Chapter 12 Reasoning and Decision Making
Deductive Reasoning: Going from a general statements (Premises) to particular cases. No new information is added. It is like Arithmetic. We use logical rules to compute conclusions that logically follow from the premises. e.g., All plants are carbon-based This thing in my hand is a plant Therefore, this plant is carbon-based Chp 11 pt 2
The Conclusion has Deductive Validity If and only if the premises are true and valid Logical Form has been followed.
Leaves Two Places for Humans to be illogical • being mistaken about the premises. • making errors in the form of their logic ≠ HUMANS ARE NOT VERY GOOD AT DEDUCTIVE LOGIC!!! Chp 11 pt 2
Syllogisms a basic reasoning puzzle – given some basic premises, does the conclusion follow? Some As are Bs Some Bs are Cs Therefore, Some Cs are As. Qualities (some, all, no, every, some are not, many) Premises are taken to be true. Is the conclusion true? Chp 11 pt 2
All Beagles are dogs, All beagles are mammals Therefore, all dogs are Mammals Sounds logical because it matches are real world knowledge, but the logic does not work. The following uses the same logic: All professional football players are male, All professional footfall players are athletes, Therefore, all males are athletes. Chp 11 pt 2
All Beagles are dogs, All beagles are mammals Therefore, some mammals are dogs. No elephants are insects, All insects are animals, Therefore some animals are not insects. Both are valid, but people rarely are able to draw these conclusions from the premises.
Why are humans so illogical? Not all premises are easy to correctly follow. Premises with “all” are easier than those with “some”. Why? They interpret “some” according to everyday meanings “some mammals are dogs and some are not”, but in logic “some” means that “at least one mammal is a dog and there may or may not be some mammals that all not dogs.” Premises with “no” or “not” are even more difficult than “some” premises. People have difficulty thinking in negations.
Conditional (Propositional) Reasoning If, then Reasoning Example: If (antecedent) p, then (consequent) q q Conclusion ? i.e., If Susan is angry, then I am upset I am upset Conclusion: Susan is angry Chp 11 pt 2
If p, then q. p q This is a Valid Conclusion: Modus Ponens (Latin for " Affirming the antecedent”) Example: If I am a professor, then I am educated. I am a professor. Therefore, I am educated. People are generally good at this form of conditional reasoning. Chp 11 pt 2
If p, then q Not q Therefore, not p. Also Valid : Modus Tollens (Latin for “denying the consequence “) Example: If I am a professor, then I am educated. I am a NOT educated. Therefore, I am NOT a professor. People generally find these more difficult that Modus Ponens Chp 11 pt 2
Fallacies - a mistaken belief based on an invalid argument. People often make these logical errors. If p, then q Not Valid – “denying the Antecedent” Not p Therefore, not q. If I am a professor, then I am educated. I am not a professor. Therefore, I am not educated. But I can be educated without being a professor, can’t I?
If p, then q Not Valid – “Affirming the Consequent” q Therefore, p. If I am a professor, then I am educated. I am educated. Therefore, I am a professor. Again, I can be educated without being a professor, can’t I? Chp 11 pt 2
Irrelevant Content Byrne (1989) found that adding irrelevant content greatly decreases syllogistic reasoning. If she has an essay to write, then she will stay late in the library. If the library stays open, then she will study late in the library She has an essay to write. Therefore? Chp 11 pt 2
Belief Bias: The tendency to accept arguments as logical if they match our real-world knowledge. We fail to see that the logic is faulty. Chp 11 pt 2
Watson Card Four Card Task Rule: If a card has an 'A' on one side then it has a '4' on the other side. A B 4 7 To test this rule which cards must be turned over? Chp 11 pt 2
If stated as a logical premise it would be: If p ( a letter on one side), then it has a 3 on the other side • 'A' only 33% turned over • 'A' and '4‘ 45% turned over • 'A' and '7’ 4% turned over • Correct answer is 'A' and '7‘ Chp 11 pt 2
Valid - People see that they need to test A to try to confirming the rule (antecedent; If p then q - test for q). They also often feel they need to see what is on the other side of 4 (even though it is irrelevant). Generally, they neglect to look for evidence that will disconfirm the rule (denying the consequence; test for not q).
Why is this difficult? People find it hard to reason with abstract terms. If you give context, people do better. Chp 11 pt 2
Beer Coke 22 16 Griggs & Cox (1982) "If a person is drinking beer, then that person is over 21". When the problem was phrased with a real-world context, over 75% of participants got the correct answer. Chp 11 pt 2
Why do people make errors on deductive reasoning tasks? • Conclusion Interpretation Approach • Representation-Explanation Approach • Surface (Heuristic) Approaches
Human Deductive Reasoning Conclusion-Interpretation Approaches People have biases about making particular conclusions. - people are biased against saying “no valid conclusion” They misinterpret premises as being reversible (Conversion error) All A’s are B’s All B’s are A’s (is reversible) Some A’s are not B’s Some B’s are not A’s (Not reversible)
2. Representation-Explanation Approaches Reasoning problems are difficult and people make errors because of either incomplete information, or because of incomplete representations of the arguments. Complex arguments put strain on WM.
Johnson-Laird (three stages) Model construction – build a mental model of the problem. Many problems have multiple representations All A’s Are B’s All B’s are C’s A B C B B B A C
Conclusion Formation: Premises are integrated so that consistent models are integrated and inconsistent ones are discarded. Four possible models or oror 3. Conclusion Validation – (All A’s are C’s): there are two possible models and none of them invalidate the conclusion - so the conclusion is valid. C B C A B C A B C B A A C A C A
Limited WM Capacity Principle of Parsimony (economy) – people form a single, simple and typical model. The more alternative models there could be, the less likely it is that people will draw valid conclusions. People with higher WM capacity are better at syllogisms. Chp 11 pt 2
If a person is in the wedding party, then they are getting a beehive hairdo. Sue is getting a bee hive hairdo. Therefore, Sue is in the wedding party. People form the Model And miss the possible model Beehive Wedding Beehive Wedding Chp 11 pt 2
3) Surface Approaches – reasoning relies on heuristics that focus on the properties of the qualifiers in the arguments rather than on logic. If the premises qualifiers are universals (ALL or No) than the conclusion should also be a universal. If the premises qualifies are not universals (Some, Many) than the conclusion will not be a universal. If the premise qualifiers are negatives (Not) the conclusion should be a negative
Pragmatic Reasoning Schema (Heuristics) People through experience, learn reasoning schema that they apply to situations rather than applying pure reasoning. E.g., Permission Schema – If person meets a certain criteria (is over the drinking age) then they get to carry out an action ( drink alcohol). Explains why people are better with the Watson Card Task when it has familiar context.
Chater and Oaksford (1999) Probability Heuristic Model Rather than assigning truth to the premises we assign probabilities. All A’s are B’s is 100% that A is a B. Some and many are assigned probabilities (between 0 and 100%). But in the real world, we rarely have 100% certainty so “All” may mean “highly likely, but not always”. Instead of making logical conclusions, we make probabilistic ones.
Inductive ReasoningReasoningfrom specifics (observations and knowledge) to broader generalizations. Unlike deductive reasoning which is about absolute truth, inductive reasoning is about the likelihood of conclusions being true. Inductive reasoning generates NEW information.
Types of Inductive Reasoning Analogical Transfer – the process of using one structural domain to interpret another domain. Category Induction – Being able to organize and reorganize a group of things as members of the same category. When we see a new instance, we not only categorize it, but we infer many properties of the category to this new instance (how to interact with it, what it is likely to do, be used for etc.).
Causal Reasoning People are constantly forming theories of how the world around us works. We seek answers in the form of cause and effect. Two factors: Covariation of two events (the degree to which the effect occurs in the presence of the cause, and fails to occur in the absence of the cause) and a belief that there is some mechanism for the relationship to be causal rather than coincidental.
Fugelsang, Thompson & Dunbar (2006) Participants in three experiments rated their beliefs that causes have the capacity to produce a given effect. Read brief stories about an event and a possible cause of the event. They answered the following about each story. How believable do you think it is that X (e.g. smoking) can cause Y (cancer)?
To determine if there is a relationship between smoking and developing lung cancer, you examine 10 patients who were smoking and 10 patients who were not smoking. • Of the 10 patients who were smoking, how many would you expect to have lung cancer? • Of the 10 patients who were not smoking, how many would you expect to have lung cancer?
Example of stories used in this study. Imagine you are a researcher who is trying to determine the cause of lung cancer in a group of patients. 11 You have a hypothesis that the lung cancer may be due to exposure to high doses of radiation. 01 You have a hypothesis that the lung cancer may be due to coughing. • You have a hypothesis that the lung cancer may be due to smoking. 00 You have a hypothesis that the lung cancer may be due to taking vitamin C supplements. Each scenario is preceded by a code (e.g., 11), which denotes the level of the BELIEF and COVARIATION manipulation (1 high and 0 low), for each scenario.
Fugelsang, Thompson & Dunbar (2006) A strong positive correlation was discovered between participants’ beliefs in causal power and their beliefs that the effect occurs in the presence of the cause. However, no relationship was found between participants’ beliefs in causal power and their belief that the effect will fail to occur in the absence of the cause. In other words, people fail to take into account evidence that disconfirms the pattern that they see in the correlation,
Hypothesis Testing Watson (1960/1972) Participants are given a number sequence 2, 4, 6, and are asked to come up with a hypothesis regarding the rule underlying this sequence. To test there hypothesis they need to produce a number sequence that follows the rule and they will receive feedback about whether the sequence follows the rule. They then need to guess the rule. Participants try sequences such as 8, 10, 12 and 17, 19, 21. They hypothesis that the rule is add 2 to each number to produce the next number.
While they produce numbers that follow the rule, the rule they identify is NOT the rule. The rule is “any three numbers that increase in value.” 29% never found the rule. The hypothesis given were generally designed to confirm the hypothesis rather than to disconfirm (falsify) it.
Confirmation Bias – people tend to look for evidence that confirms their beliefs while disregarding evidence that falsifies it. We say this in the four card example as well. People failed to turn over the 7 to see if it disconfirmed the rule.
Counterfactual (What if)Thinking Counterfactual thinking is a form of inductive thinking involving thoughts about alternatives to past events, that is, thoughts of what might have been. (E.g., If only I had studied, I would have passed the exam). Counterfactual thinking can lead to new hypothesis and to better understanding of cause and effect outcomes.
Making Decisions General Model of Decision Making (Golotti, 2002) • Setting goals - what are you trying to accomplish. • Gathering information – what are your options and what are the probabilities that each option will accomplish your goal. • Structuring the decision – How will you weigh out your options. e.g., pro and con list. • Making the decision – Generally made under high information load and uncertainty. • Evaluation – past decisions can be used to inform future decisions.
Ideal Decision Making Normative Theory – how people should make decisions (attempt to maximize utility) Expected Utility = (prob of X) x (Utility of X) While people are capable of using this type of model (e.g., pro vs. con list) we rarely even approximate this type of procedure unless it is a very important decision.
People are not good at judging probabilities! Monty Hall Problem http://math.ucsd.edu/~crypto/Monty/monty.html chap 10 Problem solving
The inner wheel represents the number of the door that the car is behind, the middle wheel represents the door that is selected by the contestant, and the outer wheel represents the door Monty Hall can show. The red means that in order to win the contestant needs to switch doors, and the blue means that the contestant should not switch. Notice that there are twice as many red sections as blue. In other words, you are twice as likely to win if you switch than if you don't switch! chap 10 Problem solving
Why is the Monty Hall Problem So Difficult? 88% Choose to Stay with original choice. • Uniformity Fallacy: Heuristic that assumes that all the available options are equally likely whether they are or not. • Cognitive Load – dual task decreases the number who solve this (De Neys & Verschueren, 2006). • Monty’s actions are seen as Random – they are not. Misunderstand the effects of Monty’s knowledge on the probabilities. chap 10 Problem solving
Algorithms (e.g., expected utility model). Generate every possible solution Systematically work through them Advantage: If done correctly it guarantees a solution! Disadvantages: Takes a great deal of time and cognitive effort. Requires full definition of the problem.
Heuristics – rules of thumb, mental short cuts, pre-stored strategies for judging probabilities. Advantages: Less cognitive effort Allow you to proceed with incomplete understanding of the problem (e.g., lack of specific information). Heuristics are based on our understanding of processes that underlie an outcome (e.g., random processes should look random) or on memory (which does not store information according to exact frequencies).
video Thinking Fast and SlowBIG IDEA #1 Dual-process framework Humans have two systems that can be used for reasoning. System one: Heuristics, nonlogical, automatic, requiring little effort, and intuitive. Influences by the content of the argument, implicit knowledge of the terms and the language used to state the argument (all, some). We use this system for fast, and less important reasoning System Two: Analytical, logical controlled processes that require effort and attention. Both systems can make errors, but for different reasons.
Big Idea #2: Anchoring and Adjustment • People begin the process of estimation with whatever information readily appears in their minds (anchoring) • They then reassess their initial answers based on rough notions of what is a not-too-silly answer (adjustment)