Heuristics and Biases

Normative Model Bayes rule tells you how you should reason with probabilities – it is a normative model But do people reason like Bayes? Prior probability Evidence Posterior Probability

Tversky & Kahneman According to Tversky & Kahneman, Bayesian decision theory does not describe human decision making very well  Bayes rate neglect, Conservatism Instead, much of decision making may be based on Biases and heuristics (mental short-cuts) Heuristics lower cognitive load and often work, but results in severe errors in some cases Examples –Representativeness heuristic –Availability heuristic

The Taxi Problem A witness sees a crime involving a taxi in Carborough. The witness says that the taxi is blue. It is known from previous research that witnesses are correct 80% of the time when making such statements. What is the probability that a blue taxi was involved in the crime?

The Taxi Problem A witness sees a crime involving a taxi in Carborough. The witness says that the taxi is blue. It is known from previous research that witnesses are correct 80% of the time when making such statements. The police also know that 15% of the taxis in Carborough are blue, the other 85% being green. What is the probability that a blue taxi was involved in the crime?

Base Rate Neglect: The Taxi Problem Failure to take prior probabilities (i.e., base rates) into account In the taxi story, the addition of: “The police also know that 15% of the taxis in Carborough are blue, the other 85% being green.” has little influence on rated probability

Base Rate Neglect (2) Kahneman & Tversky (1973). Names of 100 engineers and lawyers are written on cards and put in a container. What is probability of picking an engineer in from container A and B? Container A: 70 engineers and 30 lawyers Container B: 30 engineers and 70 lawyers People can estimate these probabilities …

Providing additional information “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” What now is probability Jack is an engineer? For both container A and B, the estimate was P =.9 Where did the base rate go?

Conservatism Once people form a probability estimate, they are often slow to change the estimate given new information URN A: 70 red balls, 30 blue balls URN B: 30 red balls, 70 blue balls A number of balls are selected from a randomly picked urn. What is probability of getting from urn A: Estimated ProbabilityActual Probability One red Two red Three red

All the families having exactly six children in a particular city were surveyed. In 72 of the families, the exact order of the births of boys and girls was: G B G B B G What is your estimate of the number of families surveyed in which the exact order of births was: B G B B B B Answer: a) 72 Representativeness Heuristic

The sequence “G B G B B G” is seen as A) more representative of all possible birth sequences. B) better reflecting the random process of B/G Representativeness Heuristic

A coin is flipped. What is a more likely sequence? A) H T H T T H B) H H H H H H A) #H = 3 and #T = 3 (in some order) B) #H = 6 Gambler’s fallacy: wins are perceived to be more likely after a string of losses Representativeness Heuristic & Gambler’s Fallacy

Does the “hot hand” phenomenon exist? Most basketball coaches/players/fans refer to players having a “Hot hand” or being in a “Hot zone” and show “Streaky shooting” However, there is little statistical evidence that basketball players switch between a state of “hot hand” and “cold hand” People often see structure in sequences that are statistically purely random (and nonchanging) (Gilovich, Vallone, & Tversky, 1985)

Availability Heuristic Are there more words in the English language that begin with the letter V or that have V as their third letter? What about the letter R, K, L, and N? (Tversky & Kahneman, 1973)

Availability Heuristic & Conjunction Fallacy Estimate the number of words that would fit the following forms: A)_ _ _ _ _ i n g B)_ _ _ _ _ _ n _ (Tversky & Kahneman, 1983)

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-nuclear demonstrations. Rate the likelihood that the following statements about Linda are true: a) Linda is active in the feminist movement b) Linda is a bank teller c) Linda is a bank teller and is active in the feminist movement Result: (c) is rated as more likely than (a) or (b). From a standard probabilistic point of view, this is strange  conjunction fallacy

Which city has a larger population? A) San Diego B) San Antonio 66% accuracy with University of Chicago undergraduates. However, 100% accuracy with German students. San Diego was recognized as American cities by 78% of German students. San Antonio: 4%  With lack of information, use recognition heuristic (Goldstein & Gigerenzer, 2002)

Are heuristics wrong? No, we use mental shortcuts because they are often right. Availability and representativeness are often ecologically valid cues. Are we really that bad in judging probabilities? According to some researchers (e.g., Gigerenzer), it matters how the information is presented and processed. Processing frequencies is more intuitive than probabilities (even it leads to the same outcome).