1. Cognition – 2/e Dr. Daniel B. Willingham Chapter 10: Decision Making & Deductive Reasoning PowerPoint by Glenn E. Meyer, Trinity University © 2004 Prentice Hall © 2004 Prentice Hall

2. ©2004 Prentice Hall 2 Do People Consistently Make Optimal Decisions? Decision Making: A situation in which a person is presented with two or more explicit courses of action, with the requirement that he or she select just one Decision Making: A situation in which a person is presented with two or more explicit courses of action, with the requirement that he or she select just one Normative or Rational Models Normative or Rational Models Normative or Rational Models Normative or Rational Models Demonstrations of Human Irrationality Demonstrations of Human Irrationality Demonstrations of Human Irrationality Demonstrations of Human Irrationality

3. ©2004 Prentice Hall 3 Normative or Rational Models Rational Decisions Rational Decisions  May not be rational - In the context of decision making, rational choices are ones that are internally consistent (e.g., that show transitivity).  Transitivity - If a relationship holds between the first and second of three elements and it holds between the second and third, it should hold between the first and third. If choices were rational, there would be transitivity of preference between choices. However, transitivity does not always hold Normative Theories: A theory of choice that describes a set of rules by which some choices are better than others and one choice can be said to be optimal. Optimal value depends on the specific theory Normative Theories: A theory of choice that describes a set of rules by which some choices are better than others and one choice can be said to be optimal. Optimal value depends on the specific theory  Expected Value Theory: A normative theory of choice in which the best choice is the one that offers that largest financial payoff. Expected values for various Casino games are seen in Table 10.1 o Example: Suppose you had a choice of 1. 0.5 chance of winning $50Expected Value =.5 x $50 = $25 2. 0.25 chance of winning $110 Expected Value =.25 x $110 = $27.5 Expected Value Theory says you pick the second choice  Expected Utility: A normative theory of choice in which the best choice is the one that offers the reward with the greatest personal value to the individual, not necessarily the greatest financial reward. The theory allows that in some situations, it may be more valuable to an individual to be very likely to get a modest reward rather than to have a small probability to get a large reward. For example: would you spend a dollar for the chance to win a dollar with a high probability or a low probability of winning several million dollars.

4. ©2004 Prentice Hall 4 Demonstrations of Human Irrationality Two principles are shown if people act rationally: Two principles are shown if people act rationally:  Description invariance People will consistently make the same choice irrespective of how the problem is described to them as long as the basic structure of the choices is the same  Procedure invariance A requirement of rational decision making, it is the idea that people will consistently make the same choice irrespective of the how their preference for that choice is measured. In fact, procedure invariance is violated Tversky and Kahneman (1986) show consistent violations of these principles due to differences in the problem frame (way the problem is described). Tversky and Kahneman (1986) show consistent violations of these principles due to differences in the problem frame (way the problem is described). Framing Effects:  People are averse to take risks if the outcome is described positively but more willing to take risks if the outcome is described negatively  Psychic framing: How we mentally categorize money we have spent or are considering spending. Another aspect of framing o Cost or gain of some part of an item is considered relative to the cost of the entire item o Sunk Costs: An investment (e.g., of money, time, emotion) that is irretrievably spent and should not affect current decisions about spending but nevertheless often does o Loss Aversion: The unpleasantness of a loss is larger than the pleasantness of a similar- sized gain  Choice changes depending on how choice is elicited (Tversky, Slovic and Kahneman, 1990)  Satisficing (Simon, 1957); To select the first choice that is satisfactory (i.e., above some threshold) rather than evaluating every choice and selecting the best of those. Psychologists believe that people must satisfice most of the time because there are usually too many choices to allow evaluation of all of them

5. ©2004 Prentice Hall 5 What Shortcuts Do People Use to Make Decisions? Heuristics Vs. Algorithms – an important distinction Heuristics Vs. Algorithms – an important distinction Algorithm: A formula that can be applied to choice situations. It has the advantage of producing consistent outcomes, but algorithms may be complex and difficult to compute. For example: Expected Value is an algorithm Algorithm: A formula that can be applied to choice situations. It has the advantage of producing consistent outcomes, but algorithms may be complex and difficult to compute. For example: Expected Value is an algorithm Heuristics: Simple cognitive rules that are easy to apply and that usually yield acceptable decisions but can lead to errors. Heuristics: Simple cognitive rules that are easy to apply and that usually yield acceptable decisions but can lead to errors. Decision Heuristics Decision Heuristics Representativeness Representativeness Representativeness Availability Availability Availability Anchoring and Adjustment Anchoring and Adjustment Anchoring and Adjustment Anchoring and Adjustment Information We Ignore Information We Ignore Information We Ignore Information We Ignore Probabilities versus Frequencies Probabilities versus Frequencies Probabilities versus Frequencies Probabilities versus Frequencies Social Factors Social Factors Social Factors Social Factors

6. ©2004 Prentice Hall 6 Representativeness Representativeness: A heuristic that leads you to judge the probability of an event as more likely to belong to a category if it has the features of the category that you deem important Representativeness: A heuristic that leads you to judge the probability of an event as more likely to belong to a category if it has the features of the category that you deem important  Example from Tversky and Kahneman (1973) “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-nuclear demonstrations.” Which is more likely? A. Linda is a bank teller B. Linda is bank teller and active as a feminist Most people choose “B” based on stereotypical impressions from the description

7. ©2004 Prentice Hall 7 Availability Availability: A heuristic in which the likelihood of an event is evaluated by the ease with which examples of the event can be called to mind Availability: A heuristic in which the likelihood of an event is evaluated by the ease with which examples of the event can be called to mind  Example: Are there more words in English that start with the letter “r” or have “r” as the third letter. The latter is true but 69% chose the first letter. That is because it is difficult to recall words based on their middle letter (Tversky and Kahneman, 1973).  Illusory Correlation: People have a bias to judge that two events or characteristics of an event go together if people had a prior belief that they go together or if they are natural associates. Illusory correlation is related to the availability heuristic because you judge that two things are correlated if you can think of many instances in which the two things co-occurred

8. ©2004 Prentice Hall 8 Anchoring and Adjustment Anchoring and adjustment: Heuristic used to estimate probabilities in which the person starts with some initial probability value (anchor) by doing a partial calculation of the problem or by using a probability statement in the problem and then adjusting that initial estimate upward or downward based on other information in the problem Example: Estimate the answer to these problems (subjects saw only one) (Tversky and Kahneman) Anchoring and adjustment: Heuristic used to estimate probabilities in which the person starts with some initial probability value (anchor) by doing a partial calculation of the problem or by using a probability statement in the problem and then adjusting that initial estimate upward or downward based on other information in the problem Example: Estimate the answer to these problems (subjects saw only one) (Tversky and Kahneman)  1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 = ?  8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 =? ■ The answer to both is 40, 320  Folks seeing the first string guessed a median answer of 512  The second string elicited a median guess of 2,250 Anchoring and Adjustment heuristic has been found to influence: Anchoring and Adjustment heuristic has been found to influence:  Preference judgments  Judgments of answers to factual questions  Estimates of probabilities of events such as nuclear war  Estimates of preferences for one’s spouse  Legal decisions such as awards in lawsuits

9. ©2004 Prentice Hall 9 Information We Ignore Ignoring Sample Size Ignoring Sample Size  Definition: number of things in a group that you are evaluating. Larger samples are better.  Sample size is crucial in determining probabilities of events, however people may tend to use the representativeness heuristic more Ignoring the Base Rate Ignoring the Base Rate  Definition: The frequency of an event in the general population.  When judging the likelihood that an event occurred, people tend to ignore the base rate if they are given any other information about the event  Example: Medical testing for breast cancer as seen in Table 10.2 (Eddy, 1982)

10. ©2004 Prentice Hall 10 Probabilities versus Frequencies Gigerenzer and Hoffrage (1995) claim that previous work has a flaw. The human mind is built to keep track of frequencies and not probabilities – based on evolutionary needs and constraints Gigerenzer and Hoffrage (1995) claim that previous work has a flaw. The human mind is built to keep track of frequencies and not probabilities – based on evolutionary needs and constraints  Subjects could be presented with problems in a probability vs. frequency format. The latter led to more correct solutions as seen in Fig. 10.2  Base rate neglect is more likely with probability information as our minds evolved in preliterate societies where information would be remembered in terms of frequencies.  Other researchers argue against this view and find other factors to explain the results  Conclusion is that presentation format is important but reasons for this are not clear

11. ©2004 Prentice Hall 11 Social Factors Researchers may have ignored social factors in decision making. Decisions may be based on: Researchers may have ignored social factors in decision making. Decisions may be based on:  Social contracts  Opportunities to cheat  Implications for future choice  Sacred Values and Principles Tetlock (1991, 1992, 2002) – pitting a secular value (like assigning a monetary value) vs. a sacred value (saving a life) is taboo. Anger is directed towards those making the taboo choice Tetlock (1991, 1992, 2002) – pitting a secular value (like assigning a monetary value) vs. a sacred value (saving a life) is taboo. Anger is directed towards those making the taboo choice

12. ©2004 Prentice Hall 12 Decision Making and Emotion Damasio and Tranel: Damasio and Tranel:  Higher stimuli cause the ventromedial prefrontal cortex to activate somatic responses, including emotional responses from the autonomic nervous system  These emotional reactions along with logical, cognitive processes limit choices of action  As seen in Fig. B10.1, subjects with ventromedial damage make poor decisions as they have lost the ability to make associations between complex stimuli and their consequences.

13. ©2004 Prentice Hall 13 Do People Reason Logically? Formal Logic Formal Logic Formal Logic Formal Logic Human Success and Failure in Reasoning: Conditional Statements Human Success and Failure in Reasoning: Conditional Statements Human Success and Failure in Reasoning: Conditional Statements Human Success and Failure in Reasoning: Conditional Statements Human Success and Failure in Reasoning: Syllogisms Human Success and Failure in Reasoning: Syllogisms Human Success and Failure in Reasoning: Syllogisms Human Success and Failure in Reasoning: Syllogisms General Models of Reasoning General Models of Reasoning General Models of Reasoning General Models of Reasoning

14. ©2004 Prentice Hall 14 Formal Logic Do people use formal logic? Do people use formal logic? Important Terms: Important Terms:  Deductive Reasoning: Problems to which one can apply formal logic and derive an objectively correct solution o Premise: statement of fact taken to be true for the purposes of a logical problem o Conclusion: A statement of fact derived by logical processes. One may confidently propose that a conclusion is true or false within a problem based on its logical relation to the premises. Whether the conclusion is true in the real world depends on the truth or falseness of the premises o Studied in terms two formats:  Conditional Statements; A logical form composed of three statements. First premise states, “If condition p is met, then q follows.” Second premise states whether p or q is true. Third is a conclusion about p or q as seen in Fig. 10.3  Syllogisms: Syllogism Logical form composed of three statements of fact: two premises & conclusion  Inductive Reasoning: Reasoning that allows one to say that a conclusion is more or less likely to be true but does not allow one to say that a conclusion must be true

15. ©2004 Prentice Hall 15 Formal Logic - Continued Brain Structures and Inductive vs. Deductive Reasoning Brain Structures and Inductive vs. Deductive Reasoning  Goel, et al. (1997) suggest deductive reasoning associated with activation in left interior frontal gyrus and inductive reasoning with broader areas of left frontal lobe and much greater activity in the superior frontal gyrus as seen in Fig. 10.2  Osherson, et al. (1998) disagree and found deductive and inductive reasoning associated with supplementary motor area, bilateral cerebellum, right caudate and left thalamus. Probability task alone with cingulate gyrus and right midfrontal gyrus. Deductive task with second visual cortex  More research is need to clarify the discrepancies in these two sets of studies.

16. ©2004 Prentice Hall 16 Human Success and Failure in Reasoning: Conditional Statements Philosophers (Aristotle) and psychologists (e.g. Piaget) have assumed that humans are rational and will make correct deductions. However, people may not reason well. Philosophers (Aristotle) and psychologists (e.g. Piaget) have assumed that humans are rational and will make correct deductions. However, people may not reason well.  Wason Card problem (Wason, 1968, 1969) The figure shows four cards. Each card has a letter on one side and a digit on the other side. You are to verify whether the following rule is true: If there is a vowel on one side, there is an even number on the other side. You must verify this rule by turning over the minimum number of cards Solution: You should turn over the “A” and the “3”. Only 15% of college students get it right. They miss turning over the three.

17. ©2004 Prentice Hall 17 Human Success and Failure in Reasoning - Continued  Concreteness or Familiarity – As shown by Griggs and Cox (1982) – more familiar and/or versions of the Wason problem are more easily solved (72% correct) The cards in front of you have information about four people sitting at a table. On one side of a card is a person’s age and on the other side of the card is what the person is drinking. Here is a rule: If a person is drinking beer, then the person must be over 19 years of age. Select the cards or cards that you definitely need to turn over to determine whether they are violating the rule. The effect might be due to Case Based Reasoning: A theory that we reason about problems by remembering similar problems and how they were solved

18. ©2004 Prentice Hall 18 Human Success and Failure in Reasoning - Continued Pragmatic Reasoning Schemas (Cheng and Holyoak, 1985): Pragmatic Reasoning Schemas (Cheng and Holyoak, 1985): Sets of rules defined in relation to goals that can be used to evaluate situations such as permissions or obligations. A key aspect of pragmatic reasoning schemas is that they encourage conclusions that are practical in the real world, as opposed to formal logic, which can lead to conclusions that are technically correct but not useful  Lead to inferences that are practical in solving problems. Logical rules may lead valid inferences that are not much help  Schemas exist for: o Permissions o Obligations o Causations  Prior knowledge activates the appropriate schema to be applied to a problem  Abstract and unfamiliar problems couched in terms of one of these schema are solved more easily.

19. ©2004 Prentice Hall 19 Human Success and Failure in Reasoning - Continued Evolutionary Perspective –as before : Evolutionary Perspective –as before :  Humans evolved as social animals  Social networks require us to help or punish other community members  Rules based on this principle are easier to understand  Example – determining who is a cheater but depends on observer’s social perspective as seen in Fig. 10.7  Cheng and Holyoak (1989) point out subjects solve precaution and permission rules well and this is not part of the social exchange structure  Evolutionary psychologists propose two modules to handle this: o Catching Cheaters o Dealing with precautions  Critics regard this as post-hoc and therefore suspect

20. ©2004 Prentice Hall 20 Human Success and Failure in Reasoning: Syllogisms Syllogism: A logical form composed of three statements of fact: two premises and a conclusion Syllogism: A logical form composed of three statements of fact: two premises and a conclusion Performance is usually bad on these sorts of reasoning tasks due to several factors: Performance is usually bad on these sorts of reasoning tasks due to several factors:  Conversion Errors: An error in dealing with a syllogism in which a person reverses one of the premises. For example the premise reads “All As are Bs” and the participant believes that it is also true that “All Bs are As.”  Conversational implicature: The tendency for people to treat the language of logic as though it has the same meaning as everyday language  Atmosphere : A situation in which two premises of a syllogism are both either positive or negative or use the same quantifier. People are biased to accept as valid a conclusion that maintains the atmosphere  Prior Bias: Real-world knowledge that can influence people’s evaluation of a syllogism. They are more likely to accept as true a syllogism with a conclusion that they know is true and to reject a syllogism with a conclusion that they know is false  No one error or factor is known to be the conclusive factor in most cases of error.

21. ©2004 Prentice Hall 21 General Models of Reasoning There are three families of deductive reasoning models: There are three families of deductive reasoning models:  Syntactic: Models proposing that humans reason by accepting premises and then applying a set of processes that manipulate the premises in an effort to evaluate a given conclusion or derive a conclusion o Braine’s (1990) Natural Logic Theory: proposes a set of simple inference schema called primary skills used in a universal reasoning program with two steps:  British Museum Algorithm: a reasoning scheme based on the play on that idea that given an infinite amount of time and a typewriter, a chimp could produce all the books in the British Museum. The algorithm is similarly extensive and time consuming. It is a direct step  Introduction of Suppositions: Something that one supposes to be true to evaluate the consequences of its being true. Suppositions are important in some theories of deductive reasoning.  The more inference schemas used, the more errors occur

22. ©2004 Prentice Hall 22 General Models of Reasoning - Continued  Semantic: Models based on the idea that a conclusion is true if it can be shown to be true under all conditions in which the premises are true o Johnson-Laird’s (1999) Mental Models Theory: Assumes meaning of a problem is crucial to its solution. Premises are used to construct a mental model of a possible situation in the world as seen in Fig. 10.8  Mental Models can be combined as seen in Fig. 10.9  Success in reasoning would depend on capacity of working memory (Evans, et al., 1999)  Many errors arise from the principle of truth: Proposal in Johnson- Laird’s model of deductive reasoning that people tend to construct models representing only what is true, not what is false

23. ©2004 Prentice Hall 23 General Models of Reasoning - Continued  Probability: An approach to studying reasoning, based on the idea that when presented with what experimenters think of as reasoning problems, participants actually treat them as probability problems o Oaksford and Charter’s Information Gain Model  People use probabilities to assess the likelihood that they will find useful information as in the Wason card problem in Fig. 10.11. They don’t assume the potential relations of P and Q are equally probable in the world  People seek out information they think is maximally informative as compared to following formal logic rules

24. ©2004 Prentice Hall 24 Mental Models, Spatial Reasoning and Brain Imaging Goel, et al. (1998) had participants evaluate three kinds of stimuli – syllogisms, spatial relational and nonspatial relational Goel, et al. (1998) had participants evaluate three kinds of stimuli – syllogisms, spatial relational and nonspatial relational Consider overlap shown in activation with each condition. Consider overlap shown in activation with each condition. Most active areas: left inferior frontal gyrus, left middle frontal gyrus, left cingulate gyrus as seen in Fig. B10.3 Most active areas: left inferior frontal gyrus, left middle frontal gyrus, left cingulate gyrus as seen in Fig. B10.3 Predominance of left hemisphere indicates that reasoning seems largely language based, even with inherently spatial problems. However, more work is needed. Predominance of left hemisphere indicates that reasoning seems largely language based, even with inherently spatial problems. However, more work is needed.