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10 – Reasoning Motion Judgment Problem Solving Decision Making

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Motion Judgment Nearly every day, people observe objects roll, fall, and slide. Yet many people hold striking false beliefs about these kinds of motion.

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Falling Bomb Question A horizontally-flying plane drops a bomb. Choose the bomb’s trajectory. A BC correct answerC common errorA one explanation of errorBombs appear to drop vertically. (McCloskey, 1983)

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Pendulum Question When the pendulum bob is at its highest point, the string breaks. Choose the bob’s trajectory. A B C D correct answer A common error D one explanation of errorMemories of jumping off swing?

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Marble Question Two identical marbles are released simultaneously. The ramps are identical except for one section that is a dip or a hill. Which marble wins? “hill” marble “dip” marble tie Modal Answer Tie “because each ramp has fast downhill & slow uphill” (continued)

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Correct Answer Dip Speed is greater at lower elevation, regardless of slope. Example slow medium fast

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Dip vs. Hill Dip vs. Flat Tip for instructor: R. click on icon and select “Packager shell…”

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Experiment Ss observed computer animations of motion for commonly-held false beliefs. For each scenario, Ss saw two animations: true motion and false belief. Results Ss rated the “false belief” version as unnatural (e.g., Kaiser, Proffitt, Whelan, & Hecht, 1992)

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Summary of Motion Judgment In one sense, people have poor understanding of motion. Examples Falling Bomb Question Broken Pendulum Question Marble Question However, people understand motion at some level. Examples Animations of false beliefs look unnatural. People can perform complicated tasks that require understanding of motion (e.g., catch fly ball)

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Problem Solving Many problems require an insight – a sudden realization of the solution. Examples Archimedes: “Eureka” Chimp suddenly realizes how to get banana Köhler (1927) Not all problems require insight (e.g., add fractions) To what extent can people improve their chance of solving insight problems?

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Examples of Problems used in Insight Studies Interpret the following: 1. oholenehole in one 2.point ______ rangepoint blank range Find a fourth word that relates to the first three words. 1. offtoptail spin 2. achesweetburn heart 3. armcoalpeachpit 4. tuggravy showboat

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Bridge Crossing Problem Four men must cross a bridge that can hold only two men at a time. It is too dark to cross without a flashlight, and they have only 1 flashlight. The men walk at different speeds. Here are the bridge crossing times for each man: Mr. One 1 min Mr. Two 2 min Mr. Five 5 min Mr. Ten 10 min How can all four men cross the bridge in 17 minutes? Solution 1 and 2 over(2 min) 1 returns (1 min) 5 and 10 over(10 min) 2 returns (2 min) 1 and 2 over(2 min)

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Demo This shape is divided into 3 congruent parts. This shape is divided into 4 congruent parts. Can you divide this shape into 5 congruent parts?

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For each problem, use bottles A, B, and C to produce the goal amount. Volume ProblemABCGoalSolution 152078B – A – C 221549B – A – C 34171115A + C Problem 3 is harder if … Ss first solve Problems 1 and 2 Thus, one’s mind set can impede ability to solve problem. (Luchins, 1941)

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When stuck on a problem, why does taking a break sometimes help? Hypothesis 1 During the break, your mind makes progress outside your awareness. Hypothesis 2 The break disrupts your mind set and allows for a fresh start Evidence supports #2 (e.g., Smith & Blankenship, 1989; 1991)

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Demo The sequence 2, 4, 8 conforms to a rule. Your job is to figure out the rule. To do so, suggest a sequence, and I will tell you if it conforms to the rule. RuleNumbers increase. ResultsSs seek data confirming their belief (confirmation bias) LessonSeek disconfirming evidence. (Wason, 1960)

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Many psychology researchers seek confirmation. Common psychology paper If our Theory is true, we should find Result R. We found Result R. Therefore, our Theory is true. Invalid What can be concluded? Our results suggest that our theory is true. Invalid Our theory predicts the results. Valid Our results are consistent with our theory. Valid Our results are consistent with many theories. Valid and Honest

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9 Dots Problem Connect the dots by drawing 4 straight lines without lifting your pen. Hint Don’t assume that each line segment starts and ends on a dot. Solution

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Cake Problem A round cake must be divided into eight pieces. Only 3 straight slices of a knife are allowed. The pieces of cake cannot be moved between slices. Hint Do not assume that slices must be perpendicular to table. Solution

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Elevator Problem Ten-year-old Suzy lives on the 16 th floor of an apartment building. When she goes to school, she takes the elevator from the 16 th floor to the 1 st floor. When she returns, she takes the elevator from the 1 st floor to the 8 th floor, and then she climbs the stairs from the 8 th floor to the 16 th floor. Why doesn’t she ride the elevator all the way to the 16 th floor? Solution She’s too short.

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Poisoned Drink Problem Mr. Sip and Mr. Gulp enter a diner. Each orders a cola with ice. Mr. Sip slowly sips his drink, but Mr. Gulp quickly gulps his drink. Later, Mr. Sip dies because the drink was poisoned. But Mr. Gulp is fine even though the drinks were identical. How can this be? Solution Poison is in the ice

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Manhole Cover Problem Why are round manholes safer than other shapes? Solution A round manhole cover will not fall through

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Overview of Previous Problems Avoid false assumptions. 9 dots problem cake slicing problem Act out the problem. elevator problem poisoned drink problem manhole cover problem

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Decision-Making Why do people sometimes make irrational decisions? Example You spent $500 for a weekend trip to the Bahamas. The cost is NOT refundable. On the day before you leave, you become very ill. You’re so ill, you’d be less miserable if you stayed home. You decide to go so you “don’t waste the money.” (continued)

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sunk cost fallacy completing an action that is not worthwhile because of prior investment aka “throwing good money after bad” Another example Congress spends $100B to build X (rocket, jet fighter, etc.) After $100B is spend, price increases to $500B. Congress agrees because it doesn’t want to waste the first $100B (e.g., Arkes & Ayton, 1999)

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Question A disease threatens an island with 600 people. If nothing is done, all 600 people will die. You have two options. Subject Group 1Option A: 200 live Option B: 1/3 chance 600 live 2/3 chance 0 live Subject Group 2Option A: 400 die Option B: 1/3 chance 0 die 2/3 chance 600 die Results Group 1: most chose A (no risk) Group 2: most chose B (risk) (continued)

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Why? When contemplating a gain, Ss are risk-averse When contemplating a loss, Ss are risk-seeking. More generally, this finding is an example of a framing effect phrasing or format of options affects person’s preference (Tversky & Kahneman, 1981)

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Experiment Group 1 “You’ve been given $300. Now choose option A or B” A. You receive another $100 B. Coin flip You receive another $200 or nothing more Group 2 “You’ve been given $500. Now choose option A or B” A. You lose $100 B. Coin flip You lose $200 or lose nothing Results Group 1 prefers A(no risk) Group 2 prefers B (risk) (Tversky & Kahneman, 1987)

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Why do more Ss avoid a “sure thing” when options are framed as losses? loss aversion people would rather avoid loss than acquire gain Example Not losing $10 is better than finding $10 Experiment Chinese factory workers were offered weekly bonus of 80 yuan if they met target. Two groups: Gain Frame “You’ll receive your bonus at the end of the week if you meet target.” Loss Frame “You’ve already received bonus, but you’ll lose it if you don’t meet target.” The bonus system continued for many weeks. Results Productivity was greater when bonus was framed as a Loss (Hossain & List, 2009)

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In Flossmoor, a wealthy suburb [of Chicago] where the average income is $117,000 a year, a monthly average of $4.48 is spent on the lottery per household. In Possen, a poor suburb where average household income is $33,000, the monthly average is $91.82. Washington Post November 12, 1995

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Is gambling foolish? Objectively, a gamble is irrational if expected value < cost. Expected Value (EV) = average winnings if you played many, many times = (probability of a win) (value of a win) Example A club sells 100 raffle tickets. Each ticket costs $1. One ticket is chosen randomly, and the ticket holder wins $300. Everyone else loses. What is the expected value of a raffle ticket? EV=(.01)($300) = $3 If EV < cost, you lose, on average. If EV > cost, you win, on average.

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Another way to measure whether a gamble is in your favor… EV Return = ----------- Cost If return < 1, you lose, on average (because EV < cost) If return > 1, you win, on average (because EV > cost) Example. If return =.99, you will, on average, win 99¢ for every $1 you pay.

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Popular GamblesApproximate Return Lottery 0.01 - 0.5 Casino Keno 0.4 Blackjack0.99 (depends slightly on rules) Are there gambles in which return exceeds 1? stock market (historically)

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But the EV measures the objective value of a win, not its subjective value Example Which would you prefer? A) 5% chance of $1 million (EV = $50,000) B) 1% chance of $10 million (EV = $100,000) If man hates his job, and $1M is enough to retire, then A is better choice. In other words, when measured subjectively, $1 M > (1/10) $10 M

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When EV is measured subjectively, some low-return gambles are arguably rational… ExamplesSubjective Value raffle ticketcharity casino fun lottery hope Example A $2 lottery ticket with EV = $1 may have additional subjective value of $2.

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The End

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Question Four cards lie on a table. Each has a letter on one side and a number on the other. Someone makes the following claim: If a card has a vowel on one side, it has an even number on other side. To verify this claim, which card(s) must you turn over? Correct AnswerA and 7 Modal AnswerA and 6 (Wason, 1968) AB67

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A better approach… If our Theory is true, we should find Result R. We found not R (i.e., the opposite of R, not just a null result) Therefore, our Theory is false. VALID Even better: Theory X predicts R and Theory Y predicts not R. Our results disprove X and are consistent with Y. Advice from J. R. Platt (1964): Upon hearing of a theory, ask “what experiment could disprove it?” Upon hearing of an experiment, ask “what theory does it disprove?”

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Tumor Problem A patient has a malignant tumor in his stomach. The tumor can be destroyed by rays of radiation. But the necessary intensity would kill surrounding tissue. At lower intensities, the healthy tissue is spared. How can these rays safely destroy the tumor?

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Fortress Problem A general wishes to capture a fortress that is surrounded by a moat. The moat is spanned by six bridges. To succeed, 600 soldiers must cross the moat at the same time. But each bridge holds only 100 soldiers. How can it be done?

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Solution to Tumor Problem Experiment Ss given tumor problem, but half first see fortress problem. Fortress problem dramatically improves ability to solve tumor problem. Finding demonstrates utility of appropriate analogy. (Duncker, 1945)

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Bookworm Problem A set of encyclopedias sits on a shelf in the usual way. It includes 26 volumes, one for each letter, in alphabetical order (as usual). Each volume is 1 inch thick, including the covers. A bookworm sits on the front cover of the A volume. It then chews its way to the back cover of the Z volume. How far did the bookworm travel? (The answer is NOT 26 inches.) Answer 24 inches front cover of A back cover of Z

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Another example of the sunk-cost fallacy Company: We make fighter jets. Congress: We’ll pay no more than $10B each. Company: It’s a deal. 10 years later… Company : We now need another $15B per jet. Congress: Okay, we’ll agree so we don’t want waste our initial investment.

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The sunk cost fallacy is also known as the Concorde effect, because the British and the French continued to fund the development of the Concorde even after it became apparent that there was no longer an economic case for the aircraft. The project was regarded privately by the British government as a "commercial disaster" which should never have been started, and was almost cancelled, but political and legal issues ultimately made it impossible for either government to pull out. (Arkes & Ayton, 1999)

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By estimating EV, one can evaluate many kinds of risky ventures. Example Should you apply for a $1000 scholarship? 1. Estimate minimum probability of winning scholarship. 5% 2. Compute EV. (.05)($1000) = $50 3. Estimate cost (including the cost of your time). $30 Since EV > cost, applying is a good gamble

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