Decisions, Judgements, and Reasoning. Cognitive Psychology Chapter 11 Decisions, Judgements, and Reasoning.

Chapter 11.3 Outline Decisions 2/22/2019 Algorithms & Heuristics “I don’t know if this is such a wise thing to do, George.” Outline Decisions Algorithms & Heuristics Representativeness The hot hand debate Availability Framing Effects Study Questions. • What is the clustering illusion? Give two examples of the illusion. How is it related to the representativeness heuristic

Decisions Algorithms and Heuristics The representativeness heuristic The birthday bet If you bet against the birthday bet, what is P(winning)? Person 2 -> 364/365 = .99 Person 3 cannot have the same birthday as 1 or 2 & Person 2 cannot have the same birthday as 1 Multiplicative Rule: The joint probability of two independent events is the product of their individual probabilities Person 3 -> 363/365 X .99 = .99 Person 4 -> 362/365 X .99 = .98 Person 5 -> 361/365 X .98 = .97 Person 6 -> 360/365 X .97 = .95

Decisions Algorithms and Heuristics The representativeness heuristic The birthday bet Person 10 -> 356/365 X .90 = .88 Person 15 -> 351/365 X .77 = .75 Person 20 -> 346/365 X .62 = .59 Person 25 -> 341/365 X .46 = .43 Person 30 -> 336/365 X .32 = .29 Person 35 -> 331/365 X .21 = .19 Person 40 -> 326/365 X .12 = .11 Person 45 -> 321/365 X .07 = .06 Person 50 -> 316/365 X .03 = .03

Decisions Algorithms and Heuristics The representativeness heuristic Misperception of random events Is the following a random sequence? (Gilovich, 1991) OXXXOXXXOXXOOOXOOXXOO “Maximally” indicative of randomness Same number of X’s and O’s Same number of X’s follow O’s as X’s following X’s (and vice versa) P(alteration) = .5 Most people expect P(alteration) =.7

Decisions Algorithms and Heuristics The representativeness heuristic The hot hand in basketball Study 1: 100 fans completed survey 91 % : a player has a better chance of making a shot after hitting the last two or three, a lower chance of hitting a shot if they have missed the last two or three 68 % for free throws 85 % believed that it was important to pass the ball to someone who had just made several shots in row. Study 2: 76ers home games from 80-81 season Conditional probabilities P(hit | 3 misses) P(hit | 2 misses) P(hit | 1 misses) P(hit) P(hit | 1 hit) P(hit | 2 hits) P(hit | 3 hits)) Julius Irving .52 .51 .51 .52 . 53 .52 .48 Andrew Tony .52 .53 .51 .46 . 43 .40 .34 Team .56 .53 .54 .52 . 51 .50 .46

Decisions Algorithms and Heuristics The representativeness heuristic The hot hand in basketball Study 3: Free throws

Decisions Algorithms and Heuristics The representativeness heuristic The hot hand in basketball Study 4: Controlled shooting: Cornell varsity players Determined 50 % range Paid for hitting baskets and predicting hits and misses 14/26 had higher P(hit|miss) than P(hit|hit) P(hit | 3 misses) P(hit | 2 misses) P(hit | 1 misses) P(hit) P(hit | 1 hit) P(hit | 2 hits) P(hit | 3 hits)) Mean .45 .47 .47 .47 . 48. 48 .49

Decisions Algorithms and Heuristics The representativeness heuristic The hot hand in basketball Predicting: > Bet either “high” (5 cents for a hit, lose 4 cents for a miss) > Or “low” (2 cents for a hit, lose 1 cent for a miss) > Shooters and observers bet Shooter & shot Obs. & shot Shooter & last shot Obs. & last shot Correlation .02 .04 .40 .42

Decisions Algorithms and Heuristics The representativeness heuristic Similar misconceptions (The clustering illusion) Winning streaks as team momentum Hitting slumps in baseball Siwoff et al. (1988) -> 1984-1987 seasons. Calculated batting averages of players in games right after: -> “hot” streak (more than 5 games batting at least .400) -> “cold” streak (more than 5 games batting less than.125) -> compared these batting averages to the players’ overall record. • batting averages were just as likely to be higher following cold streaks as following hot streaks. Cancer Clusters • The Texas Sharpshooter Fallacy • Finding clusters of cancer 7-8 times normal is normal > Thyroid cancer in children living near Chernobyl -> 100X

Decisions Algorithms and Heuristics The Availability Heuristic Our estimates of how often things occurs or are influenced by the ease with which relevent examples can be remember This leads to a number of biases 1) Which is a more likely cause of death in the United States: being killed by falling airplane parts or being killed by a shark? 2) Do more Americans die from a) homicide and car accidents, or b) diabetes and stomach cancer? 3) Which claims more lives in the United States: lightning or tornadoes?

Decisions Algorithms and Heuristics The Availability Heuristic Important factors affecting saliency Factors that effect the ease of remembering Vividness, recency, familiarity Saliency ‘Contaminants’ • Vividness • Recency • Familiarity True Frequency Availability Estimated

Decisions Algorithms and Heuristics The Availability Heuristic Vividness E.g., Gardening and the full moon. Repetition MacLeod & Campbell (1992) • Recall happy/sad events from one’s past • Higher estimates of happy events in the future for ‘happy’ group Imagining Kahneman & Tversky (1973) • Imagining Jimmy Carter or Gerald Ford as President

Decisions Algorithms and Heuristics The Availability Heuristic Recency Pauker & Kopelman (1992) New England Journal of Medicine - • Physician reluctant to perform a procedure because of a recent complication

Decisions Algorithms and Heuristics The Availability Heuristic Familiarity Physicians ratings of likelihood of fatality of various diseases Correlated with number of articles published about the disease …. Regardless of what the article said about the disease Role of media Population estimate of El Salvadore -> 12 million (5 actual) Population estimate of Indonesia -> 19.5 million (180 actual) Who has a larger population, Iraq or Nigeria?

Decisions Government cutbacks are about take a hit on students. It is expected that 600 people will lose their bursaries. The student union has proposed two alternative programs to fight the cutbacks: If Program A is adopted, 200 students will have their bursaries saved. If Program B is adopted (a legal option), there is a one-third probability that 600 students will have their bursaries saved, and a two-thirds probability that no students will have their bursaries saved. Which program would you favour?

Decisions The framing effect (Kahneman & Tversky) The wording of question in conjunction with the background context can influence the decision. Both of the previous plans were rejected, consider the following: If Plan C is adopted, 400 people will lose their bursaries. If Plan D is adopted, there is one-third probability that nobody will lose their bursary, but a two-thirds probability that 600 people will lose their bursary. Kahneman & Tversky’s results (disease outbreak) Plan A 1/3 Saved Plan B P=1/3 Saved Plan C 2/3 Die Plan D P=2/3 Die 72% 28 % 22% 78 %

Decisions The framing effect (Kahneman & Tversky) Risk seeking and avoidance When questions are framed in terms of gains we avoid risk (Prefer A over B) When framed in terms of losses we are risk-seekers (Prefer D over C) Other findings relating to the Framing Effect It is unrelated to statistical sophistication It is not eliminated when the contradiction is pointed out

Decisions The framing effect (Kahneman & Tversky) You buy an advance ticket for $ 20 to see the Harlem Globetrotters play at the Oland Centre. When you get to the game, you discover that you have lost your ticket. Do you shell out $ 20 for another? You go to the Oland Centre to see the Harlem Globetrotters play. Tickets cost $20. When you get to the ticket booth, you discover that you have lost twenty bucks. Do you buy a ticket anyway?

Decisions The framing effect (Kahneman & Tversky) T & K’s results (theatre ticket for $10) Lose ticket -: 46 % buy another ticket Lose $10 - 88 % buy another ticket The Framing effect has been demonstrated in a number of contexts: Vaccinations Treating lung cancer Genetic counseling Gambling choices Buying refrigerators

Decisions The framing effect (Kahneman & Tversky) Loss aversion Receive a mug for participating in an experiment What price would you sell this mug for? What price would you pay for his mug? Sell: $7.12, Buy: $2.87 Combining Framing effects and loss aversion

Decisions The framing effect (Kahneman & Tversky) (1) You have decided to leave your current job, because it is an 80 min commute each way even though you like the pleasant social interaction with your co-workers. You have two options for a new job Job A Limited contact with others; 20 min commute Job B Moderately social; 60 min commute Loss aversion We are far more sensitive to losses than to gains K & T: Receive $ 20 for a heads, pay $ 10 for a tails:

Decisions The framing effect (Kahneman & Tversky) (2) You have decided to leave your current job, because it leaves you isolated from your co-workers even though you like the 10 min commute in each direction. You have two options for a new job Job A Limited contact with others; 20 min commute Job B Moderately social; 60 min commute Loss aversion Scenario (1) - 67 % chose Job B Scenario (2) - 70 % chose Job A

Decisions The framing effect (Kahneman & Tversky) Some weeks ago, you saw an add in the newspaper for a reduced rate for a week-end at a nearby resort. You sent in a $ 100 nonrefundable deposit. When the weekend arrives you set off with your partner. Both of you are extremely tired and somewhat ill and about half way to the resort you both realize that you would probably have a more pleasurable weekend at home. Do you turn back? The sunk-cost effect: A tendency toward taking extravagant steps to ensure that a previous expense was “not in vain”.

Decisions The framing effect (Kahneman & Tversky) Implications for the legal system You are to decide an only-child sole-custody case. Parent A Average income Average health Average working hours Reasonable report with the child Relatively stable social life Parent B Above average income Very close relationship with child Extremely active social life Lots of work-related travel Minor health problems To whom do you award sole custody? -> 64 % Chose Parent B To whom would you deny sole custody? -> 55 % Chose Parent B.