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Speaking of Losses
“This reform will not pass. Those who stand to lose will fight harder than those who
stand to gain.”
“Each of them thinks the other’s concessions are less painful. They are both wrong,
of course. It’s just the asymmetry of losses.”
“They would find it easier to renegotiate the agreement if they realized the pie was
actually expanding. They’re not allocating losses; they are allocating gains.”
“Rental prices around here have gone up r Brro Qup r Brrecently, but our tenants
don’t think it’s fair that we should raise their rent, too. They feel entitled to their
current terms.”
“My clients don’t resent the price hike because they know my costs have gone up,
too. They accept my right to stay profitable.”
P
The Fourfold Pattern
Whenever you form a global evaluation of a complex object—a car you may buy, your
son-in-law, or an uncertain situation—you assign weights to its characteristics. This is
simply a cumbersome way of saying that some characteristics influence your assessment
more than others do. The weighting occurs whether or not you are aware of it; it is an
operation of System 1. Your overall evaluation of a car may put more or less weight on
gas economy, comfort, or appearance. Your judgment of your son-in-law may depend
more or less on how rich or handsome or reliable he is. Similarly, your assessment of an
uncertain prospect assigns weights to the possible outcomes. The weights are certainly
correlated with the probabilities of these outcomes: a 50% chance to win a million is much
more attractive than a 1% chance to win the same amount. The assignment of weights is
sometimes conscious and deliberate. Most often, however, you are just an observer to a
global evaluation that your System 1 delivers.
Changing Chances
One reason for the popularity of the gambling metaphor in the study of decision making is
that it provides a natural rule for the assignment of weights to the outcomes of a prospect:
the more probable an outcome, the more weight it should have. The expected value of a
gamble is the average of its outcomes, each weighted by its probability. For example, the
expected value of “20% chance to win $1,000 and 75% chance to win $100” is $275. In
the pre-Bernoulli days, gambles were assessed by their expected value. Bernoulli retained
this method for assigning weights to the outcomes, which is known as the expectation
principle, but applied it to the psychological value of the outcomes. The utility of a
gamble, in his theory, is the average of the utilities of its outcomes, each weighted by its
probability.
The expectation principle does not correctly describe how you think about the
probabilities related to risky prospects. In the four examples below, your chances of
receiving $1 million improve by 5%. Is the news equally good in each case?
A. From 0 to 5%
B. From 5% to 10%
C. From 60% to 65%
D. From 95% to 100%
The expectation principle asserts that your utility increases in each case by exactly 5% of
the utility of receiving $1 million. Does this prediction describe your experiences? Of
course not.
Everyone agrees that 0 5% and 95% 100% are more impressive than either 5%
10% or 60%
65%. Increasing the chances from 0 to 5% transforms the situation,
creating a possibility that did not exist earlier, a hope of winning the prize. It is a
qualitative change, where 5 10% is only a quantitative improvement. The change from
5% to 10% doubles the probability of winning, but there is general agreement that the
psychological value of the prospect does not double. The large impact of 0
5%
illustrates the
possibility effect
, which causes highly unlikely outcomes to be weighted
disproportionately more than they “deserve.” People who buy lottery tickets in vast
amounts show themselves willing to pay much more than expected value for very small
chances to win a large prize.
The improvement from 95% to 100% is another qualitative change that has a large
impact, the
certainty effect
. Outcomes that are almost certain are given less weight than
their probability justifies. To appreciate the certainty effect, imagine that you inherited $1
million, but your greedy stepsister has contested the will in court. The decision is expected
tomorrow. Your lawyer assures you that you have a strong case and that you have a 95%
chance to win, but he takes pains to remind you that judicial decisions are never perfectly
predictable. Now you are approached by a risk-adjustment company, which offers to buy
your case for $910,000 outright—take it or leave it. The offer is lower (by $40,000!) than
the expected value of waiting for the judgment (which is $950,000), but are you quite sure
you would want to reject it? If such an event actually happens in your life, you should
know that a large industry of “structured settlements” exists to provide certainty at a heft y
price, by taking advantage of the certainty effect.
Possibility and certainty have similarly powerful effects in the domain of losses.
When a loved one is wheeled into surgery, a 5% risk that an amputation will be necessary
is very bad—much more than half as bad as a 10% risk. Because of the possibility effect,
we tend to overweight small risks and are willing to pay far more than expected value to
eliminate them altogether. The psychological difference between a 95% risk of disaster
and the certainty of disaster appears to be even greater; the sliver of hope that everything
could still be okay looms very large. Overweighting of small probabilities increases the
attractiveness of both gambles and insurance policies.
The conclusion is straightforward: the decision weights that people assign to
outcomes are not identical to the probabilities of these outcomes, contrary to the
expectation principle. Improbable outcomes are overweighted—this is the possibility
effect. Outcomes that are almost certain are underweighted relative to actual certainty. The
expectation principle
, by which values are weighted by their probability, is poor
psychology.
The plot thickens, however, because there is a powerful argument that a decision
maker who wishes to be rational
must
conform to the expectation principle. This was the
main point of the axiomatic version of utility theory that von Neumann and Morgenstern
introduced in 1944. They proved that any weighting of uncertain outcomes that is not
strictly proportional to probability leads to inconsistencies and other disasters. Their
derivation of the expectation principle from axioms of rational choice was immediately
recognized as a monumental achievement, which placed expected utility theory at the core
of the rational agent model in economics and other social sciences. Thirty years later,
when Amos introduced me to their work, he presented it as an object of awe. He also
introduced me Bima a me Bimto a famous challenge to that theory.
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