- 1. Reasoning & Decision Making Monty Python The Search for the The Holy Grail: Witch Scene http://www.youtube.com/watch?v=yp_l5ntikaU
- 2. • The folly of mistaking a paradox for a discovery, a metaphor for a proof, a torrent of verbiage for a spring of capital truths, and oneself for an oracle, is inborn in us. -- Paul Valery
- 3. Reasoning & Decision Making Backbone of Problem Solving & Creativity –Logic –Decision making
- 4. Reasoning, Decision Making and Problem solving – Logic • As you have noticed by now, there is very little that is logical about how the brain processes information. So, it will not surprise you that we have problems with doing logic. – Decision making
- 5. Test for Reasoning Four ( 4 ) questions and a bonus question. You have to answer them instantly. You can't take your time, answer all of them immediately . Let's find out just how clever you really are....
- 6. First Question Answer: If you answered that you are first, then you are absolutely wrong! If you overtake the second person and you take his place, you are second! Try not to screw up next time. You are participating in a race. You overtake the second person. What position are you in?
- 7. Second Question don't take as much time as you took for the first question, OK ? Answer: If you answered that you are second to last, then you are wrong again. Tell me, how can you overtake the LAST Person? You're not very good at this, are you? If you overtake the last person, then you are...?
- 8. Third Question Did you get 5000? The correct answer is actually 4100. If you don't believe it, check it with a calculator! Today is definitely not your day, is it? Very tricky arithmetic! Note: This must be done in your head only . Do NOT use paper and pencil or a calculator. Try it… Take 1000 and add 40 to it. Now add another 1000. Now add 30. Add another 1000. Now add 20. Now add another 1000. Now add 10. What is the total?
- 9. Fourth Question Did you Answer Nunu? NO! Of course it isn't. Her name is Mary. Read the question again! Mary's father has FIVE daughters: Nana, Nene, Nini, Nono. What is the name of the fifth daughter?
- 10. Bonus Question He just has to open his mouth and ask.... It's really very simple… A mute person goes into a shop and wants to buy a toothbrush. By imitating the action of brushing his teeth he successfully expresses himself to the shopkeeper and the purchase is done. Next, a blind man comes into the shop who wants to buy a pair of sunglasses; how does HE indicate what he wants?
- 20. If, then statements • If, then statements = conditional logic – If the first part of a statement is true then the second part must also be true If it rains the street gets wet It rained The street gets wet Is this a valid or invalid conclusion? -valid! 1
- 21. If, then statements If it rains then the street gets wet It rained The streets get wet p q Antecedent Consequent If p, Then q
- 22. If it rains, then the streets get wet. It doesn’t rain. Therefore, I conclude that the streets don’t get wet. This argument is valid This argument is invalid 2 If, then statements
- 23. If it rains, then the streets get wet. The streets are not wet. Therefore, I conclude that it has not rained. This argument is valid This argument is invalid 3 If, then statements
- 24. If it rains, then the streets get wet. The streets are wet. Therefore, I conclude that it must have rained. This argument is valid This argument is invalid 4 If, then statements
- 25. If p, then q. I observe p. Therefore, I conclude that q must be the case. This argument is valid This argument is invalid 5 If, then statements
- 26. If p, then q. I don’t observe p. Therefore, I conclude that q is not the case. This argument is valid This argument is invalid 6 If, then statements
- 27. If p, then q. I don’t observe q. Therefore, I conclude that p must not be the case. This argument is valid This argument is invalid 7 If, then statements
- 28. If p, then q. I observe q. Therefore, I conclude that p must be the case. This argument is valid This argument is invalid 8 If, then statements
- 29. If it rains, then the streets get wet. It rains. Therefore, the streets gets wet. p q p q If, then statements
- 30. If, then statements • Tree Diagrams – Critical information represented along “branches”. – Help to determine validity of a statement If it rains, then the streets get wet It rains Therefore the streets get wet
- 31. if it rains it doesn’t rain the streets get wet the streets get wet the streets don’t get wet p q q ~q ~p If, then statements If it rains, then the streets get wet It rains Therefore the streets get wet AFFIRMING THE ANTECEDANT: VALID
- 32. If it rains, then the streets get wet. It rains. Therefore, the streets gets wet. p q If p, then q. Antecedent Consequent p q Affirming the antecedent If, then statements Valid!
- 33. If it rains, then the streets get wet. It doesn’t rain. Therefore, I conclude that the streets don’t get wet. This argument is valid This argument is invalid 2 If p, then q. I don’t observe p. Therefore, I conclude that q is not the case. 6 Denying the antecedent If, then statements
- 34. if it rains it doesn’t rain the streets get wet the streets get wet the streets don’t get wet p q q ~q ~p If, then statements If it rains, then the streets get wet It doesn’t rain Therefore I conclude that the streets don’t get wet DENYING THE ANTECEDENT: INVALID
- 35. If it rains, then the streets get wet. The streets are not wet. Therefore, I conclude that it has not rained. This argument is valid This argument is invalid 3 If p, then q. I don’t observe q. Therefore, I conclude that p must not be the case. 7 Denying the consequent If, then statements
- 36. if it rains it doesn’t rain the streets get wet the streets get wet the streets don’t get wet p q q ~q ~p If, then statements If it rains, then the streets get wet The streets are not wet Therefore I conclude that it has not rained DENYING THE CONSEQUENT: VALID
- 37. If it rains, then the streets get wet. The streets are wet. Therefore, I conclude that it must have rained. This argument is valid This argument is invalid 4 If p, then q. I observe q. Therefore, I conclude that p must be the case. 8 Affirming the consequent If, then statements
- 38. if it rains it doesn’t rain the streets get wet the streets get wet the streets don’t get wet p q q ~q ~p If, then statements If it rains, then the streets get wet The streets are wet Therefore I conclude that it must have rained AFFIRMING THE CONSEQUENT: INVALID
- 40. “If a card has a vowel on one side, then it has an even number on the other side” Which cards do you need to turn over to test the validity of the rule? E K 4 7
- 41. Wason (1966) Selection Task “If a card has a vowel on one side, then it has an even number on the other side” If p, then q Answer: p ~p q ~q E K 4 7 p ~p q ~q Affirming the antecedent Denying the antecedent Affirming the consequent Denying the consequent E K 4 7
- 42. if vowel consonant even number even number odd number p q q ~q ~p If, then statements
- 43. Griggs & Cox (1982) • If a person is drinking beer, then the person must be over 21 Drinking beer Drinking Coke 16 years of age 22 years of age p ~p ~q q
- 44. if drinks beer drinks coke older than 21 older than 21 younger than 21 p q q ~q ~p If, then statements
- 45. Griggs & Cox (1982) • If a person is drinking beer, then the person must be over 21 Drinking beer Drinking Coke 16 years of age 22 years of age p ~p ~q q
- 46. if drinks beer drinks coke older than 21 older than 21 younger than 21 p q q ~q ~p If, then statements
- 47. Griggs & Cox (1982) • If a person is drinking beer, then the person must be over 21 Drinking beer Drinking Coke 16 years of age 22 years of age p ~p ~q q
- 48. if drinks beer drinks coke older than 21 older than 21 younger than 21 p q q ~q ~p If, then statements
- 49. Griggs & Cox (1982) • If a person is drinking beer, then the person must be over 21 Drinking beer Drinking Coke 16 years of age 22 years of age p ~p ~q q
- 50. if drinks beer drinks coke older than 21 older than 21 younger than 21 p q q ~q ~p If, then statements
- 51. Griggs & Cox (1982) • If a person is drinking beer, then the person must be over 21 Drinking beer Drinking Coke 16 years of age 22 years of age p ~p ~q q
- 52. • Why difficulty with 4-card task, not the drinking task? – Permission schema: If true then we have permission to do it! • Ex: If a passenger has been immunized against cholera, then he may enter the country. – Obligation schema: If true then obligated to do something else • Ex: If you pay me $100,000, then I’ll transfer the house to you. If, then statements
- 62. • Daniel Ariely Why We Think It’s Ok To Lie (sometimes) http://www.youtube.com/watch?v=nUdsTizSxSI
- 64. Probability in the Real World Frequentists and Bayesians
- 65. Probability in the Real World Bayesian Probability
- 66. Probability in the Real World • Bayes Theorem is “normative” – It takes into account more information – It includes all the information into its formulas – The formulas produce the most moderate outcomes; as close to a normal distribution as you can get for any given problem – Even simple sea-slugs exhibit habituation and many invertebrates show classical conditioning, all of which are forms of Bayesian inferences • Not surprisingly, we humans don’t do it…at least not consistently, thoroughly, or very well.
- 67. Probability in the Real World
- 68. Probability in the Real World
- 69. Probability in the Real World
- 70. Probability in the Real World
- 71. Probability in the Real World
- 72. Probability in the Real World
- 73. Probability in the Real World
- 74. Probability in the Real World
- 75. Probability in the Real World
- 76. The Need to Assess Probabilities • People need to make decisions constantly, such as during diagnosis and therapy • Thus, people need to assess probabilities to classify objects or predict various values, such as the probability of a disease given a set of symptoms • People employ several types of heuristics to assess probabilities • However, these heuristics often lead to significant biases in a consistent fashion • This observation leads to a descriptive, rather than a normative, theory of human probability assessment
- 77. Three Major Human Probability- Assessment Heuristics/Biases (Tversky and Kahneman, 1974) • Representativeness – The more object X is similar to class Y, the more likely we think X belongs to Y • Availability – The easier it is to consider instances of class Y, the more frequent we think it is • Anchoring – Initial estimated values affect the final estimates, even after considerable adjustments
- 78. A Representativeness Example • Consider the following description: “Steve is very shy and withdrawn, invariably helpful, but with little interest in people, or in the world of reality. A meek and tidy soul, he has a need for order and structure, and a passion for detail.” • Is Steve a farmer, a librarian, a physician, an airline pilot, or a salesman?
- 79. The Representativeness Heuristic • We often judge whether object X belongs to class Y by how representative X is of class Y • For example, people order the potential occupations by probability and by similarity in exactly the same way • The problem is that similarity ignores multiple biases
- 80. Representative Bias (1): Insensitivity to Prior Probabilities • The base rate of outcomes should be a major factor in estimating their frequency • However, people often ignore it (e.g., there are more farmers than librarians) – E.g., the lawyers vs. engineers experiment: • Reversing the proportions (0.7, 0.3) in the group had no effect on estimating a person’s profession, given a description • Giving worthless evidence caused the subjects to ignore the odds and estimate the probability as 0.5 – Thus, prior probabilities of diseases are often ignored when the patient seems to fit a rare-disease description
- 81. Representative Bias (2): Insensitivity to Sample Size • The size of a sample withdrawn from a population should greatly affect the likelihood of obtaining certain results in it • People, however, ignore sample size and only use the superficial similarity measures • For example, people ignore the fact that larger samples are less likely to deviate from the mean than smaller samples
- 82. Representative Bias (3): Misconception of Chance • People expect random sequences to be “representatively random” even locally – E.g., they consider a coin-toss run of HTHTTH to be more likely than HHHTTT or HHHHTH • The Gambler’s Fallacy – After a run of reds in a roulette, black will make the overall run more representative (chance as a self-correcting process??) • Even experienced research psychologists believe in a law of small numbers (small samples are representative of the population they are drawn from)
- 83. Representative Bias (4): Insensitivity to Predictability • People predict future performance mainly by similarity of description to future results • For example, predicting future performance as a teacher based on a single practice lesson – Evaluation percentiles (of the quality of the lesson) were identical to predicted percentiles of 5-year future standings as teachers
- 84. Representative Bias (5): The Illusion of Validity • A good match between input information and output classification or outcome often leads to unwarranted confidence in the prediction • Example: Use of clinical interviews for selection • Internal consistency of input pattern increases confidence – a series of B’s seems more predictive of a final grade-point average than a set of A’s and C’s – Redundant, correlated data increases confidence
- 85. Representative Bias (6): Misconceptions of Regression • People tend to ignore the phenomenon of regression towards the mean – E.g., correlation between parents’ and children’s heights or IQ; performance on successive tests • People expect predicted outcomes to be as representative of the input as possible • Failure to understand regression may lead to overestimate the effects of punishments and underestimate the effects of reward on future performance (since a good performance is likely to be followed by a worse one and vice versa)
- 86. The Availability Heuristic • The frequency of a class or event is often assessed by the ease with which instances of it can be brought to mind • The problem is that this mental availability might be affected by factors other than the frequency of the class
- 87. Availability Biases (1): Ease of Retrievability • Classes whose instances are more easily retrievable will seem larger – For example, judging if a list of names had more men or women depends on the relative frequency of famous names • Salience affects retrievability – E.g., watching a car accident increases subjective assessment of traffic accidents
- 88. Availability Biases (2): Effectiveness of a Search Set • We often form mental “search sets” to estimate how frequent are members of some class; the effectiveness of the search might not relate directly to the class frequency – Who is more prevalent: Words that start with r or words where r is the 3rd letter? – Are abstract words such as love more frequent than concrete words such as door?
- 89. Availability Biases (3): Ease of Imaginability • Instances often need to be constructed on the fly using some rule; the difficulty of imagining instances is used as an estimate of their frequency – E.g. number of combinations of 8 out of 10 people, versus 2 out of 10 people – Imaginability might cause overestimation of likelihood of vivid scenarios, and underestimation of the likelihood of difficult-to-imagine ones
- 90. Availability Biases (4): Illusory Correlation • People tended to overestimate co-occurrence of diagnoses such as paranoia or suspiciousness with features in persons drawn by hypothetical mental patients, such as peculiar eyes • Subjects might overestimate the correlation due to easier association of suspicion with the eyes than other body parts
- 91. The Anchoring and Adjustment Heuristic • People often estimate by adjusting an initial value until a final value is reached • Initial values might be due to the problem presentation or due to partial computations • Adjustments are typically insufficient and are biased towards initial values, the anchor
- 92. Anchoring and Adjustment Biases (1): Insufficient Adjustment • Anchoring occurs even when initial estimates (e.g., percentage of African nations in the UN) were explicitly made at random by spinning a wheel! • Anchoring may occur due to incomplete calculation, such as estimating by two high-school student groups – the expression 8x7x6x5x4x3x2x1 (median answer: 512) – with the expression 1x2x3x4x5x6x7x8 (median answer: 2250) • Anchoring occurs even with outrageously extreme anchors (Quattrone et al., 1984) • Anchoring occurs even when experts (real-estate agents) estimate real-estate prices (Northcraft and Neale, 1987)
- 93. Anchoring and Adjustment Biases (2): Evaluation of Conjunctive and Disjunctive Events • People tend to overestimate the probability of conjunctive events (e.g., success of a plan that requires success of multiple steps) • People underestimate the probability of disjunctive events (e.g. the Birthday Paradox) • In both cases there is insufficient adjustment from the probability of an individual event
- 94. Anchoring and Adjustment Biases (3): Assessing Subjective Probability Distributions • Estimating the 1st and 99th percentiles often leads to too-narrow confidence intervals – Estimates often start from median (50th percentile) values, and adjustment is insufficient • The degree of calibration depends on the elicitation procedure – state values given percentile: leads to extreme estimates – state percentile given a value: leads to conservativeness
- 95. Strategies for Comprehension 1. Questioning and Explaining (SQ3R) 2. Concept Maps 3. Hierarchies 4. Networks 5. Matrices
- 96. Collins and Quillian’s Semantic Network Model
- 97. “I once shot an elephant in my pajamas. Who was wearing the pajamas? How he got in my pajamas, I’ll never know…”
- 98. More… • Used Cars: Why go elsewhere to be cheated? Come here first! • Spotted in a safari park: Elephants please stay in your car. • Panda mating fails; veterinarian takes over.
- 99. Language and Memory: Tricks with Retrieval How many animals of each kind did Moses take on the ark? ________ How confident are you? (1=not at all, 7= very confident) ____ In the biblical story, what was Joshua swallowed by? ________ How confident are you? (1=not at all, 7= very confident) _____
- 100. Aspects of memory: Retrieval • Moses didn’t have an ark—Noah did! • Joshua wasn’t swallowed by a whale: Jonah was!
- 101. Imagine that Santa Cruz is preparing for the outbreak of an unusual disease, which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed. Assume that the exact scientific estimate of the consequences of the programs are as follows: • If Program A is adopted, 200 people will be saved. • If Program B is adopted, there is a 1/3 probability that 600 people will be saved, and 2/3 probability that no people will be saved. Which of the two programs would you favor?
- 102. Imagine that Santa Cruz is preparing for the outbreak of an unusual disease, which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed. Assume that the exact scientific estimate of the consequences of the programs are as follows: • If Program C is adopted, 400 people will die. • If Program D is adopted, there is a 1/3 probability that nobody will die, and 2/3 probability that 600 people will die. Which of the two programs would you favor?
- 103. • If Program A is adopted, 200 people will be saved. • If Program B is adopted, there is a 1/3 probability that 600 people will be saved, and 2/3 probability that no people will be saved. • If Program C is adopted, 400 people will be die. • If Program D is adopted, there is a 1/3 probability that nobody will die, and 2/3 probability that 600 people will die.
- 104. • Famous study by Tversky & Kahneman (1981) – A: 72% – B: 28% – C: 22% – D: 78%
- 105. • Anchoring – Related to framing – Unconscious use of an easily accessible “starting point” for making a judgment about a quantity or cost – How much to spend or donate • $25 $50 $75 $100 • Buy one get one free! -why not just adjust the price? – What do we anchor? • We make jusdgments and evaluations relative to some frame of reference
- 106. Problem planning and representation • Lets’ try some! People in the community have a fear of crime! Redefine it! “Fear of crime” - - - - - - > “reducing crime” Solutions: 1. Make capital punishment the law 2. Incarcerate criminals for life if they are convicted of three major crimes
- 107. Problem planning and representation People in the community have a fear of crime! Redefine it again! “Fear of crime” - - - - - - > “Make life safer for citizens” Solutions: 1. Provide better security 2. Offer self-defense course 3. Organize anti-crime groups in the neighborhoods 4. “Neighborhood watch”
- 108. Problem planning and representation People in the community have a fear of crime! Redefine it again! “Fear of crime” - - - - - - > “Reduce the # of criminals” Solutions: 1. Send criminals to Siberia 2. Return to using gallows, public humiliation, beheading, etc.. . 3. Increase afterschool activities 4. Improve educational program
- 109. Problem planning and representation People in the community have a fear of crime! Redefine it again! “Fear of crime” - - - - - - > “Change public perspective of crime” Solutions: 1. Give people anti-anxiety drugs 2. Provide public info that crime is down (may be true or false) - It is changing perception of crime not the crime rates themselves! (not necessarily ethical!)
- 110. Problem planning and representation People in the community have a fear of crime! Redefine it again! “Fear of crime” - - - - - - > “Reducing violent crime” Solutions: 1. Make guns illegal to own 2. Legalize drug use