21% chance (or 84% chance) to spend a weekend painting someone’s three-bedroom apartment
21% chance (or 84% chance) to clean three stalls in a dormitory bath Bmun qbath Bmuroom after a weekend of use
The second outcome is surely much more emotional than the first, but the decision weights for the two outcomes did not differ. Evidently, the intensity of emotion is not the answer.
Another experiment yielded a surprising result. The participants received explicit price information along with the verbal description of the prize. An example could be:
84% chance to win: A dozen red roses in a glass vase. Value $59.
21% chance to win: A dozen red roses in a glass vase. Value $59.
It is easy to assess the expected monetary value of these gambles, but adding a specific monetary value did not alter the results: evaluations remained insensitive to probability even in that condition. People who thought of the gift as a chance to get roses did not use price information as an anchor in evaluating the gamble. As scientists sometimes say, this is a surprising finding that is trying to tell us something. What story is it trying to tell us?
The story, I believe, is that a rich and vivid representation of the outcome, whether or not it is emotional, reduces the role of probability in the evaluation of an uncertain prospect. This hypothesis suggests a prediction, in which I have reasonably high confidence: adding irrelevant but vivid details to a monetary outcome also disrupts calculation. Compare your cash equivalents for the following outcomes:
21% (or 84%) chance to receive $59 next Monday
21% (or 84%) chance to receive a large blue cardboard envelope containing $59 next Monday morning
The new hypothesis is that there will be less sensitivity to probability in the second case, because the blue envelope evokes a richer and more fluent representation than the abstract notion of a sum of money. You constructed the event in your mind, and the vivid image of the outcome exists there even if you know that its probability is low. Cognitive ease contributes to the certainty effect as well: when you hold a vivid image of an event, the possibility of its not occurring is also represented vividly, and overweighted. The combination of an enhanced possibility effect with an enhanced certainty effect leaves little room for decision weights to change between chances of 21% and 84%.
Vivid Probabilities
The idea that fluency, vividness, and the ease of imagining contribute to decision weights gains support from many other observations. Participants in a well-known experiment are given a choice of drawing a marble from one of two urns, in which red marbles win a prize:
Urn A contains 10 marbles, of which 1 is red.
Urn B contains 100 marbles, of which 8 are red.
Which urn would you choose? The chances of winning are 10% in urn A and 8% in urn B, so making the right choice should be easy, but it is not: about 30%–40% of students choose the urn Bmun q urn Bmu with the larger number of winning marbles, rather than the urn that provides a better chance of winning. Seymour Epstein has argued that the results illustrate the superficial processing characteristic of System 1 (which he calls the experiential system).
As you might expect, the remarkably foolish choices that people make in this situation have attracted the attention of many researchers. The bias has been given several names; following Paul Slovic I will call it denominator neglect. If your attention is drawn to the winning marbles, you do not assess the number of nonwinning marbles with the same care. Vivid imagery contributes to denominator neglect, at least as I experience it. When I think of the small urn, I see a single red marble on a vaguely defined background of white marbles. When I think of the larger urn, I see eight winning red marbles on an indistinct background of white marbles, which creates a more hopeful feeling. The distinctive vividness of the winning marbles increases the decision weight of that event, enhancing the possibility effect. Of course, the same will be true of the certainty effect. If I have a 90% chance of winning a prize, the event of not winning will be more salient if 10 of 100 marbles are “losers” than if 1 of 10 marbles yields the same outcome.
The idea of denominator neglect helps explain why different ways of communicating risks vary so much in their effects. You read that “a vaccine that protects children from a fatal disease carries a 0.001% risk of permanent disability.” The risk appears small. Now consider another description of the same risk: “One of 100,000 vaccinated children will be permanently disabled.” The second statement does something to your mind that the first does not: it calls up the image of an individual child who is permanently disabled by a vaccine; the 999,999 safely vaccinated children have faded into the background. As predicted by denominator neglect, low-probability events are much more heavily weighted when described in terms of relative frequencies (how many) than when stated in more abstract terms of “chances,” “risk,” or “probability” (how likely). As we have seen, System 1 is much better at dealing with individuals than categories.
The effect of the frequency format is large. In one study, people who saw information about “a disease that kills 1,286 people out of every 10,000” judged it as more dangerous than people who were told about “a disease that kills 24.14% of the population.” The first disease appears more threatening than the second, although the former risk is only half as large as the latter! In an even more direct demonstration of denominator neglect, “a disease that kills 1,286 people out of every 10,000” was judged more dangerous than a disease that “kills 24.4 out of 100.” The effect would surely be reduced or eliminated if participants were asked for a direct comparison of the two formulations, a task that explicitly calls for System 2. Life, however, is usually a between-subjects experiment, in which you see only one formulation at a time. It would take an exceptionally active System 2 to generate alternative formulations of the one you see and to discover that they evoke a different response.
Experienced forensic psychologists and psychiatrists are not immune to the effects of the format in which risks are expressed. In one experiment, professionals evaluated whether it was safe to discharge from the psychiatric hospital a patient, Mr. Jones, with a history of violence. The information they received included an expert’s assessment of the risk. The same statistics were described in two ways:
Patients similar to Mr. Jones are estimated to have a 10% probability of committing an act of violence against others during the first several months after discharge.
Of every 100 patients similar to Mr. Jones, 10 are estimated to commit an act of violence against others during the first several months after discharge.
The professionals who saw the frequency format were almost twice as likely to deny the discharge (41%, compared to 21% in the probability format). The more vivid description produces a higher decision weight for the same probability.
The power of format creates opportunities for manipulation, which people with an axe to grind know how to exploit. Slovic and his colleagues cite an article that states that “approximately 1,000 homicides a year are committed nationwide by seriously mentally ill individuals who are not taking their medication.” Another way of expressing the same fact is that “1,000 out of 273,000,000 Americans will die in this manner each year.” Another is that “the annual likelihood of being killed by such an individual is approximately 0.00036%.” Still another: “1,000 Americans will die in this manner each year, or less than one-thirtieth the number who will die of suicide and about one-fourth the number who will die of laryngeal cancer.” Slovic points out that “these advocates are quite open about their motivation: they want to frighten the general public about violence by people with mental disorder, in the hope that this fear will translate into increased funding for mental health services.”
A good attorney who wishes to cast doubt on DNA evidence will not tell the jury that “the chance of a false match is 0.1%.” The statement that “a false match occurs in 1 of 1,000 capital cases” is far more likely to pass the threshold of reasonable doubt. The jurors hearing th
ose words are invited to generate the image of the man who sits before them in the courtroom being wrongly convicted because of flawed DNA evidence. The prosecutor, of course, will favor the more abstract frame—hoping to fill the jurors’ minds with decimal points.
Decisions from Global Impressions
The evidence suggests the hypothesis that focal attention and salience contribute to both the overestimation of unlikely events and the overweighting of unlikely outcomes. Salience is enhanced by mere mention of an event, by its vividness, and by the format in which probability is described. There are exceptions, of course, in which focusing on an event does not raise its probability: cases in which an erroneous theory makes an event appear impossible even when you think about it, or cases in which an inability to imagine how an outcome might come about leaves you convinced that it will not happen. The bias toward overestimation and overweighting of salient events is not an absolute rule, but it is large and robust.
There has been much interest in recent years in studies of choice from experience, which follow different rules from the choices from description that are analyzed in prospect theory. Participants in a typical experiment face two buttons. When pressed, each button produces either a monetary reward or nothing, and the outcome is drawn randomly according to the specifications of a prospect (for example, “5% to win $12” or “95% chance to win $1”). The process is truly random, s Bmun qm, s Bmuo there is no guarantee that the sample a participant sees exactly represents the statistical setup. The expected values associated with the two buttons are approximately equal, but one is riskier (more variable) than the other. (For example, one button may produce $10 on 5% of the trials and the other $1 on 50% of the trials). Choice from experience is implemented by exposing the participant to many trials in which she can observe the consequences of pressing one button or another. On the critical trial, she chooses one of the two buttons, and she earns the outcome on that trial. Choice from description is realized by showing the subject the verbal description of the risky prospect associated with each button (such as “5% to win $12”) and asking her to choose one. As expected from prospect theory, choice from description yields a possibility effect—rare outcomes are overweighted relative to their probability. In sharp contrast, overweighting is never observed in choice from experience, and underweighting is common.
The experimental situation of choice by experience is intended to represent many situations in which we are exposed to variable outcomes from the same source. A restaurant that is usually good may occasionally serve a brilliant or an awful meal. Your friend is usually good company, but he sometimes turns moody and aggressive. California is prone to earthquakes, but they happen rarely. The results of many experiments suggest that rare events are not overweighted when we make decisions such as choosing a restaurant or tying down the boiler to reduce earthquake damage.
The interpretation of choice from experience is not yet settled, but there is general agreement on one major cause of underweighting of rare events, both in experiments and in the real world: many participants never experience the rare event! Most Californians have never experienced a major earthquake, and in 2007 no banker had personally experienced a devastating financial crisis. Ralph Hertwig and Ido Erev note that “chances of rare events (such as the burst of housing bubbles) receive less impact than they deserve according to their objective probabilities.” They point to the public’s tepid response to long-term environmental threats as an example.
These examples of neglect are both important and easily explained, but underweighting also occurs when people have actually experienced the rare event. Suppose you have a complicated question that two colleagues on your floor could probably answer. You have known them both for years and have had many occasions to observe and experience their character. Adele is fairly consistent and generally helpful, though not exceptional on that dimension. Brian is not quite as friendly and helpful as Adele most of the time, but on some occasions he has been extremely generous with his time and advice. Whom will you approach?
Consider two possible views of this decision:
It is a choice between two gambles. Adele is closer to a sure thing; the prospect of Brian is more likely to yield a slightly inferior outcome, with a low probability of a very good one. The rare event will be overweighted by a possibility effect, favoring Brian.
It is a choice between your global impressions of Adele and Brian. The good and the bad experiences you have had are pooled in your representation of their normal behavior. Unless the rare event is so extreme that it comes to mind separately (Brian once verbally abused a colleague who asked for his help), the norm will be biased toward typical and recent instances, favoring Adele.
In a two-system mind, the second interpretation a Bmun qon a Bmuppears far more plausible. System 1 generates global representations of Adele and Brian, which include an emotional attitude and a tendency to approach or avoid. Nothing beyond a comparison of these tendencies is needed to determine the door on which you will knock. Unless the rare event comes to your mind explicitly, it will not be overweighted. Applying the same idea to the experiments on choice from experience is straightforward. As they are observed generating outcomes over time, the two buttons develop integrated “personalities” to which emotional responses are attached.
The conditions under which rare events are ignored or overweighted are better understood now than they were when prospect theory was formulated. The probability of a rare event will (often, not always) be overestimated, because of the confirmatory bias of memory. Thinking about that event, you try to make it true in your mind. A rare event will be overweighted if it specifically attracts attention. Separate attention is effectively guaranteed when prospects are described explicitly (“99% chance to win $1,000, and 1% chance to win nothing”). Obsessive concerns (the bus in Jerusalem), vivid images (the roses), concrete representations (1 of 1,000), and explicit reminders (as in choice from description) all contribute to overweighting. And when there is no overweighting, there will be neglect. When it comes to rare probabilities, our mind is not designed to get things quite right. For the residents of a planet that may be exposed to events no one has yet experienced, this is not good news.
Speaking of Rare Events
“Tsunamis are very rare even in Japan, but the image is so vivid and compelling that tourists are bound to overestimate their probability.”
“It’s the familiar disaster cycle. Begin by exaggeration and overweighting, then neglect sets in.”
“We shouldn’t focus on a single scenario, or we will overestimate its probability. Let’s set up specific alternatives and make the probabilities add up to 100%.”
“They want people to be worried by the risk. That’s why they describe it as 1 death per 1,000. They’re counting on denominator neglect.”
Risk Policies
Imagine that you face the following pair of concurrent decisions. First examine both decisions, then make your choices.
Decision (i): Choose between
A. sure gain of $240
B. 25% chance to gain $1,000 and 75% chance to gain nothing
Decision (ii): Choose between
C. sure loss of $750
D. 75% chance to lose $1,000 and 25% chance to lose nothing
This pair of choice problems has an important place in the history of prospect theory, and it has new things to tell us about rationality. As you skimmed the two problems, your initial reaction to the sure things (A and C) was attraction to the first and aversion to the second. The emotional evaluation of “sure gain” and “sure loss” is an automatic reaction of System 1, which certainly occurs before the more effortful (and optional) computation of the expected values of the two gambles (respectively, a gain of $250 and a loss of $750). Most people’s choices correspond to the predilections of System 1, and large majorities prefer A to B and D to C. As in many other choices that involve moderate or high probabilities, people tend to be risk averse in the domain of gains and risk seeki
ng in the domain of losses. In the original experiment that Amos and I carried out, 73% of respondents chose A in decision i and D in decision ii and only 3% favored the combination of B and C.
You were asked to examine both options before making your first choice, and you probably did so. But one thing you surely did not do: you did not compute the possible results of the four combinations of choices (A and C, A and D, B and C, B and D) to determine which combination you like best. Your separate preferences for the two problems were intuitively compelling and there was no reason to expect that they could lead to trouble. Furthermore, combining the two decision problems is a laborious exercise that you would need paper and pencil to complete. You did not do it. Now consider the following choice problem:
AD. 25% chance to win $240 and 75% chance to lose $760
BC. 25% chance to win $250 and 75% chance to lose $750
This choice is easy! Option BC actually dominates option AD (the technical term for one option being unequivocally better than another). You already know what comes next. The dominant option in AD is the combination of the two rejected options in the first pair of decision problems, the one that only 3% of respondents favored in our original study. The inferior option BC was preferred by 73% of respondents.
Broad or Narrow?
Thinking, Fast and Slow Page 39