Thinking and Deciding

OTHER BIASES IN RISK JUDGMENTS 509
Proportions versus differences
An opposite effect seems to happen when people consider changes in risk. They
worry more about the proportion of risk reduced than about the number of people
helped. But utilitarianism implies that the number is what matters, because each
person’s good is independent of the good of others; each person must be considered
as a unique individual. Likewise, expected-utility theory says that the number is
what matters, because number translates into probability for a single person, and
differences in probability are the relevant measures (p. 498).
This may be part of a more general confusion about quantities. Small children
confuse length and number, so that, when we ask them to compare two arrays for
length or number, they will answer with little regard to which question we asked
(Baron, Lawson, and Siegel, 1975). In general, they tend to answer as if they were
asked about length when the number of items in the array is larger than they can
count easily, so they are correct when asked which array is longer but incorrect if
asked which array has more items. When the number of items is small, for example,
three to five items, they are correct when asked which has more but incorrect when
asked which is longer. Similar quantitative confusions are found in older children
and adults. As noted in Chapter 6, older children and even adults are confused about
probability, so that they answer probability questions according to frequency rather
than relative frequency.
News media and perhaps even scientific journals confuse other quantities. Newspapers
often tell us that “inflation increased by 2.9%” when they mean that prices
increased by this much. The literature on risk effects of pollutants and pharmaceuticals
commonly reports relative risk, the ratio of the risk with the agent to the risk
without it, rather than the difference. Yet, the difference between the two risks, not
their ratio, is most relevant for decision making: If a baseline risk of injury is 1 in
1,000,000, then twice that risk is still insignificant; but if the risk is 1 in 3, a doubling
matters much more.
Stone, Yates, and Parker (1994) found that relative risk information, as opposed
to full information about the two absolute risks involved, made people more willing
to pay for safety when risks were small. Fetherstonhaugh, Slovic, Johnson, and
Friedrich (1997) found that people placed more value on saving lives when the lives
saved were a larger proportion of those at risk. For example, subjects were told about
two programs to save Rwandan refugees from cholera by providing clean water. The
two programs cost about the same and both would save about 4,500 lives. One
program would take place in a refugee camp with 250,000 refugees; the other, in a
camp with 11,000. Subjects strongly preferred the program in the smaller camp.
I have suggested that these results were the result of quantitative confusion between
relative and absolute risk (Baron, 1997b). In one study, subjects expressed
their willingness to pay (WTP) to reduce eighteen causes of death (heart disease,
stroke, chronic liver disease, etc.) by 5% or by 2,600 people, in the United States.
The typical (median) responses to these two questions correlated .96. Some causes of
death were much more likely than others. For example, heart disease is about twenty