd 271 15/11/13 11:00 AM
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