C81COG: Cognitive Psychology 1 PROBABILISTIC REASONING Dr. Alastair D. Smith Room B22 – School of Psychology

Aims & Objectives Aims –This lecture will introduce some of the problems people have reasoning with uncertain information and some of the strategies they may use in such circumstances. Learning Objectives –Describe the availability heuristic, and give examples of biases in probability judgement that could be caused by people using it. –Describe the representativeness heuristic, and give examples of biases in judgement that could be caused by people using it. –Give examples where the way in which a question is framed can change the degree of bias observed. –Contrast situations in which people correctly use base-rate information with those in which they do not.

Normative and Human Reasoning Real problems often only include probable information, not certainties. Nonetheless there is often a mathematically correct way of making the best possible decision based on parts of probability theory e.g. Bayes Theorem. These calculations provide normative answers to probabilistic questions. Much psychological research has looked at situations where human reasoning is not normative. Kahneman & Tversky looked systematically at some of the situations where human reasoning is biased. They proposed that these biases come about because people often use heuristics (cognitive short-cuts) to answer complex probabilistic questions.

The Representativeness Heuristic Kahneman & Tversky (1972) The likelihood of an event is evaluated by the degree to which it is representative of the major characteristics of the process or population from which it originated. –e.g. Sequences of Heads and Tails. Experimental demonstrations: Judging professions from brief character descriptions (Kahneman & Tversky, 1973) A box contains 100 brief descriptions of people, 30 of the descriptions are of engineers, 70 of the descriptions are of lawyers. Subjects draw cards out of the box, read the description, and have to guess whether the person described is a lawyer or an engineer.

The Representativeness Heuristic Jack is a 45-year-old man. He is married and has four children. He is generally conservative, careful, and ambitious. He shows no interest in political and social issues and spends most of his free time on his many hobbies which include home carpentry, sailing, and mathematical puzzles. Probability: Lawyer / Engineer _________ Dick is a 30-year-old man. He is married with no children. A man of high ability and high motivation, he promises to be quite successful in his field. He is well liked by his colleagues. Probability: Lawyer / Engineer _________ A blank card with no description. Probability: Lawyer / Engineer _________

The Representativeness Heuristic Linda is 31 years old, single, outspoken and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-war demonstrations. –Linda is a bank teller. –Linda is a bank teller and is active in the feminist movement. –90% of subjects feel that Linda is more likely to be a feminist bank teller than just a bank teller.

The Representativeness Heuristic The conjunction or co-occurrence of two events cannot be more likely than the probability of either event alone. AKA the conjunction fallacy. According to Tversky & Khaneman (1982) the fallacy occurs because specific scenarios appear more likely than general ones. This is because they are more representative of how we imagine them. Bank Tellers Feminists Feminist bank tellers As the amount of detail in a scenario increases, its probability can only decrease steadily, but its representativeness and hence its apparent likelihood may increase. (p. 98).

The Representativeness Heuristic The gamblers fallacy: The mistaken belief that future tosses of a coin (or some other random event) are influenced by past events. –Possible consequence - expecting a losing streak to end Kahneman & Tversky (1972) Proposed that some sequences of events represent our conception of randomness better than others. ? What comes next?

The Representativeness Heuristic The representativeness heuristic gives rise to the gamblers fallacy by means of the law of small numbers. –The belief that a successful outcome is due after a run of bad luck, or that tails is more likely after a run of heads. –More formally, that a series of independent trials with the same outcome will be followed by an opposite outcome sooner than expected by chance. ? What comes next?

The Availability Heuristic Which of the following are more likely : –Being killed by a shark? –Being killed by falling airplane parts? –Diabetes –Murder –Tornado –Lightening –Car accident –Stomach cancer Most people get these wrong because more information available about the wrong answer, largely because of media coverage. In short it is a memory effect. The availability heuristic is a rule of thumb in which decision- makers: assess the frequency of a class or the probability of an event by the ease with which instances or occurrences can be bought to mind. (Tversky & Kahneman,1974, p. 1127)

The Availability Heuristic Judged Frequency of Lethal Events (Lichtenstein et al., 1978)

The Availability Heuristic Combs & Slovic (1979) looked at the actual reporting of different forms of death in newspapers. Although diseases killed 16 times as many people as accidents, the newspapers reported 7 times more people dying through accidents than disease. Percentage of work on a Thesis: (Ross & Sicoly, 1979). Individuals tend to overestimate their relative contributions to collaborative endeavours. Thus, the sum of group members estimates of the percentage they each contributed to a joint task typically exceeds the logically allowable 100%. All things considered I was responsible for ___ percent of the entire research effort. Mean for I: _______% Mean for supervisor: _______% Note : The way we frame the question affects the result we obtain.

The Availability Heuristic Tversky & Kahneman (1973) asked participants which of the following was more frequent: –A word in English has K as the 1 st letter –A word in English has K as the 3 rd letter 69% answered incorrectly. In fact, there are twice as many words with K as the 3rd letter as there are with K as the 1 st. Tversky & Kahneman argue that because our lexicon is organised by spelling (or at least phonetics) more words beginning with K are available for retrieval.

Base rate neglect Consider the following problem from Tversky & Kahneman (1982): –A cab was involved in a hit and run accident at night. Two cab companies, the Green and the Blue, operate in the city. You are given the following data : 85% of the cabs in the city are green and 15% are blue. A witness identified the cab as blue. The court tested the reliability of the witness under the same circumstances that existed on the night of the accident and concluded that the witness correctly identified each one of the two colours 80% of the time and failed 20% of the time. –What is the probability that the cab involved in the accident was blue rather than green?

Base rate neglect Prior probability =.15 (proportion of blue cabs) Witness hit rate =.80 (identified correct colour) Witness false alarm rate =.20 (failed to identify correct colour) Witness sees a green taxi and mistakenly call it blue =.85 x.20 =.17 Witness sees a blue taxi and correctly identifies it =.15 x.80 =.12 Thus, given the witness reports a blue cab (this happens =.29 of the time) the probability that the taxi was blue = 12/(12+17)=.41 However, people tend to think that the taxi was more likely to be blue than green ie >.50, and many say p =.80. Kahneman & Tversky attributed this error to the representativeness heuristic. –Participants focus on the witness accuracy and neglect the base rate of cabs in the city.

Base rate neglect The medical diagnosis problem –Casscells et al (1978) asked medical students the following question: –If a test is to detect a disease whose prevalence is 1/1000 has a false positive rate of 5%, what is the chance that a person found to have a positive result actually has the disease? Assuming that you know nothing about the persons symptoms or signs: __% –18% responded 2% the correct Bayesian inference. –45% responded 95% the response that ignores the base rate. –Thus even medical students ignore base rates for diagnosis problems. This is normally attributed to the representativeness heuristic.

Base rate neglect Cosmides & Tooby (1996) presented the problem in both probability and frequency formats: –1 out of every 1000 Americans has disease X. A test has been developed to detect when a person has disease X. Every time the test is given to a person who has the disease, the test comes out positive (i.e., the "true positive" rate is 100%). But sometimes the test also comes out positive when it is given to a person who is completely healthy. Specifically, out of every 1000 people who are perfectly healthy, 50 of them test positive for the disease (i.e., the "false positive" rate is 5%). Imagine that we have assembled a random sample of 1000 Americans. They were selected by a lottery. Those who conducted the lottery had no information about the health status of any of these people. –Given the information above: on average, How many people who test positive for the disease will actually have the disease? __ out of __

Base rate neglect

Conclusions There are many situations where people fail to respond normatively when required to make probabilistic judgements. This may be because they are using heuristics such as availability and representativeness. Often framing the question differently can make people behave more normatively. Even though people fail to respond normatively in laboratory studies, they may still behave rationally in real situations.

Sample Questions People tend to neglect base rate information when: –The problem is presented in terms of probabilities –The problem is presented in terms of frequencies –Because they are biased by the availability heuristic –Because they use the information available to them The conjunction fallacy is occurs because: –specific scenarios appear less likely than general ones –of base-rate neglect –The availability heuristic –specific scenarios appear more likely than general ones

Reading –Eysenck (1998). Psychology: An integrated approach. Chapter 8. –Smyth, et al.. (1994). Cognition in action (2nd Edition), Chapter 13. –Anderson (1995). Cognitive psychology and its implications (4th Edition). Chapter 10. –Garnham & Oakhill (1994). Thinking and reasoning. Chapter 9.