Read the following problem, what is your intuitive answer?

“Last night, a bus was involved in a traffic accident. Two bus companies, the Yellow and the Brown, operate in the area. 80% of the busses are Yellow and 20% are Brown. A witness declared the bus being Brown. The reliability of the witness in similar circumstances was tested: the witness correctly identified each color 75% of the time and failed 25% of the time. What is the probability that the bus was Brown?”

There are two pieces of information: a base rate and the not fully reliable testimony of the witness. Without the witness, the probability of the bus being Brown is 20%: the base rate. If the bus companies had been equally large, the base rate would be useless (50/50) and merely the reliability of the witness would be considered. Most people ignore the base rate and answer 75%. Both sources of information should have been combined by the probability rule of Bayes.

Now consider the following story, in which the base rate is differently presented. “The two bus companies operate the same number of busses, but Yellow busses are involved in 80% of traffic accidents”. The versions are psychologically different, although they are mathematically the same. People who read the first story tend to ignore the base rate, because they don’t know what to do with it. The base rate regards the number of Yellow and Brown busses in the area, which does not explain the bus driver getting into an accident. People who read the second version give more weight to the base rate, their judgments are closer to the right answer. Drivers of Brown busses cause four times as many accidents, which leads to the instant conclusion that Brown drivers are dangerous drivers. You have formed a stereotype of Brown drivers, which fits easily into a causal story.

The bus examples demonstrates two types of base rates: statistical base rates (irrelevant facts about a population) and causal base rates. Statistical base rate are often underweighted or even neglected when specific information about the individual case is available. Causal base rates are used as information about a concrete case and are easily combined with other relevant facts. The causal version of the bus problem was formulated as a stereotype. Stereotypes: statements about a group that are accepted as facts about individual members. System 1 is known for representing categories as prototypical exemplars and norms, our memory holds a representation of one or more regular members of a category (cats, blenders). A representation is called a stereotype when the category is social. In the bus problem, stereotyping the Brown drivers improved the accuracy of judgment. In other cases, like profiling or hiring, stereotyping is seen as morally (and lawfully) wrong and causal base rates get rejected. However, rejecting valid stereotypes results in judgments that are not optimal. It might be politically correct, but it is not costless.

The concept of causal base rates was proposed by psychologist Ajzen. His experiment contained a manipulation of causal base rates. He showed the participants short descriptions of university students who had taken a test and asked them to judge the probability that an individual student had passed it. Manipulation: one group was told that 75% of the class passed the test, the other group was told 25% passed. The base rate of passing indicates that the test that 25% students passed must have been extremely difficult. The difficulty level is only one causal factor that determines an individual students’ result. The participants were very sensitive to the causal base rates. The probability of every student passing was judged much higher in the successful class. A merely statistical base rate had less influence on their judgments. This proves that System 1 performs poorly in statistical reasoning, it is better at dealing with stories in which the elements are causally connected.

The bus driver and the difficult test experiments demonstrate that stereotypical traits of individuals and a significant feature of a situation that influences individual outcomes are two inferences that are drawn from causal base rates. The well-known ‘helping experiment’ illustrates that people won’t draw inferences from base-rate information if they conflict with other beliefs. It also suggests that teaching psychology is hard. Participants sat in individual boots and spoke over an intercom about their lives. They had to talk in turns, the microphones of others were switched off when someone was talking. Among the participants was one that followed instructions from the researchers. He faked getting a seizure, asked for help and said he was going to die. Then his microphone was switched off, as his speaking time was over. The participants knew someone needed help and that there were others who could provide it. Only four out of fifteen responded instantly to the cry for help. Five came out when it would have been too late and six never left their booth. This shows that people feel relieved of responsibility when they know that other people heard to same appeal for help. This is surprising, because we tend to see ourselves as decent people who would immediately help others in need. This expectation proved to be wrong, which is something psychology teachers try to make their students aware of. It is, however, not easy to (negatively) change their minds about human nature and our behavior in certain situations.

Borgida and Nisbett expected that students would be able to recite the findings of the helping experiment, but doubted it would actually change their beliefs about human nature. They showed the students videos of short interviews with two participants of the helping experiment. They came across as kind, decent and normal. The students were asked to guess how quickly the interviewees had offered help. Following the Bayes’ rule means starting with asking yourself what your guess would be if you had not seen the videos: what is the base rate? 4 out of 15 participants rushed to help, so the probability of any participant immediately responding is 27%. The next step is adjusting your judgment if there is relevant information. The videos provided no relevant information about the helpfulness of the participants, so you need to stay near the base rates. One group of students was told about both the procedure of the helping experiment and its outcome. The other group was not told about the outcome, the prediction of the students in this group was that both participants would instantly rush to help. The group that knew the outcome gave the same prediction, statistics did not matter at all. Despite knowing the base rate, the videos convinced them the participants would rush to help. Conclusion: psychology is hard to teach. What might help is surprising students with individual cases, like telling them that two nice people did not help.