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Chapter 13

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PSYC 221
Yaroslav Konar

Page 360-384, 24 pages Page 1 of9 Chapter 13: Reasoning & Decision Making DEDUCTIVE REASONING: SYLLOGISMS & LOGIC • Decisions: Making choices between alternatives. Reasoning: The process of drawing conclusions, and the cognitive processes by which people start with information and come to those conclusions. • Decisions are often the outcome of reasoning, but reasoning is also used in other situations – such as problem-solving and making inferences. • Binary Decisions: Decisions with only two outcomes, including many survival decisions, e.g. eat = live; starve = die. Similarly, in a two-alternative forced choice detection task, you either answer “yes” or “no”. • Deductive Reasoning: Using sequences of statements called syllogisms (invented by Aristotle), to arrive at a definitive conclusion. • Syllogism: Consists of two premises, followed by a conclusion. In a categorical syllogism, the statements begin with all, no, or some. o Premise 1: All dogs are canines o Premise 2: All canines chase felines o Conclusion: Therefore, all dogs chase felines o Others: No A are B; some A are B; some A are not B Validity and Truth in Syllogisms • Validity: A syllogism is valid when its conclusion follows logically from its two premises. In the above example: o Premise 1: All A are B o Premise 2: All B are C o Conclusion: All A are C • Validity depends on the form of the syllogism. Truth refers to the content of the premises, to be evaluated to determine whether they are consistent with the facts. E.g. All birds are animals. All animals have four legs. All birds have four legs  this is valid, but not true • Valid syllogisms can result in false conclusions, but syllogisms can be invalid even though the premises and conclusion seem reasonable. Conditional Syllogisms • Conditional Syllogisms have two premises and a conclusion as well, but the first premise has the form “If p, then q”, where p is the antecedent and q is the consequent. There are four major types: o If it’s a cat, then it’s cute. o 1) Affirming the Antecedent = Modus Ponens: Valid. It’s a cat  It’s cute o 2) Denying the Consequent = Modus Tollens: Valid. It’s not cute  It’s not a cat o 3) Affirming Consequent: Not valid. It’s cute  Does not mean it is a cat. Could be a puppy. o 4) Denying Antecedent: Not valid. It’s not a cat  Does not mean it’s not cute. Could be a puppy. Page 360-384, 24 pages Page 2 of9 • Most (close to 100%), correctly judge that syllogism 1 is valid. However, only 60% judge syllogism 2 is valid. Affirm Deny Antecedent Modus Ponens Consequent Modus Tollens Conditional Reasoning: The Wason Four-Card Problem • People are often better at judging the validity of syllogisms when real-world problems are used instead of abstract symbols. • Wason Four-Card Problem: Four cards are shown, each with a letter on one side and a number on the other. You must indicate which cards you would need to turn over to test the rule: If there is a vowel on one side, then there is an even number on the other side. • Turning over the E affirms the antecedent (53% correctly chose to turn over this card). However, we also need to turn over the 7 to deny the consequent o Most subjects missed this, and decided to turn over 4 (affirm consequent). However, this tells us nothing about the rule, since the rule does not say all even numbers must be paired with vowels o Turning over the 7 is important, since revealing a vowel would disconfirm the rule • Falsification Principle: To test a rule, it is necessary to look for situations that would falsify the rule. For example, to falsify “If P, then Q”, find an instance of “P and not Q”  have to turn over cards “P” and “not Q” The Role of “Regulations” in the Wason Task • Are there general reasoning mechanisms that are responsible for the improved performance when a task is stated in real-world terms? Relating to real-life regulations makes it easier to solve the task. • Griggs & Cox (1982): Each card has an age on one side, and the name of a beverage on the other side. Imaging you are a police officer who is applying the rule, “If a person is drinking beer, then s/he must be over 19 years old.” Which of the cards must be turned over to determine if the rule is being followed? • With this version, 73% of participants correctly determined that you must flip over both the “beer” (confirm antecedent) and “16 years” (deny consequent) cards. The Role of “Permissions” in the Wason Task • Pragmatic reasoning schema is a way of thinking about cause and effect that is learned as part of experiencing everyday life. This includes the permission schema, that states if a person satisfies condition A (being over 19), then they get to carry out action B (drink alcohol). • People apply a real-life schema like the permission schema to the card task, causing the differences in performance between the abstract version and the beer/drinking-age version. • Cheng & Holyoak (1985): “You are an immigration officer at the International Airport in Manila. You have to check a document called Form H. One side indicates whether the passenger is entering the country or in transit, the other side lists names of tropical diseases. You have to make sure that if the form says “Entering” on one side, the other includes cholera among the list of diseases. Which forms do you have to turn over to check?” Page 360-384, 24 pages Page 3 of9 • In this condition, 62% of participants chose the correct cards: “Entering” (confirm antecedent) and “Typhoid, Hepatitis” (deny consequent). • Subjects in another group heard the same instructions, but heard “The form listed inoculations the travelers had received in the past 6 months. This is to ensure the entering passengers are protected against the disease.” • Now, the immigration officer is checking to see whether the travelers had the inoculations to give them permission to enter the country. This activation of the permission schema resulted in 91% correct answers. An Evolutionary Approach to the Four-Card Problem • A proposed alternative to the permission schema is that performance on the Wason task is governed by a built-in cognitive program for detecting cheating. This evolutionary perspective on cognition is related to the social exchange theory, which states that an important aspect of human behaviour is the ability for two people to cooperate in a way that is beneficial to both. • However, problems arise when someone cheats and does not reciprocate – the ability to detect cheating is evolutionarily advantageous. People do well in the cholera task because they can detect someone who cheats by entering the country without a cholera shot. • Cosmides & Tooby (1992): Devised a number of four-card scenarios involving unfamiliar situations – removing familiarity with various rules in permission schema. Subjects are read statements about a hypothetical culture called the Kulwane, and then given the condition “If a man eats cassava root, then he must have a tattoo on his face”. Subjects are given four cards: 1) eats cassava roots, 2) eats molo nuts, 3) tattoo, and 4) no tattoo • Subject performance was high on this task even though the rule was unfamiliar, since they could detect cheating where a man who eats the cassava root without a tattoo. What has the Wason Problem Taught Us? • Some believe permission is important, others cheating, and other propose alternative explanations • The context within which conditional reasoning occurs makes a big difference. Stating the four- card problem in terms of familiar situations can often generate better reasoning than abstract statements. However, familiarity is not always necessary, as seen by the tattoo problem. INDUCTIVE REASONING: REACHING CONCLUSIONS FROM EVIDENCE • Inductive Reasoning: Arriving at conclusions that are probably true, based on the evidence from observation of one or more specific cases. This is the case for scientific research. The Nature of Inductive Reasoning • In inductive reasoning, conclusions are suggested, with varying degrees of certainty, but do not definitely follow from the premises. • We do not consider validity, instead we decide how strong the argument is. A number of factors contribute to the strength of an inductive argument: o 1) Representativeness of Observations: How well do observations about a particular category represent all members of that category? Are all crows black, or are there rare blue crows in Australia? o 2) Number of Observations: The argument is made stronger by adding more observations. o 3) Quality of Evidence: Stronger evidence makes for stronger conclusions. Page 360-384, 24 pages Page 4 of 9 • Anytime we make a prediction about what will happen based on observations about what has happened in the past, we are using inductive reasoning. E.g. Professor X’s course exams ask a lot about experimental procedures, so the next exam I take with Professor X will probably have similar questions. • Inductive reasoning thus provides the mechanism for using past experience to guide present behaviour, saving you a lot of energy than if you had to approach every experience as if for the first time. • Heuristics are rules of thumb that are likely to provide the correct answer, but are not foolproof. The Availability Heuristic • Which is more prevalent in English, words that begin with the letter “r” or words where “r” is the third letter? • Availability Heuristic: Events that are more easily remembered are judged as being more probable than events that are less so. 70% choose words that begin with ‘r” as more common although in reality 3 times more words have “r” in the third position. • People judging more likely causes of death are affected by cases publicized by the media. For example, 58% think more deaths are caused by tornadoes than by asthma, when in reality 20x more die from asthma. • McKelvie (1997): Present lists of 26 names to subjects. In the “famous men” condition, 12 names were famous men (Ronald Reagan, Mick Jagger) and 14 were nonfamous women. In the “famous women” condition, 12 names were famous women (Margaret Atwood, Miley Cyrus) and 14 were nonfamous men. • Subjects are asked to estimate whether there were more males or females in the list they heard, their answer was influenced by whether they had famous males or females – the famous names are more easily remembered. • Illusory Correlations occur when a correlation between two events appears to exist, but in reality there is no correlation or it is much weaker than assumed. “So Frank, you have long hair. Does that make you a woman?” “You have a wooden leg. Does that make you a table?” • This can take the form of a stereotype, an oversimplified generalization about a group or class of people, often focusing on the negative. • A stereotype may lead one to pay particular attention to behaviours associated with that stereotype, creating an illusory correlation that reinforces the stereotype. The Representativeness Heuristic • Representativeness Heuristic: The probability that A is a member of class B can be determined by how well the properties of A resemble the properties associated with class B – how much one event resembles another event. • E.g. We randomly pick one male from the population of Canada. That male, Robert, wears glasses, speaks quietly, and reads a lot. Is it more likely that Robert is a librarian or a farmer? • More people guess that Robert is a librarian, as his characteristics matched many people’s image of a typical librarian – they used the representativeness heuristic. However, they ignored the base rate, the relative proportion of different classes in the population – in this case, there are more male farmers than male librarians, so statistically it is more likely that Robert was a farmer. • When base rate information is available, people more often use that information to make their estimates. E.g. “In a group of 100 people, there are 70 lawyers and 30 engineers. What is the chance that if we pick one person from the group that the person will be an engineer”, subjects correctly respond with 30%. • However, when any descriptive information is available, people disregard the base rate information. E.g. The person picked is Jack, a 45 year-old man. He shows no interest in political and social issues and spends most of his free time on his hobbies, which include home carpentry and math puzzles. His last job involved determining the structural characteristics of a bridge that was being built. Page 360-384, 24 pages Page 5 of 9 Making Judgements without Considering the Conjunction Rule • “Linda is 31 years old, 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.” Which of the following is more probable? 1) Linda is a bank teller; 2) Linda is a bank teller and a feminist • The statistically correct answer is that statement 1 has a greater probability of being true, but most pick statement 2 due to the representativeness heuristic. • The conjunction rule states that the probability of a conjunction of two events (A + B) cannot be higher than the probability of the single constituents (A alone or B alone). Incorrectly Assuming Small Samples are Representative • Law of Large Numbers: The larger the number of individuals that are randomly drawn from a population, the more representative the resulting group will be of the entire population. • Although typically 50% of all babies are boys, a smaller hospital that births about 15 babies each day (compared to a larger hospital that births about 45 each day) will have more days where over 60% of babies born are boys. The Confirmation Bias • Confirmation Bias: Tendency to selectively look for information that conforms to our hypothesis, and to overlook information that argues against it. • Wason (1960): You will be given three numbers which conform to a simple rule I have in mind. Your aim is to discover this rule, by writing down sets of 3 numbers. After you write down each set, I shall tell you whether your numbers conform to the rule or not. When you feel confident you have di
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