4/1/2017 Outline Study Question. Decisions The representativeness heuristic The availability heuristic Anchoring and adjustment The simulation heuristic Undoing and hindsight biases Limited domain knowledge Processing resources The Framing Effect Limitations in reasoning Naïve Physics Limitations in resources Study Question. • Compare and contrast the representativeness and the availability heuristics. • Describe the framing effect. What is loss aversion? When do we tend to become risk takers when maker decisions?

Decisions Algorithms and Heuristics Reasoning under uncertainty: Inductive reasoning Algorithms: A specific rule or solution procedure that is guaranteed to furnish the correct answer if it is followed. E.g., finding a forgotten phone number Heuristics: A strategy or approach that works under some circumstances, but is not guaranteed to produce the correct answer. Kahneman and Tversky’s work Behavioural decision work Ups and downs of heuristics Cf. Visual illusions

Decisions Algorithms and Heuristics The representiveness heuristic E.g., Flip a coin 6 times, which is more likely HHHHHH or HHTHTT Which lottery ticket is most likely to win the next 6-49? 04-11-19-29-33-39 or 01-02-03-04-05-06 The representativeness heuristic - samples are like the populations that they are pulled from. The representativeness heuristic leads to a number of decision biases

Decisions The representiveness heuristic The law of small numbers Who is more likely to have days where more than 60% of the births are male? St. Martha’s or the IWK? Ignoring base rates John: Truck driver or classics professor at Dalhousie? The Gambler’s fallacy The hot hand in basketball

Decisions The Representativeness Heuristic, revisited 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 The Representativeness Heuristic, revisited 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 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 E.g. Listen to this list of names E.g., Answer the following: 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? In the United States, the chance of dying from falling airplane parts is 30 times greater than dying from a shark attack. 2) Do more Americans die from a) homicide and car accidents, or b) diabetes and stomach cancer? More Americans die from diabetes and stomach cancer than from homicide and car accidents, by a ratio of nearly 2:1. 3) Which claims more lives in the United States: lightning or tornadoes? Lightning

Decisions The Availability Heuristic Important factors Vividness and Saliency E.g., the full moon Repetition effects Anything that makes recollection easier Role of the media

Decisions The simulation heuristic Counterfactual thinking Forecasting how some event might have turned out under another set of circumstances E.g., Mr. Tees and Mr. Crane E.g.,Medvec et al. (1995) Examined tapes of 41 athletes from ‘92 Games Judges rated athletes on scales from “agony” to “ecstasy” Bronze medalists happier than silver medalists Counterfactual thinking Undoing heuristic

Decisions The hindsight bias Anchoring and adjustment I-knew-it-all-along phenomenon Anchoring and adjustment Determine the following: 8 X 7 X 6 X 5 X 4 X 3 X 2 X 1 1 X 2 X 3 X 4 X 5 X 6 X 7 X 8 Kahneman and Tversky found 1) 2.250 2) 512 (Actually: 10,320)

Decisions A large city is on the verge of a rare asian bird flu outbreak and it is expected that 600 people will be infected. Two alternative programs have been proposed to fight the disease. Assume that these are the exact scientific estimates of the two programs: If Program A is adopted, 200 people will be saved. If Program B is adopted, there is a one-third possibility that 600 people will be saved, and a two-thirds probability that no people will be 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 die. If Plan D is adopted, there is one-third probability that nobody will die, and a two-thirds probability that 600 people die. Kahneman & Tversky’s results 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? The Framing effect has been demonstrated in a number of contexts: Vaccinations Treating lung cancer Genetic counseling Gambling choices Buying refridgerators

Decisions The framing effect (Kahneman & Tversky) 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? T & K’s results (theatre ticket for $10) Lose ticket -: 46 % buy another ticket Lose $10 - 88 % buy another ticket The framing effect works for background information as well wording

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.

Decisions The framing effect (Kahneman & Tversky) 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) 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 Limitations in reasoning Limited domain knowledge Our cognitive representation of the situation (AKA mental model) often has incomplete information. Thermostats do not work like water faucets Hitting the elevator button 5 times is not faster than hitting it once 20° C is not twice as warm as 10 °C Quasi-magical behaviour

Decisions Limitations in reasoning Limited domain knowledge Our cognitive representation of the situation (AKA mental model) often has incomplete information.

Decisions Limitations in reasoning Naïve Physics and Mental Models (McCloskey et al.)

Decisions Limitations in reasoning Results (A & B)

Decisions Limitations in reasoning Results (C)

Decisions Limitations in reasoning Domain of knowledge Our domain of knowledge concerning physics is poor. Impetus theory: a pre-Newtonian and incorrect concept concerning “curvature momentum” Linda is 31 years old, single outspoken, and very bright. She majored in philosophy. As a student she was deeply concerned with the issues of discrimination and social justice, and also participated in anti-globalization demonstrations. Rank the following in terms of their likelihood of describing Linda Linda is a teacher at a local elementary school Linda is a bank teller and is active in the feminist movement Linda is an insurance agent Linda is psychiatric social worker Linda is a bank teller

Decisions Limitations in reasoning Conjunction fallacy: Judging the probability of a conjunction to be greater than the probability of a constituent event. Representativeness heuristic Very Unlikely 6 4 Very Likely Likelihood ratio 5 3 Statiscally Naive Intermediate Statistically Sophisticated

Decisions Limitations in reasoning Limitations in processing resources Waltz et al. Tested temporal lobe injured, prefrontal lobe injured, and normals Two tests TransitiveiInference problems E.g., John is taller than Sam; Sam is taller than Tim (2 propositions) Raven Standard Progressive Matrices test

Decisions Limitations in reasoning Limitations in processing resources Waltz et al. Transitive inference Raven’s Matrices Dashed = Controls Dotted = Temporal lobe Solid = Prefrontal lobe

Problems for upcoming lecture • Complete the following Sequence: O, T, T, F, F, S, S, E, N, …. • A Buddhist Monk leaves for a retreat atop a nearby mountain. He leaves at 6:00 AM and follows the only path that leads up the mountain. He travels quickly some of the way, he travels slowly, he stops for breaks. He arrives at the top of the mountain at 6:00 PM. The next morning, at 6:00 AM, he descends the mountain, again travelling at varying paces and with breaks. He arrives at 6:00 PM Is there a point on the trail that the monk would have passed at exactly the same time of day on the way up and on the way down the trail? • Three hobbits and three orcs need to cross a river. There is only one boat, and it can only hold two creatures at a time. This presents a problem: Orcs are vicious and whenever there are more orcs than hobbits they immediately attack and eat the hobbits. Thus, you can never let orcs outnumber hobbits on either side of the river. Can you schedule a series of crossing that will get everyone safely across the river?

Problems for upcoming lecture • Connect these nine dots with four connected straight lines. • Three people play a card game. Each player has money in front of them (their ante). One each hand of this game, one player loses and the other two players win. The rules state that the loser must use the money in front of them to double the amount of money in front of each of the other two players. They stake their antes and play three hands. Each of them loses once and no one goes bust. The each finish with $8.00. What were the original antes (Hint: it is not $2 each). • A landscaper has been instructed to plant four new trees such that each one is exactly the same distance away from each of the other trees. Is this possible?