Judgement and decision making

• Judgement refers to the way in which people “integrate multiple, incomplete, and sometimes conflicting cues to infer what is happening in the external world” (Hastie, 2001, on Canvas).
• Of 1000 people who are pinged and have symptoms, maybe 400 have the disease, so chance she has COVID, given a positive test, is now 400/412 (400 have COVID and test +; 12 don’t have COVID and test +).
• Decision making is a wider process that includes judgement as a part: “How do people choose what action to take to achieve labile, sometimes conflicting goals in an uncertain world?” (also Hastie, 2001).
• Bayes’ theorem (how you modify your beliefs according to the evidence you collect)
• p(H after E) = p(H before E) x p(E if H was true) / p(E whether H true or not).
• Bayes’ theorem can be summarized as: You should believe a hypothesis to the extent that it is credible to start with, to the extent to which the evidence at hand is consistent with it, and to the extent that that evidence is not consistent with loads of other (more) plausible hypotheses.
• Of the taxi-cabs in the city, 85% belonged to the Green company and 15% to the Blue company.
• However, when her ability to identify cabs under appropriate visibility conditions was tested, she was wrong 20% of the time.
• Koehler (1996) summarized that base-rate information is almost always used to some extent in experiments but is less often used in everyday life, possibly because in the real world, there are often numerous base rates and many of these are conflicting.
• Cosmides & Tooby (1996) found that base-rate neglect was minimized when frequencies were used, as opposed to probabilities.
• In a causal condition, the problem was rephrased, stating that although taxi firms were equal in size, 85% of the accidents involved Green cabs.
• Base-rate information is often neglected in everyday life, as there are often numerous base rates and many of these are conflicting.
• In the absence of any other evidence, the probability of having COVID is about 1/21 if you test positive, but if you have symptoms, the probability increases to about 1/2.
• Base rates are not so neglected in this example, but they are still neglected somewhat.
• People often fail to take base rates fully into account.
• Even experts are not immune to failing to take base rate into account.
• Tversky and Kahneman (1982) found that participants in a taxi cab problem said there was an 80% likelihood that the taxi was Blue, but only took into account the testimony, not the base rate.
• Koehler (1996) defined base-rate information as “The relative frequency with which an event occurs or an attribute is present in the population”.
• Hoffrage et al. (2000) found that advanced medical students made percentage correct inferences in four realistic diagnostic tasks expressed in probabilities or frequencies.
• The probability that the cab was Blue is calculated as: The prior probability you would have said it was blue before you got the woman’s evidence (15% or 0.15) multiplied by the probability that she would have given her evidence if it was Blue (80% or 0.8) divided by how often (weighted by the prior probability) she would have said it was Blue under the various different possibilities.
• If it was Blue and she called it Blue (0.15 x 0.8) = 0.12.
• If it was Green and she called it Blue (0.85 x 0.2) = 0.17 (percentage of green 85% x probability it would be green according to her evidence 20%).
• So prob (Blue) = 0.15*0.8/(0.12+0.17) = 0.41 or 41%.
• Even given the eye-witness evidence, it’s more likely the cab was Green.
• Natural sampling is what generally happens in everyday life.
• It is assumed that as a result of our evolutionary history we find it easy to work out the frequencies of different kinds of events.
• In the real world, we actually encounter only a sample of events, which might be unrepresentative.
• Heuristics are useful “rules of thumb” that you can use to make quick judgements, without going through a big palaver of working something out in detail.
• These are a bit like the “constructivist” models that we saw earlier in the course.
• Heuristics often work well, and therefore save us time overall (compare non-accidental properties).
• On the other hand, heuristics sometimes lead us astray (compare with assumptions causing visual illusions).
• Kahneman & Tversky suggested that people often use a representativeness heuristic (rule-of-thumb): “events that are representative or typical of a class are assigned a high probability of occurrence.
• If an event is highly similar to most of the others in a population or class of events, then it is considered representative” (Kellogg, 1995).
• Redelmeier et al (1995) found that subjective probabilities are higher for explicit descriptions even with experts, comparing doctors making more explicit or less explicit diagnoses of a particular abdominal pain.
• Johnson et al (1993) found evidence that Ss offered to pay more for insurance policies that covered a detailed range of illnesses, than for one that covered all illnesses.
• Tversky and Kahneman (1974) proposed that if a word of three letters or more is sampled at random from an English text, it is more likely that the word starts with “r” than has “r” as its third letter.
• The numerosity heuristic involves over-inferring quantity or amount from numerosity, such as the number of units into which something is divided.
• The conjunction fallacy states that it is more likely that Linda is a bank teller than a feminist bank teller because she is a bank teller.
• Tversky and Koehler (1994) proposed their support theory, which states that any given event will appear more or less likely depending on how it is described.
• The availability heuristic is the process of estimating the frequencies of events on the basis of how easy or difficult it is to retrieve relevant information from long-term memory.