Problem Solving & Decision Making

Higher-Order Thinking Problem Solving Creativity Decision-Making and Reasoning Copyright © Allyn & Bacon 2005 Problem Solving  Problem solving:  Thinking that is directed toward the solving of a specific problem that involves the formation of responses and the selection among possible responses Goal Directedness– the behavior is clearly organized toward achieving a specific end Sub-goal Decomposition– decompose original goal into subtasks or sub-goals Operator Application– applying operators to help achieve the sub-goals  Operator: an action that will transform the problem state into another problem state the solution to a problem is a sequence of known operators Copyright © Allyn & Bacon 2005  Three Essential Features:    Problem Solving  Problem solving operators generate a space of possible states through which the problem solver must search to find a path to the goal. Problem Space:  Various states of the problem  Problem solving is described in terms of searching the problem space  Problem State: representation of the problem in some degree of solution  Start state: initial situation of the problem  Intermediate state: situations on the way to the goal  Goal state: desired situation  Well-defined Problems vs. Ill defined problems:  Well-defined problems are those when the Problem Space (start, intermediate and goal states) plus all the possible operators to transform from one state to another are clear and unambiguous– have a clear path  Tic-tac-toe, find the area of a triangle;  most often kind in education (math, history, geography)  Most well known in cog psych = missionaries & cannibals or some variation  All the other problems are ill-defined in one way or another (some area not specified)  ―be a good person‖, improve the economy You and your friend Johnny are walking in a Brazilian rain forest when you come to a big gorge (40 feet deep, 60 feet wide, several miles long). You have a 20 foot latter, a pair of pliers, a box of matches, a candle and an endless supply of rope. How do you get across?  Copyright © Allyn & Bacon 2005 Newell & Simon Problem Solving  Three ways to acquire new problem solving operators:   Discovery: often involves complex human reasoning but it only method most other creatures use  Thorndyke’s cats in puzzle boxes, Sultan and his 2 sticks Analogy: the process by which a problem solver extract the operators used to solve one problem and maps them onto the solution for another problem  Used for Isomorphic problems- formal structure is the same and only the content differs   Solar system as a model for the structure of an atom (electrons revolve around the nucleus of atom in the same way planets revolve around the sun) – we used mind as computer, bottleneck & attention  Research suggests analogical problem solving is nearly unique to humans and depends on advanced development of prefrontal cortex  Research suggests analogy is difficult/rare across varied context (oh oh for education!) Direct Instruction: Research suggest the best method includes verbal giving of operators plus examples of use Copyright © Allyn & Bacon 2005 Anderson Problem Solving Copyright © Allyn & Bacon 2005 Problem Solving   Three criteria humans use to select operators: Back-Up Avoidance: avoidance of operators that undo the effects of previous operators (unwillingness to take a backwards step even if necessary to solving the problem) Difference Reduction: tendency for humans to select the non-repeating operator that most reduces the difference between the current state and the goal state  Also called Hill Climbing: goal is highest piece of land, then one approach is to always take steps that go up– take a step ―higher‖ towards the goal (but note can also work backwards– from goal state to start state) Means-End Analysis: describes the creation of a new goal (end) to enable the operator (means) to apply Sultan’s new goal became the creation of a new means (create tool) for achieving the old goal (get banana)  Dependent on advanced Prefrontal cortex to maintain goal/sub-goal structure  More sophisticated method of operator selection than Difference Reduction  Will not abandon an operator if it cannot be applied immediately  Focuses on enabling blocked operators by creating sub-goals to eliminate the difference between the current state and the condition for applying a desired operator    Want to drive child to school keys locked in car Copyright © Allyn & Bacon 2005 Problem Solving Cycle     Problem Identification:  recognize there is a goal state that you need to get to (Goal Directedness) Problem Definition:  CRITICAL step– research show if inaccurately represent the problem, much less able to solve it  Problem Representation: how the problem is depicted in the mind Strategy Construction:  Involves Analysis (breaking down into sub-goals-- Sub-goal Decomposition) or Synthesis (putting together various elements to make something useful-MEA)  Research shows most common strategy is hypothesis testing (Top-down analysis)  Divergent Thinking: first generate a diverse assortment of possible alternative operators to a problem (For how many things can you use a brick?)  Convergent Thinking: narrow down the multiple possibilities to single, best set of operators (what is the capital of Montana?)  First divergent, then convergent, then test to check Information Organization:  Organization of information is strategic–finding a representation that best enables you to implement your strategy (may include adjusting problem representation, use of external supports) Problem Solving Cycle- Sternberg Copyright © Allyn & Bacon 2005 Problem Solving    Resource Allocation:  Research suggests that expert problem solvers/better students tend to devote more mental resources to global (big picture) planning – actual Operator Application than novices/poor students, who allocate more mental resources to local (detail-orientated planning)– beginning stages Monitoring:  Efficient Problem Solvers continually check during problem solving to make sure they are getting closer to the goal (metacognition), re-assess and re-strategize if needed Evaluating:  Efficient Problem Solvers check the solution after problem solving completion, seek feedback  New problems may be recognized  Problem may be redefined  New strategies come to light  New resources become available/old resources become more efficient Problem Solving Cycle- Sternberg Copyright © Allyn & Bacon 2005 Problem Solving  Common Strategy Hypothesis testing (Hypothesis = best guess)  Simultaneous scanning  start off with all possible hypotheses and eliminate the untenable ones (convergent) start off with a single hypothesis, maintain if successful, change it if not formulate a hypothesis, select a positive instance of it as a focus, make a series of reformulations, changing one feature and noting positive/negative outcomes Formulate a hypothesis, select a positive instance of it as a focus, make a series of reformulations, changing multiple features at a time Copyright © Allyn & Bacon 2005  Successive scanning   Conservative focusing   Focus Gambling  Conservative Focusing is most effective! Problem Solving  For Ill-defined problems (no clear path)  Called Insight Problems because often involves mentally rerepresenting a problem or strategy for its solution in a totally new way  Insight (from the Gestalts): instant when important intermediate operators fall into place in an moment of brilliant awareness– because perceive sub-goal as whole (MEA- Sultan & sticks)  Researchers today debate whether this really happens, distinguishable as a special type of thinking  The way that a problem is mentally represented can influence the ease by which it is solved  Mental Representation is dependent on the actual presentation of the problem (wording/shown)  Mental Representation is dependent on prior knowledge (information stored in memory)  Mental Representation may be dependent on motivation Of course, I could go out and buy one, but that would take time and money. I could make one from old newspaper or wrapping paper but the paper must be sturdy. Then there is the matter of use. Streets aren’t so good, the beach is perfect and open fields are ok. Finally, the weather should be good– windy but not rainy ( unless you are foolishly into physics). Copyright © Allyn & Bacon 2005 Problem Solving  Gestalt Psychologists (perceptual wholes)  The way that a problem is mentally represented can influence the ease by which it is solved  Can produce mental sets (like perceptual sets) which block operator acquisition  Functional Fixedness:   Tendency to perceive things in terms of their familiar uses based on education/culture such that it is difficult to perceive them in an unfamiliar way that would actually solve a problem People ―fix‖ on representing an object in a conventional function and fail to represent a novel function A commonly used example of functional fixedness is Maier's two-string problem (Maier, 1931). In this problem, the subject is in a room with two strings tied to the ceiling. Both strings are of equal length. The objective is to tie the ends of the two strings together. The problem is that while the strings are long enough to be tied together they are short enough that one is unable to just take hold of one string, walk over to the other string, and tie them together. Scattered around the room there are a number of objects. These objects include a plate, some books, a chair, a pair of pliers, an extension cord, and a book of matches. Duncker (1926, 1945) demonstrated functional fixedness in an experiment where participants were given a candle, a box of tacks, and several other objects, and asked to attach the candle to the wall so that it did not drip onto the table below. Subjects tried to nail the candle directly to the wall will little success instead of the dumping the tacks out of the box, nailing the box to the wall and affixing the candle to the box with a drop of was. Subjects “fixed” on the box as a holder of tacks, rather than a container that could potentially hold anything. Copyright © Allyn & Bacon 2005 Problem Solving  The way that a problem is represented can influence the ease by which it is solved  Set Effect: people become biased by their previous experiences to prefer certain operators when solving a problem (don’t go easier/faster route)  3 Also called the Einstelling effect (mechanization of thought) Capacity of Jug A Capacity of Jug B Capacity of Jug C Desired quantity 21 Problem 1 2 3 4 5 6 7 8 9 10 21 14 18 9 20 23 15 28 18 14 127 163 43 42 59 49 39 76 3 25 10 6 4 3 3 3 4 8 100 99 5 21 31 20 18 25 22 6 The subject is given a set of jugs of various stated capacities, and is asked to measure out a desired quantity of water. 127 A48 36 All problems except 8 can be solved by B - 2C - A. For problems 1 through 5 this solution is simplest. For problem 7 and 9 the simpler solution is A + C. Problem 8 cannot be solved by B - 2C - A, but can be solved by A - C. Problems 6 and 10 can be solved more simply as A - C. Subjects who worked through all problems in order: 83% used B- 2C - A on problems 6 and 7. 64% failed to solve problem 8. 79% used B - 2C - A on problems 9 and 10.Subjects who saw only last 5 problems. Fewer than 1% used B - 2C - A. Only 5% failed to solve problem 8. Problem can be overcome by warning subjects. B C Copyright © Allyn & Bacon 2005 Luchins (1942) Problem Solving  Incubation Effect: Where interruption of the task (taking a break for hours, days, weeks, etc.) improves eventual success rate.  Examples from scientific literature:  Poincaré (mathematical discovery whilst taking a walk on the beach)  Tesla (invention of the alternating current motor after years of thinking about the problem, while quoting Goeth, inspired by watching a sunset)  Kekulé (discover of benzene rings, who dreamed of carbon atoms dancing in a circle and joining hands). Incubation explained by: •Recovery from fatigue •Selective forgetting of irrelevant information •Release from inappropriate set/fixedness •Unconscious work on problem The cheap-necklace problem experiment (Silveira 1971) ―You are given four separate pieces of chain that are each three links in length. It costs 2¢ to open a link and 3¢ to close a link. All links are closed at the beginning of the problem. Your goal is to join all 12 links of chain into a single circle at a cost of no more than 15¢.‖ Control group: Worked on the problem for half an hour. 55% solved the problem. Experimental group 1: Worked for half an hour, interrupted by a halfhour break in which other activities were performed. 64% solved the problem. Experimental group 2: As 1, but with a 4 hour break. 85% solved the problem. Subjects were asked to talk as they worked on the problem. They came back to the problem where they left off, and did not have preformed solutions– so suggests not subconsciously working on it while breaking. Instead– can be explained by set effects. Subjects will bring particular knowledge structures to bear on solving the problem. If however they are not appropriate, the subject may be stuck with them through the process of spreading activation. Taking a break may allow the activation to subside—break set effect, try different approach and other structures get a chance. B C Copyright © Allyn & Bacon 2005 Problem Solving  Cognitive Flexibility: Thinking about the problem from different perspectives (negates functional fixedness and set effect) Connect all the dots using only four lines, however, do not lift your pen.  Cognitive Flexibility = Thinking outside the box! Copyright © Allyn & Bacon 2005 Creativity Paul McGuffin was born in 1986 in St. Louis. His father was Irish; his mother was Native American. Fifty-two years later, he dies while playing chess with Albert Einstein in Nebraska. However, he dies in 1999.  So complex, hard to try to define!  Creativity: The process of producing something that is both original and worthwhile  Still subjective and open to interpretation  Often involves Cognitive Flexibility at its heart! Copyright © Allyn & Bacon 2005 Creativity  Some Major perspectives from which it is studied:  Production: study creative people producing more (measure the diversity, numerosity and appropriate of responses to open-ended questions)  Knowledge: study underlying cognitive processes by focusing on problem solving and insight  As a matter of expertise  Importance of divergent thinking to creativity  Related to spreading activation and knowledge representations  Personality and Motivation: study internal vs. external motivation factors (intrinsic shown to be key) and personality type effects (creativity related to openness and risk-taking)  External Factors (place and time): study immediate social, intellectual and cultural contexts (role of nurture affecting the nature of an individual creator), study domain and field effects  Synthesis of all of the above: studies multiple individual factors and environmental factors Copyright © Allyn & Bacon 2005 Creativity  4 stages of creativity (from the problem solving perspective):  Empirical support is lacking, but subjective reports abound  Preparation — formulation of problem  Time varies from minutes to a life time  Incubation — leaving the problem while considering other things Illumination — achieving insight Verification — testing and/or carrying out the solution   Copyright © Allyn & Bacon 2005 Creativity  Investment Theory of Creativity  Creative individual ―buys low, sells high‖  Buying Low:  Creator initially sees the hidden potential of ideas that are resumed by others to have little value  Creative ventures often initially appear foolish  Focuses attention o this idea– which is unrecognized/unvalued by peers but has great potential creative development Creator develops idea into meaningful, significant creative contribution which is at last recognized as an idea with merit. Then others jump on board, but those people aren’t given credit for being creative, only the first person (or few) who risked trying something new Mean while, creator moves on– influencing the field by staying a step ahead of the rest Copyright © Allyn & Bacon 2005  Selling High:    Who is the best example? Hint: Selling high means it is in Vogue! Creativity  Sternberg & Lubart’s theory of 6 facets of creativity:  Processes of intelligence     Intellectual style Knowledge Personality Motivation  Environmental context  Offers a synthesis perspective to creativity– not a single trait but combination of several factors and all their interactions  Suggests true creativity rare not because people don’t have some/all attributes but hard to get all 6 working together. Copyright © Allyn & Bacon 2005 Creativity  Judging/Measuring Creativity  Highly subjective  Sometimes standards set by authority in the field culture and education affect ability to think creatively Possible to train people to be more flexible in their thinking, to score higher on tests, to solve puzzles, to think more deeply about issues.   Cultural Blocks   Teaching Creativity (depends on your definition of creativity)  Training though likely can’t produce highly creative individuals (painters, musicians, writers, etc).  Creativity can be enhanced:    Develop a knowledge base. Create the right atmosphere for creativity. Search for analogies. A steel pipe is imbedded into the concrete floor of a bare room. The inside diameter is .6 inches larger than the diameter of a tennis ball which is resting gently at the bottom of the pipe. You are one of a group of 6 people in the room, along with the following: 100ft clothesline, a hammer, a chisel, a box of cheerios, a file, a wire coat hanger, a monkey wrench and a light bulb. List as many ways to get the ball out of the pipe as possible. Copyright © Allyn & Bacon 2005 Judgment and Decision Making 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 antinuclear demonstrations.          Based on the description above, list the likelihood that the following statements about Linda are true: A. Linda is a teacher in an elementary school B. Linda works in a bookstore and takes yoga classes C. Linda is active in the feminist movement D. Linda is a psychiatric social worker E. Linda is a member of the League of Women Voters F. Linda is a bank teller G. Linda is an insurance sales person H. Linda is bank teller and is active in the feminist movement Tversky Allyn & Bacon 2005 Copyright © & Kahneman Judgment and Decision Making  Decision Making:  To select from among choices or evaluate opportunities   yellow bike or periwinkle bike which of two job offers would benefit your career the most in the long run  Reasoning:  Process of drawing a conclusion on the basis of evidence or to derive a coherent conclusion from certain premises/principles  Fallacy:  a misconception resulting from incorrect reasoning  an argument which seems to be correct but which contains at least one error and, as a consequence, produces a final statement which is clearly wrong In the course of our every day lives, we constantly make decisions! Copyright © Allyn & Bacon 2005 Decision Making   Classical Decision Theory:  Earliest models were devised by economists & statisticians  Assumed decision makes based on ―unlimited rationality‖ = people are fully informed of all options, sensitive to distinctions among options, fully rational in regards to choice among options with the goal of carefully computing maximum gain and minimum loss Bounded Reality:  Simon (1957) proposes we are rational– but within limits  Acknowledges we do not always make ideal decisions and often include subjective considerations  Satisficing: decision-making strategy where we consider options one by one and then select an option as soon as we find one that is satisfactory or just good enough to meet our minimum level of acceptability  Elimination by Aspects: (Tversky, 1970): focus on one aspect (attribute) of various options and form a minimum criteria for that aspect– them eliminate all options that don’t meet the criteria, for remaining options, select a second aspect, set minimum criteria to eliminate additional options– continue sequence until one option remains  Heuristics and Biases:  Heuristic: a specific rule-of-thumb or argument derived from experience– a mental shortcut  Lighten load of cognitive decision but increase chance of error Copyright © Allyn & Bacon 2005 Decision Making Statistical Reasoning   In real life, we frequently we do not know absolutely whether something is true or false (we are uncertain), so rather than formal logic, instead we estimate of likely or probable something is and then decide in favor of the better chance if there is a decision to be made.  Most decisions are related to an estimate of the probability of success! Statistical Reasoning:  Simple Probability of A [p(A)] = likelihood that a given event (A) will occur = Johnny is 1 of 10 highly qualified students applying for 1 scholarship, what is Johnny’s chance?= probability = 1/10 or .1 = 10%  Negation of Probability of A [1-p(A)]= likelihood that given event (A) will not occur= If Johnny is 1 of 10 highly qualified students, what is Johnny’s chance of not getting the scholarship? = 1- .1 = .9 = 90%  Combined probability of 2 mutually exclusive events [p(A) + p(B)]= If the likelihood that that both events A and B will both occur is 0, what is the probability that either will occur = Johnny & Johnny’s roommate are among 10 highly qualified students, what is the chance the one of them will get the scholarship?= .1 +.1=.2 = 20% Copyright © Allyn & Bacon 2005 Decision Making Statistical Reasoning  Statistical Reasoning:   Combined probability of two independent events [p(A) x p(B)]= Johnny owns 4 pair of shoes and randomly rotates wearing them. What are the chances that one of the 2 roommates will get the scholarship while Johnny is wearing his brown shoes?= .25x.2=.05 = 5% Conditional Probablity [P(H|E)]=likelihood that particular evidence is true if a particular hypothesis is true= what is the chance of Johnny getting the scholarship if his grades are higher the other 8 students? To figure this out, you use Bayes Theorum, where E is the evidence and H is the hypothesis I believe probability of getting scholarship is high if grades are high (8 out of 10), so P(E|H)=.8, now figure out E if H is not true, suppose I know that chances are 1 out of 100 that Johnny would not get the scholarship with higher grades, so P(E|~H)= .01 Bayes equation= P(E|H) x P(H) P(H|E) x P(H) + P(E|~H) x P(~H) P(H|E) = (.8) x (.1) (.8) x (.1) + (.01) x (.9) =.89 Most people do not use Bayes Theorum in every day decision-making (too complexaccurate estimates of the probabilities of events is difficult to ascertain), however, it is essential to evaluating scientific hypotheses, formulating medical diagnoses, analyzing demographic data and other real-world tasks. Tversky Allyn & Bacon 2005 Copyright © & Kahnman Decision Making Heuristics & Biases  Kahneman and Tversky (1984) have shown that instead of using the formal rules of probability to make judgments about the likelihood or probability of events (especially related to combined or conditional probability) , people use a set of heuristics (rules of thumb, mental shortcuts)  Mathematics vs. previous experience  The Representativeness Heuristic  States that people judge how likely or probable something is to be a member of a category according to whether its features seem typical of the category features or not -- i.e., to whether it seems representative of the category. Thus, for example, if one wears certain kinds of clothes and is interested in certain topics, then one might conclude that he/or she is likely to be an engineer. People use this heuristic because it probably works most of the time, but it does lead to some problems in reasoning about probabilities.   Often works– judge weather by month/yesterday’s weather Gambler’s Fallacy: gambler mistakenly believes that probability of a given random event (winning/losing) is influenced by previous random events [similar is the Streak Shooter Fallacy for basketball)  Discounting Base Rate Information:  People will ignore actual statistics about the numbers of instances of categories (base rate information) and base their probability judgments solely on representativeness. For example, participants in a study judged people described as having an appearance and interests that fit the stereotype of an engineer as very likely to be engineers even if told that in the town of 100 they live in that there are 70 lawyers and 30 engineers (and hence the people are more likely to be lawyers). In fact, the estimates were the same whether they were told there are 70 lawyers and 30 engineers, or whether they were told there were 30 lawyers and 70 engineers. In other words the base rate information was ignored and the probability judgments were made solely on representativeness. Tversky Allyn & Bacon 2005 Copyright © & Kahnman Decision Making Heuristics & Biases   Conjunction Fallacy:  Sometimes people judge something to be more likely to be in the intersection of two sets (A and B) and than in the sets themselves (A, B). Clearly this cannot be the case because the intersection (conjunction) is a subset of each of the sets. This happens when the conjunction has more features in common with the instance than the whole set does so by representativeness the instance is judged more likely to be in the conjunction than in the set. Thus, for example, a woman described as "a political activist when in college, whose politics are leftist, has an interest in women’s literature, ..." is judged more likely to be a "bankteller who is active in the feminist movement" than to be a "bankteller" even though all feminist banktellers are also banktellers. Anchoring and Adjustment Heuristic:  The Anchoring and Adjustment Heuristic says that when making a judgment, people will start with any stated figures (the anchor) and adjust from there. Thus they will give quite different answers to questions depending on what anchoring figures are contained in the question. For example, if asked whether the number of African countries in the UN is greater than 10 they will answer yes, but people will then underestimate the actual number because 10 is a low anchor that they are adjusting from. On the other hand, if they are asked if the number is less than 100 they will answer yes, buy then give an overestimate because they are adjusting down from the high anchor of 100. Thus, if we want accurate answers, we have to be careful how we ask questions in interviews or questionnaires so that the anchoring and adjustment heuristic will not throw off people’s judgments of frequencies. Tversky Allyn & Bacon 2005 Copyright © & Kahnman Decision Making Heuristics & Biases  Availability Heuristic:  The availability heuristic states that people judge how likely or probable something is by how easy it is to think of an example of it. Thus, the easier it is to think of an example, the more probable people think it is. People have this heuristic because it works most of the time: i.e., the more probable something is the more often we are likely to think of it and thus the stronger it is going to be in our memories. However, other factors than frequency of occurrence can affect memory and these can throw off probability estimates using the availability heuristic. For example, if we read two lists of names and one has a number of famous (and thus memorable) names on it while the other doesn’t, then we think the list with the famous names is longer (eventhough the lists are of equal length) because it is easier to remember the famous names than the nonfamous ones. For another example, people will say the probability of having a word begin with k (in English) it greater than the word having a k as the third letter, because it is much easier to think of words that begin with k (first letters are a good memory cue) than it is to think of words with k in the third position (third position is a bad memory cue. However, having a k in the third position is more likely so the availability heuristic yields the wrong probability estimate.  Politicians (coached by advisers) use the availability heuristic to manipulate public opinion. One poignant memorable example of a problem or proposed benefit (even having people stand up in a TV debate audience to embody the problem or benefit) will lead the public to think the problem (e.g., overcrowded classrooms) or benefit (e.g., paying less tax) is likely because it is easy to remember the striking example. Presenting actual statistics related to the problem is a much more valid argument but has much less impact on people’s probability judgments (because they discount base rate information) and thus opinions. Events portrayed in the media can have a striking impact on public beliefs through the availability heuristic. For example, a high profile, memorable portrayal of a gay character on TV or in the movies can lead the audience to wildly overestimate the likelihood that people are gay because these media portrayals are easy to remember. Tversky Allyn & Bacon 2005 Copyright © & Kahnman Decision Making Heuristics & Biases  Some Fallacies:  Illusionary Correlation:  We tend to see particular events or attributes as going together because we are predisposed to do so. For events– see (not real) cause-effects relationships. For attributes– use personal prejudices to form/use stereotypes (perhaps result of representative heuristic). For example, if you expect people of a certain political party to show particular intelligence or moral characteristics, then instances in which people show those characteristics more available in memory than instances that contradict the biased expectations  Overconfidence:  Tendency for an individual to over-estimate his/her own skills, knowledge or judgments. Can result from: people not realizing how little they really know, not realizing what they are assuming when call on knowledge they have, ignorance of information coming from unreliable sources.  Sunk-cost Fallacy:  Decision to continue to invest in something because you have invested before and hope to recover investment. For example: you buy a car that’s a total lemon and keep sinking more and more money into repair. Now one more major repair $$, you think of all you have already spent and reason you need to do additional repair rather than buy new car (but throwing more money into car will not get previous money back– better to write off previous $$ as a sunk cost and buy new car)  Hindsight bias:  Once look back at a situation, we ―see‖ all the signs and events leading up to a particular outcome. Example: everything is fine and then big blow up with boy/girlfriend, ugly breakup– in retrospect, tell friend you knew it wouldn’t work out, you stopped communicating, s/he was distant, non attentive, etc. Tversky Allyn & Bacon 2005 Copyright © & Kahnman Decision Making Heuristics & Biases  Some More Fallacies:  Fallacy of Reification:  To reify is to assume an idea is real when it may be hypothetical or metaphorical. For example, student having problems with classes says ―The college is out to get me‖. Includes such expressions as ―the government‖, ―the democrats‖, ―big business‖, ―nature‖, ―the gods‖….  Ad Hominem and Personal Arguments:  Arguments that attach a person’s character rather than the substance of an argument (back to good ol’ politics!). A candidate presents well-reasoned idea but is rebutted not for the ideas but on the basis of moral character. Also, personal arguments ―it must be true because it happened to me, or my Aunt DeDe or my super professor‖  Arguments that appeal to Force and Power:  Basing a decision or argument on virtues that may have nothing to do with the actual situation (US was justified in entering the Vietnam war because we are a mighty and moral nation)  Appeals to Authority and Fame:  Basing a decision because of the endorsement of someone in authority and/or famous people. Practice is common for US advertisers to use athletes, movie stars, singers to endorse products of which they have little/no knowledge– Britney drinks Pepsi, so should you! Four out of five doctors agree…..  Majority-must-be-right Arguments: If most people do something it must be right (but they may all just be stupid!). Over 90 billion served ….. Straw Man Argument (also called lightning rod):  Set up a weak argument and attribute it to someone else so you can knock it down. Example: present well-reasoned argument for giving aid to Philippines, includes saving wild mountain animals, opponent attacks whole argument by showing mountain animals are abundant  Copyright © Allyn & Bacon 2005  Decision Making Heuristics & Biases  Research on Heuristics & Biases:  Shows human rationality is limited– people often fail to utilize intellectual competence in daily life, intuition is often wrong But irrationality is also limited because we do act rationally in many instances Decision making can improve with     Practice, particularly with feedback on decision-making strategies Gaining accurate information on probabilities and how to use them appropriately Avoiding overconfidence (suppresses self-monitoring)   Important to note that research suggests that heuristics can be amazingly simple ways for drawing sound conclusions-- often good when take deciders goals in mind   ―take the best’ heuristic can be very effective in decision situations Behavior based on experience often corresponds to correct probabilities Copyright © Allyn & Bacon 2005 Decision Making Framing Effects  Decision Frames:  Perceptions of the acts, outcomes, and contingencies associated with a particular choice When there is no clear basis for making a decision, people are influenced by the way in which the problem is framed (presented)   Framing Effects:  Different frames can lead to different outcomes, even when the exact same information is used: You have to make a $15 dollar purchase, you can purchase it where you are or to a store 20 blocks away where you have a $5 off coupon for the same item. You have to make a $125 dollar purchase, you can purchase it where you are or to a store 20 blocks away where you have a $5 off coupon for the same item. US preparing for Asian Flu which will potentially kill 600 people. Two alternate plans available: Program A = 200 will be saved Program B = 1/3 chance that 600 people will be saved and 2/3 chance that not people will be saved Alternative 2 choices: Program C = 400 people will die Program D = 1/3 chance no one will die and 2/3 chance that 600 people will die Research by Kahneman & Tversky shows when given choice A Or B, 72% prefer Program A, when given choice between C and D, only 22% prefer choice C (notice choice between A and B, C And D is actually the same choice! Research by Kahneman & Tversky show a person is more likely to go to the 2nd store in the first instance than the second instance (difference between $15 and $10 is perceived Difference in decision may be not on basis of which is the best choice but instead on which as larger than the difference between $125 and choice is easiest to justify (to ourselves/others). Different Frames = easier or harder to justify. $120, even though the difference is the same in Copyright © Allyn & Bacon 2005 Logical Reasoning    Logic:  to advance an account of valid and fallacious (incorrect) inference to allow one to distinguish good from bad arguments.  Where thinking refers to the general process of considering an issue in the mind LOGIC is the science of thinking  2 people can think about the same thing but conclusions reached can be different– one logical and one illogical Reasoning:  Process of drawing a conclusion on the basis of evidence or to derive a coherent conclusion from certain premises/principles  Involves moving from what is already known to infer a new conclusion or evaluate a proposed conclusion Logical Reasoning:  Sorting through true/untrue inferences to draw a valid conclusion BASED ON MAKING AN INFERENCE (implied but not given information)  Two Main Types: Deductive Reasoning and Inductive Reasoning  Deductive Reasoning:  Specific conclusions are drawn with certainty from more general principles * General to Specific  Inductive Reasoning:  General conclusion are probabilistically drawn from more specific principles * Specific to General Given: Janna is the sister of Alyse. Janna is the mother of Mikey. Deduction: Alyse is the aunt of Mikey (certainly true given family relations) Induction: Alyse is older than Mikey (probably true but not necessarily true) Copyright © Allyn & Bacon 2005 Logical Reasoning Deduction  Aristotle formalized deductive reasoning in syllogisms. Syllogisms have pairs of given statements followed by a conclusion. Aristotle’s syllogisms involved properties (men are mortal), quantifiers (e.g., all, some) and set relations (Socrates is a man) like these. Socrates laid out a series of rules for valid syllogistic reasoning that stood as the foundation of logic until the beginning of the 20th Century. For example, IF All men are mortal AND Socrates is a man THEN Socrates is mortal  (IF part is called the antecedent) (THEN part is called the consequent) Here, the first two statements are the givens and the last statement is the conclusion. In this particular example the first two statements are true and so is the conclusion.  Modus Ponens: Rule of Logic stating that a if/then conditional statement is true and its antecedent is true, then its consequent must be true   Infer the consequent from the antecedent: IF P then Q and given the proposition P, we can infer Q  IF Johnny comes to class, THEN he will get a good grade [P then Q]  Johnny came to class. [P]  So, infer  Johnny got a good grade [Q] by Modus Ponens= is a valid deduction For this type of reasoning, have to treat facts as certainties and suspend other real world knowledge (may have slept through class!) Modus Ponens: infer the consequent from the antecedent Deduction: Specific conclusions are drawn with certainty from more general principles Copyright © Allyn & Bacon 2005 Logical Reasoning Deduction IF Johnny goes to class. THEN He will get a good grade Johnny did not get a good grade. Infer: Johnny did not go to class  (IF part is called the antecedent) (THEN part is called the consequent) Here, the first three statements are the givens and the last statement is the conclusion. In this particular example the first two statements are true and so is the conclusion.  Modus Tollens: Rule of Logic stating that if we are given a proposition P implies Q and the fact that Q is false, we can infer that P is false  Infer the consequent from the antecedent    IF Johnny comes to class, THEN he will get a good grade [P implies Q] Johnny did not get a good grade. [Q is false] So, infer  Johnny did not go to class [P is false] by Modus Tollens= is a valid deduction  For this type of reasoning, have to treat facts as certainties and suspend other real world knowledge (may have slept through class!) Modus Tollens: infer the negation of the antecedent from the negation of the consequent Deduction: Specific conclusions are drawn with certainty from more general principles Copyright © Allyn & Bacon 2005 Logical Reasoning Deduction  Watson Selection Task:  There is a rule that states: All cards have a letter on one side and a number on the other side. There is a rule that states: if a card has a vowel on one side, it has an even number on the other side. What card(s) do you need to turn over to find out if this rule is true?  There is a rule that states: if anyone is drinking a beer, then the person must be over 21 years old. What card(s) do you need to turn over to find out if this rule is true? Deduction: People often fail to apply modus tollens Copyright © Allyn & Bacon 2005 Logical Reasoning Deduction  Research shows people often do not apply Modus Tollens to the letter/number problem but do for the beer Problem  Cheng and Holyoak (1985) provided an explanation of these seemingly contradictory findings:  People have certain pragmatic reasoning schemas that they have acquired through experience in the everyday world and that if a logical reasoning task is interpretable in terms of one of these then they tend apply it and get the reasoning correct.  Pragmatic reasoning schemas can in some cases provide meaning for the formal logical reasoning rules. One major class of pragmatic reasoning schemas are contractual schemas like permission and obligation (concepts that are part of our practical experience). The beer-drinking case is an example of the permission schema which interprets: P IMPLIES Q as You have permission to do P if Q is true   So if one is doing Q (drinking beer) then P must be true (you must be 19 or over) and if Q is not true (you are not 19 or over) then you do not have permission to do P (so you must drink coke instead of beer). Other research has shown that training in formal logic (e.g., taking a logic course in college) does not increase the likelihood one will do logical reasoning correctly in other contexts, but that even short-term training in these pragmatic reasoning schemas substantially increases the likelihood that one will reason correctly in other contexts (Cheng, Holyoak, Nisbett and Oliver,1986) Performance can be greatly enhanced when the material to be judged has meaningful content Copyright © Allyn & Bacon 2005 Logical Reasoning Deduction  Performance can be influenced by the form of the argument Other errors in syllogistic reasoning are considered a consequence of the ―mood‖ or ―atmosphere‖ of the argument, rather than on the basis of formal logical deduction.  Atmosphere Hypothesis: for categorical syllogisms (which contain some, all, no and not) there is a tendency to accept or reject an argument on the basis of its form merely presenting the argument in a certain way may influence its believability. Atmosphere biases:  Tend to accept a positive conclusion to positive premises and negative conclusions to negative premise and when mixed, tend to prefer the negative conclusion  Tend to accept a universal conclusion (all or no) if the premises are universal. When one premise is particular (some or not some) and the other universal, tend to prefer particular conclusion. All republicans are human. All democrats are human. Therefore, All republicans are democrats. All A are B All C are B Therefore, All A are C  The term ―all‖ suggests a universal affirmative atmosphere so when people come to a conclusion which mimics the form, they tend to accept it– but the obvious invalidity is apparent if substitute letters for content. All men are humans. Some humans are women. Therefore, Some men are women. All A’s are B’s Some B’s are C’s Therefore, Some A’s are C’s Note: Atmosphere hypothesis doesn’t explain what people are thinking– only tries to predict what conclusion they will accept and people often only approximate the predictions and are often more accurate than this hypothesis would predict Copyright © Allyn & Bacon 2005 Logical Reasoning Induction  Going from specific instances to general rules (remember language)   WHY INDUCTION?: Cognitive psychologist believe people use induction ALL THE TIME to become increasingly able to make sense out of the great variability in their environment and to predict events in their environment, thereby reducing uncertainty. Copyright © Allyn & Bacon 2005 You find out that all students in your PSY 200 class are on the dean’s list (honor roll). You reason inductively (through inference) that all students who enroll in PSY 200 are excellent students  But we cannot logically leap from ―all observances to date of X are Y‖ to therefore ―all X are Y‖  possible next observation will not be Y (hope it is not you!) Regardless of # of observations or soundness of reasoning, NO inductively based conclusion can be proved– only supported to greater or lesser degree by more evidence  So say things like ―99% chance of rain‖ Therefore, induction involves the generation and testing of hypotheses   Logical Reasoning Induction  Going from specific instances to general rules  WHY INDUCTION?: Cognitive psychologist believe people use induction ALL THE TIME to become increasingly able to make sense out of the great variability in their environment and to predict events in their environment, thereby reducing uncertainty. Copyright © Allyn & Bacon 2005 Do not have mind-staggering abilities to calculate every covariation and specific probability Instead, induction often occurs through the use of heuristics (short cuts)– such as mentioned related to decision making   When using heuristics, people often pay particular attention to unusual events and when 2 unusual events co-occur or occur in proximity, people tend to assume events connected in some way (usually causally) When doing categorical inferencing, people tend to use both top-down and bottom-up strategies Induction is the basis for scientific study and hypothesis testing   Rationality   It may seem that humans are hopelessly irrational However, Cohn points out that:  Rationality cannot be determined by laboratory experiments that don’t capture everyday decision-making. It is unreasonable to expect ordinary people to be sophisticated in probability and statistics. The laws of logic and rationality are not relevant to ordinary human behavior.   Copyright © Allyn & Bacon 2005