PSYC 358 - Ch 11 Decisions, Judgements, and Reasoning
SNARC effect: Spatial-Numerical Association of Response Codes
- Judgments about smaller numbers are made more quickly with the left hand and judgments of larger numbers are made more quickly with the right ◦ Because we're mentally representing them on a Left-right number line
Memory Errors
According to Johnson-Laird, we don't use formal logic to complete reasoning tasks Instead create mental models ◦ Mental representations of meanings of the terms in the reasoning problem Difficult to represent and use abstract logical structures, so we represent them as meaningful problems If I am a freshman, (then) I have to register today Evidence: I am a freshman Therefore, I have to register today If I am a freshman, (then) I have to register today Evidence: I do not have to register today Therefore, I am not a freshman More models must be derived - higher load More complexity increases working memory load, which leads to interference with reasoning
Improving our thinking about validity
Euler Circles (Venn diagrams) are a useful tool ◦ Individuals are generally better at evaluating validity of syllogisms when shown how to create diagrams and generate specific examples (Helsabeck, 1975) Adopting a skeptical attitude and attempting to find counter examples to the conclusion is another helpful strategy ◦ More improvement when using both diagrams and a skeptical approach ◦ Trying to find diagrams that demonstrate the conclusion being false (Chater & Oaksford, 1989)
Recency:
Example: subjective probability of traffic accidents rises temporarily when one sees an overturned car on the side of the road
Design
Experiment 1: conditional reasoning Experiment 2: conclusion from two conditional statements
Gestalt problem solving
Gestalt: a whole pattern, a form or a configuration • A cohesive grouping; a perspective from which the entire field can be seen • Much of the early research on problem solving came from the gestalt approach • Köhler: explored problem solving with primates • Maier & Duncker: explored problem solving with human participants
Fast and frugal heuristics
Recognition heuristics - a decision is based on whether you recognize the thing to be judged ◦ Think of multiple choice test "Take the Best" Heuristic - deciding between alternatives based on the first useful information retrieved about the alternatives
Simulation heuristic - Recap
Related biases and heuristics ◦ Counterfactual reasoning ◦ Downhill change ◦ Blaming the victim ◦ Hindsight Bias
Hypothesis Testing
We use conditional reasoning in science Null hypothesis testing (think back to stats) If the null hypothesis is true, then there will be no effect of the variable We obtain evidence for an effect of the variable Therefore, the null hypothesis is false
Limitations in Reasoning
We use heuristics because of limitations ◦ Not just lack of effort ◦ Limitations in knowledge ◦ Limitations in algorithms Knowledge continuum ◦ Expertise is rare ◦ Usually partial or incomplete knowledge ◦ Can have no knowledge at all
SNARC Effect
demonstrates role of embodied cognition in decision making ◦ People have a mental number line going from left to right ◦ Tend to start counting on left hand ◦ People who start counting on left hand demonstrate stronger SNARC effects Our representation of numbers has an impact on how we make decisions ◦ SNARC effect disrupted when engaging in a visuo-spatial dual task situation --> suggests that we use the visuo-spatial sketch pad to represent the number line ◦ SNARC effect is found in blind people, suggesting that its more spatial than visual
Availability heuristic
estimates are influenced by the ease with which relevant examples can be remembered Availability heuristic is often reliable ◦ Often only source of information we have immediately available to make an estimate ◦ When we have relevant information stored in memory, the accuracy of the availability heuristic is related to the accuracy of our memory If our memory is incomplete, inaccurate, or influenced by other factors, then we see biases and distortions in our reasoning
Decisions, judgements, and reasoning involve slower deliberate kinds of thinking
◦ How do we reason? ◦ How do we make decisions under conditions of uncertainty? ◦ Reasoning heavily influenced by our general world knowledge
Naïve Physics
People's conceptions of the physical world ◦ Particularly, principles of motion
Ill-defined problems
Do not necessarily have one "correct" answer, and the path to their "solution" is unclear Which puppy should I choose?"
Luchins (1941)
Given 3 water jugs, each with a different capacity, and are asked to measure a quantity of water using just the three jugs Critically, Luchins manipulated the solution to the problem across multiple trials so participants developed a particular set or approach • Trials 1-7 have the solution procedure B - 2C - A • Participants applied this solution procedure to trials 6 & 10 • These trials have a simpler solution: A - C • 80% of participants failed to notice the simpler solution and applied the initial procedure Solution • Empty Jug A into destination jug • Refill Jug A using Jug B and repeat • Empty Jug C into destination jug
Negative set
Luchins (1941) data provided evidence of a negative set or set effects • Negative set: bias or tendency to solve problems in one particular way, using a single specific approach, even when a different approach might be more productive • Past experiences or previous learning can be strong enough to bias later solution attempts and prevent us from seeing all the possibilities
Criticisms of the Gestalt approach
Somewhat limited in its applicability • Really only concerned with "Insight Problems" • Many problems do not involve an 'insight' to solve, but rather implementing a series of known operations • Leaves out consideration of the processes that lead to restructuring. • What happens in between initial representation and restructured representation?
Gestalt problem solving part 2
They provided evidence of insight learning and problem solving • Insight: sudden perception of useful or proper relations for solving a problem • i.e., "Eureka!" or "Ah-ha!" moments They also identified two major barriers in problem solving: • Functional Fixedness - an inability to use objects outside of its normal use. • Negative Set - a bias to solve problems in the same way using a single approach.
Functional fixedness:
a tendency to use objects and concepts in the problem environment in only their customary and usual way • Comprehend problems through semantic memory • When we retrieve an object from semantic memory, its normal uses are most accessible • However, insight problems often involve nonstandard uses of objects and concepts • Participants have difficulty divorcing themselves from standard uses of objects and concepts retrieved from semantic memory to consider potential nonstandard uses Maier (1931): Pliers are typically used for grabbing objects and applying force to them, not as a pendulum • Duncker (1945): Boxes are typically used as containers, not as a shelf
Algorithm
- specific rule or solution procedure, often detailed and complex that is guaranteed to furnish the correct answer if it is followed correctly ◦ Examples: Normative model - method provided by mathematics and probability ◦ The procedure for multiplying large numbers by hand
Errors in Conditional Reasoning
1. Form Errors ◦ Use an invalid form of the argument 2. Search Errors ◦ Errors in how we search for evidence 3. Memory Errors ◦ Errors in how we mentally represent meaning
Decision making process
1. Search for evidence ◦ Can be positive and/or negative ◦ Is all of the evidence available to us? 2. Evaluate evidence 3. Decide based on some criterion or rule
Wason Card part 2
46% of people turn over the 'E' card and the '4' card ◦ 'E' conforms to gathering evidence to test modus ponens ◦ We know the card has a vowel on one side, does it follow the rule and have an even number on the back? ◦ '4' conforms to gathering evidence for the invalid form of affirming the consequent Only 4% of people turn over both the 'E' and '7' cards ◦ Conforms to gathering evidence to test modus ponens AND modus tollens ◦ Those are the two valid forms of the conditional argument, so both must be supported for the rule to be accurate ◦ We know the card has an odd number on one side, does it follow the rule and NOT have an vowel on the back?
Retrievability of instances
A class whose instances are easily retrieved will appear more numerous than a class of equal frequency whose instances are less retrievable ◦ Familiarity bias: judging events as more frequent or important because they are more familiar ◦ Salience/vividness: overestimating likelihood for salient events because they receive more attention and make a stronger impression ◦ Recency: recent occurrences are likely to be more available than earlier ones
Counterfactual reasoning
A line of reasoning deliberately contradicts the facts in a "what-if" kind of way ◦ Nearly happened, could have occurred, might have happened if only, etc.
Counterfactual reasoning: downhill change
A specific type of counterfactual reasoning is downhill change Downhill change: altering an unusual story element, substituting a more typical or normal element in its place ◦ More easily imagined ◦ More plausible ◦ Tendency to judge unusual events as the cause ◦ People focus on actions not failures to act
Adaptive thinking: fast and frugal heuristics
Algorithmic answers involve more memory and prior knowledge People use heuristics not only because we have limited memory and limited knowledge but because they work! ◦ Heuristics are adaptive Satisficing - we settle for finding a satisfactory way to answer a question, rather than searching for the ideal or optimal method
Experience and Knowledge
Acquiring a fuller knowledge of the domain is an important part of making more accurate decisions But structure and complexity of the problem affect whether knowledge will be used appropriately Processing resources available affect how we use knowledge as well
Representativeness: misconceptions of chance
After tossing 6 coins, consider the two following outcomes: ◦ Outcome 1: H-T-H-T-T-H ◦ Outcome 2: H-H-H-T-T-T Using a heuristic, participants often select outcome 1 as being a more probable outcome ◦ Representative heuristic: Outcome 1 'seems' like it was produced by a random outcome, so we estimate it as being more probable Evaluating this question algorithmically: ◦ Calculate the total number of possible outcomes: 2 ^ 6 = 64 ◦ Each is 1 possible outcome out of 64 possible outcomes: (1 / 64) * 100 ◦ In reality, both are equally probable: 1.6% chance of happening
Syllogisms are a type of logical argument
Applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted to be true ◦ Earliest forms defined by Aristotle
Theories of Syllogistic Reasoning part 2
Atmosphere heuristic: favor conclusions that superficially match the premises ◦ Bias to favor a conclusion containing "NOT" if that same modifier is included in the premises ◦ "No cigarettes are inexpensive." - more likely to select a conclusion that contains "NO" than a conclusion that does not regardless of validity of the syllogism Illicit conversion: people inappropriately swap the terms of a statement ◦ "All B are A" = "All A are B" ◦ "All mammals are dogs" is false; the argument is not valid, and we cannot draw a conclusion ◦ "All dogs are mammals" is true; by making an illicit conversion, people erroneously evaluate the conclusion based on this premise
Illusory correlation
Bias in the judgment of the frequency with which two events co-occur Illusory correlation ◦ Based on strength of associative bond ◦ When the association is strong one is likely to conclude that the events have been frequently paired ◦ Strong associates will be judged to have occurred together frequently ◦ Extremely resistant to contradictory data
Non-human problem solving
Chimpanzees are not the only non-human animals to demonstrate an ability for insight problem solving Crows are also able to solve problems through insight learning
Search Errors
Confirmation bias: people only search for evidence that supports or confirms their beliefs ◦ Despite the rules for determining if a logical statement has a valid structure, we tend to seek out and consider only information that supports the conclusion In the Wason card problem, participants demonstrate a confirmation bias ◦ Only search for confirming evidence for the rule --- Modus ponens ◦ Continued to search for confirming evidence by testing an invalid form of the rule -- affirming the consequent ◦ Unlikely to search for negative evidence that would disprove the rule -- modus tollens
Semantic Congruity Effect
Consider both panels... ◦ In each panel, which dot is higher? Quicker to respond for panel D than panel C ◦ Why? ◦ Based on our discussion of making decisions about physical differences - Distance effect / Discriminability Effect ◦ D has greater distance, so its easier to discriminate and faster to respond Now both dots are the same distance in each panel. ◦ What if change the question? The wording of the question influences our response ◦ Faster to respond to the balloon question when asked which is higher ◦ Faster to respond to the yo-yo question when asked which is lower
Conjunctive and disjunctive events
Consider the three examples: 1. Simple event: drawing a red marble from a bag containing 50% red marbles, 50% white marbles Probability = .50 2. Conjunctive event: drawing red marble seven times in a row with replacement from a bag containing 90% red marbles, 10% white marbles ◦ Probability = .48 3. Disjunctive event: drawing a red marble at least once during seven successive trials, with replacement from a bag containing 10% red marbles, 90% white marbles Probability = .52 People tend to overestimate the probability of conjunctive events People tend to underestimate the probability of disjunctive events
Decision making recap and preview
Decision making ◦ Rapid and fairly automatic ◦ We are often only aware of the outcome ◦ Have most, if not all, of the information needed to make the decision ◦ Find similar effects across distinct tasks -- Distance/discriminability effect -- Congruent effects Decision making under uncertainty - Slower and more deliberate ◦Often have some awareness of the process ◦ Do not have most of the information needed to make the decision
Formal Logic and Reasoning Two types of reasoning
Deductive reasoning: starts with a general statement or hypothesis, then examines the possibilities to reach a specific conclusion ◦ E.g.., exploring predictions of hypotheses made by theories in scientific experiments ◦ Going from the general to the specific Inductive reasoning: starting with specific observations (data), then drawing conclusions from the specific observations ◦ E.g., building scientific theories based on empirical data ◦ Going from the specific to the general
Testing Feelings of Rightness
Determinants of the FOR ◦ Answer fluency - ease with which the initial conclusion comes to mind -- Different from processing fluency ◦ Probability that conclusion is accepted as valid -- Decision to accept a conclusion is accompanied by higher FOR than decision to reject it ◦ Presence or absence of competing responses -- Presence of conflict lowers FORs ◦ Ex: conclusion is valid but not believable
Number Magnitude
Distance effect ◦ Takes longer to discriminate between numbers that are closer together ◦ E.g., 2 vs. 2 & 2 vs. 5 Congruity effect ◦ Judgments of smallness are faster for smaller numbers ◦ Judgments of largeness are faster for larger numbers ◦ E.g., 1 vs. 3 & 5 vs. 7 When people make mental comparisons of symbolic quantities, there is a pronounced semantic distance effect ◦ Similar to physical difference effects ◦ Our symbolic representations of numbers is also nonlinear -- Distances between larger numbers are compressed relative to smaller numbers -- Remember the brightness of a light example in our discussion of physical differences When we judge magnitudes, the dimension of judgement must match the implied semantic dimension for comparison to be made quickly ◦ E.g., choose the larger one when both are small numbers is slower than choose the smaller one
Decisions
Every day we make an incredibly large number of decisions... Range from mundane decisions ◦ What to wear? ◦ What to eat for my next meal? ◦ Which is larger? To more fairly important decisions ◦ What response will I provide on this exam? ◦ Should I study or have fun? To major life decisions ◦ What job offer should I accept? ◦ Should I get married?
Salience
Example: seeing a burning house will impact subjective probability of such accidents greater than reading about a fire in the paper
Availability: retrievability of instances
Familiarity ◦ Subjects heard lists of male (N = 20) and female (N = 19) names ◦ Subjects either recalled as many names as they could or estimated the proportion of male/female names ◦ Either male or female names of famous individuals ◦ Participants were able to recall more famous names than non-famous names -- More familiar ◦ Participants estimated that there were more names in the list that contained the famous names ◦ Familiarity bias: judging events as more frequent or important because they are more familiar
Duncker (1945)
Find a way to mount a candle on the wall using just the objects shown in the picture • Candle, matchbook, box of thumb-tasks Again, this problem is difficult for participants to solve Solution • Empty box of thumb tacks • Use a single thumb tack to attach the box to the wall • Place the candle in the box
Much of the research on reasoning and decision making explores why individuals might deviate from a normative model and use a heuristic
Heuristics are prone to distortions, inaccuracies, and omissions ◦ Yet, heuristics can often be used more quickly and easily
Geographic distances
Holyoak & Mah (1982) ◦ Rate distances between American cities on a 1-9 scale. ◦ No geographical reference point given -- Individuals tended to base judgements on their own geographical location (Michigan) -- Distance effect: The farther away the cities are from the participant, the closer together they are in mental representation
Conditional Reasoning - Another Example
If I am a driver then I have a driver's license. Valid: ◦ Evidence --> Affirming antecedent: I am driver. ◦ Conclusion: I have a driver's license. ◦ Evidence ---> Denying the consequent: I do not have a driver's license. ◦ Conclusion: I am not a driver. Invalid: ◦ Evidence ---> Denying the antecedent: I am not a driver ◦ I might or might not have a driver's license ◦ Evidence --> Affirming the consequent: I have a driver's license ◦ I might or might not be a driver
The Circle Problem
If the radius of the circle has length r, how long is x? x = r Answer does not require mathematical computation Must restructure the problem as a rectangle w/ 2 diagonals.
Need to consider two dimensions to evaluate a syllogism:
Is the argument valid? In other words, is the form of the argument correct. ◦ P1: All A are B. ◦ P2: All B are C. ◦ C: Therefore, all A are C. 2. Is the argument sound? In other words, is the argument valid and are its premises true.
Virtues of Representativeness Heuristic
Judgements based on representativeness can - at times - produce quick and accurate responses ◦ Most people who act friendly are friendly ◦ A professional athlete who is very tall and thin is much more likely to play basketball than football ◦ People with a PhD are more likely to read classical literature for pleasure than a high school drop out ◦ Young men are more likely than elderly women to drive aggressively Adaptive when: ◦ Representativeness comes from base-rate information (i.e., the more probable events are also the most representative ones) ◦ Representativeness reflects accurate stereotypes (i.e., actual relationships in the world)
Representativeness: beliefs
Kim & Ahn (2002) ◦ Clinical psychologists' diagnoses are often guided by their 'theories' or beliefs about mental disorders ◦ If a clinician believes that symptom X is a central cause of disorder Y -- They are more likely to diagnose disorder Y ◦ If a clinician believes that symptom X is peripheral to disorder Y -- They are more likely to diagnose with different disorder ◦ There's a manual for that - the DSM -- If evidence is consistent with beliefs, clinicians weight the evidence congruent with the beliefs more heavily when considering a diagnosis -- Confirmation bias: we pay more attention to evidence that support our beliefs
Limitations in Resources
Limitations in working memory ◦ How many subtasks are required for the task? ◦ Ex: (calculating 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) 1. performing calculations 2. while keeping information in memory 3. keeping track of steps 4. retrieving information from long-term memory Limitations in time to perform the task ◦ Unlimited time vs. time restrictions Limitations in amount of effort we are willing to put in
Conditional Reasoning
Logical determination if the conclusion is true given a condition and evidence Form: ◦ If P then Q ◦ Evidence ◦ Conclusion Example: ◦ Conditional statement: If I am going to drive a car, I have to buckle up ◦ Evidence: I need to drive my car to campus today ◦ Conclusion: I must buckle up Four possibilities: ◦ Valid arguments ◦ Affirming the antecedent or denying the consequent ◦ Invalid argument ◦ Denying the antecedent or affirming the consequent
Conditional statements are another type of logical argument
Logical determination of whether the evidence supports, refutes, or is irrelevant to the stated if-then relationship
Theories of Syllogistic Reasoning
Many theoretical propose that we evaluate logical arguments and reason through a set of heuristics ◦ Heuristic: strategy or approach that works under some circumstances but is not guaranteed to yield the correct answer ◦ "general rules of thumb" instead of evaluating for form of arguments and the truth of the conclusion given the truth of the premises ◦ Generally heuristics increase speed and decrease effort relative to formal reasoning
Conclusions
Metacognitive Reasoning Theory ◦ Initial Type 1 output is accompanied by a metacognitive judgment called the Feeling Of Rightness ◦ Which in turn, determines the extent of analytic engagement as well as the outcome of that engagement ◦ FOR predicted length of time spent reaching the final answer as well as the probability of changing the answer
Maier (1931) part 2
Only 39% of subjects could figure out the correct solution to the problem after 10 minutes Solution • Tie the pliers to one string • Swing the string with the pliers like a pendulum • Go to the other string, grab it and catch the pliers to tie the strings together Difficult, because the solution involves a nonstandard use of pliers
Copeland, Gunawan, & Bies-Hernandez (2011)
Participants evaluated two types of syllogisms: -- Necessary syllogism ◦ Valid - conclusion must follow Some married people are skiers All skiers are tennis players Some tennis players are married people Possible strong syllogism ◦ Invalid - conclusion does not logically flow All racquetball players are recyclers Some recyclers are not cyclists Some racquetball players are not cyclists Half of the syllogisms were randomly associated with Zane and the other Half Quinten ◦ Experiment 1 - corresponds to honest or dishonest source ◦ Experiment 2 - corresponds to expert or novice source
Form Errors - Rader & Sloutsky (2002)
Participants read a series of 4 sentences long stories containing a conditional premise ◦ Manipulated whether stories included modus ponens (MP) or affirming the consequent (AC) ◦ Inference condition receives the evidence for the argument, while no inference does not. No inference conditions (didn't present evidence in the argument) had a lower rate of accepting the conclusion at test ◦ All premises seem necessary for accepting conclusion Participants did not differ in their acceptance of the conclusion regardless of whether they had read a valid argument (MP) or invalid argument (AC)
Evans, Barston, & Pollard (1983)
Participants read syllogisms and had to decide whether or not the conclusion follows logically from the premises (i.e., to judge validity) Believability had a large effect on how participants judged syllogisms ◦ Less likely to accept syllogisms as valid if they were unbelievable ◦ More likely to accept invalid syllogisms as valid when they were believable Participants were more likely to accept believable syllogisms as valid regardless of their actual validity!
Evans, Barston, & Pollard (1983) part 2
Participants read syllogisms and had to decide whether or not the conclusion follows logically from the premises (i.e., to judge validity) ◦ Syllogisms varied in whether or not they were valid or not and whether or not the premises were believable ◦ Participants were explicitly told to assume all premises were true and only evaluate structure. Yet, participants were more likely to accept believable syllogisms as valid regardless of their actual validity! Belief Bias: people are prone to ignore the logical form of an argument and focus only on their prior world knowledge
Representativeness: insensitivity to sample size
Participants responses: ◦ 56% of participants claimed it would be about the same for two hospitals ◦ 24% of participants claimed it would be more likely in in the larger hospital ◦ 20% of participants claimed it would be more likely in the smaller hospital (correct answer) Large samples are more representative of its population ◦ Less likely to deviate from the norm ◦ Larger number of events are similar to the expected proportion (50%) Small samples are more likely to have extreme observations ◦ Smaller hospital is more likely to deviate from the norm, so it will have more days above 60% (and below 40%) than the larger hospital
Results: Experiment 1 and 2
Participants spent longer rethinking an answer that was produced with low FOR and were more likely to change answers relative to one that was produced for high FOR ◦ Feeling of Rightness was predicted by answer fluency ◦ FOR was higher for conclusions that participants accepted than those they rejected Type 2 processing: ◦ Participants gave the same answer after additional thought as the one after little thought ◦ When participants did change answers, they were just as likely to change it to an incorrect answer as the correct answer
Form Errors
People make the same inference when the antecedent is affirmed (valid) as when the consequent is affirmed (invalid) ◦ People don't appear to be sensitive to the validity of logical arguments when making inferences during reading (Rader & Sloutsky, 2002) People also have a tendency to reversing conditional statement, but treat it as if it wasn't reversed ◦ The order is meaningful (cause-effect) ◦ If P then Q = If Q then P (an illicit conversion)
Search Errors
People often rely on first impression, first example, or first mental model that comes to mind instead of searching for evidence Confirmation bias: people only search for evidence that supports or confirms their beliefs
Results: Experiment 3
Problems for which the personality description and the base rates pointed to the same answer (congruent) were advantaged in term of FOR and rethinking times FORs were lower for answers that were changed
Both syllogisms and conditional reasoning are examples of propositional logic
Propositions which can be either true or false Rules for combining propositions to both create arguments and evaluate the form of an argument
Decisions: Physical Differences
Psychophysics: How does our perceptual experience differ from physical stimulation that is being perceived ◦ Psychological dimension - our representation of magnitude is different from the physical magnitude of the stimulus Just noticeable difference - amount of change needed to detect a change ◦ Example: brightness depends on: ◦ Absolute level of brightness ◦ Brightness of the background ◦ Duration of the stimulus Distance effect / Discriminability Effect: the greater the distance or difference between two stimuli, the faster the decision that they differ
Measuring the problem solving processes
Reaction time is not a relevant measure • Accuracy is a key measurement - Did participants correctly solve the problem? - Did they use a correct solution procedure? What each step completed accurately? • Verbal protocol - transcription and analysis of subject's verbalizations as he or she solves the problem - How valid is this measure?
Metacognition and reasoning
Reasoning and decision-making are accomplished by two qualitatively different types of processes: ◦ Type 1: fast and automatic ◦ Type 2: slow and deliberate Interaction between these two systems: ◦ What predicts the degree of Type 2 engagement ◦ A third category of process monitor Type 1 outputs and determines the extent of Type 2 engagement (depth of Type 2 thinking)
Availability heuristic Recap
Related biases and heuristics ◦ Familiarity bias ◦ Salience / Vividness ◦ Recency ◦ Imaginability ◦ Illusory correlation ◦ Anchoring ◦ Conjunctive and disjunctive events
Representative heuristic Recap
Related biases and heuristics ◦ Misconceptions of chance ◦ Insensitivity to sample size ◦ Stereotypes ◦ Beliefs ◦ Illusion of validity ◦ Regression to the mean
Evidence on Conditional Reasoning
Rips and Marcus (1977) When the antecedent is given as evidence (modus ponens), people made correct conclusion 100% of the time When the consequent is denied (modus tollens), only 57% of the people made the right conclusion ◦ 77% made the right conclusion when the problem was easier
Supporting Search in the Wason Card Problem
Same task as before, but if we make it more concrete If the envelope is sealed ,then it must carry the expensive stamp 88% of people turn over both the 'sealed' and 'inexpensive stamp' cards ◦ Conforms to gathering evidence to test modus ponens AND modus tollens ◦ Making the task more concrete (more like something you would encounter in the real world) led to participants adopting a more skeptical strategy and to search for disconfirming evidence
Wason Card Problem
Shown a series of cards that have letters on one side and numbers on the other Task is to pick the card(s) you would turn over to gather evidence for the following rule: - If a card has a vowel on one side, then it has an even number on the back 33% of people turned over only the 'E' card ◦ Conforms to gathering evidence to test modus ponens ◦ We know the card has a vowel on one side, does it follow the rule and have an even number on the back?
Decisions and reasoning under uncertainty
Some judgments are made automatically and it is difficult to introspect on how we make these decisions ◦ Familiar ◦ Clear solution Other judgment require conscious processing ◦Unfamiliar material or situation ◦ Several solutions
Syllogisms
Syllogisms consist of three statements ◦ First two statements (premises) are taken to be true ◦ Third statement is the conclusion based on the first two statements Form: ◦ Statement 1 (P1): All A are B. ◦ Statement 2 (P2): All B are C. ◦ Conclusion (C): Therefore, all A are C 1 and 2 are premises that state a class inclusion relation. By apply rules we can extend the class inclusion relation to A and C in 3. Example: ◦ P1: All beagles are dogs ◦ P2: All dogs are animals ◦ C: Therefore, all beagles are animals Both premises are true, the conclusion follows logically, so the conclusion is valid
Symbolic Differences
Symbolic Comparisons: comparison of symbols or objects represented by written or spoken symbols Symbolic difference effect - we judge differences between symbols more rapidly when they differ on some symbolic dimensions Semantic congruity effect - decision is faster when dimension being judged matches implied semantic dimension
Symbolic Differences
Task: ◦ Presented with numbers (0 - 9) ◦ Judge whether each number odd or even ◦ Respond with a left hand key press if odd, right hand key press if even (counterbalanced) ◦ Subtracted RT of left keys - Right keys -- Positive numbers = RT quicker for left hand responses -- Negative numbers = RT quicker for right hand responses
Hindsight bias
The after -the -fact judgment that some event was very likely to happen or was very predictable, even though it wasn't predicted to happen beforehand ◦ Connection between event and outcome are more available after the fact ◦ Makes other possible connections seems less plausible than they otherwise would Affects our actual memory for the event ◦ Remember original position as more consistent with actual outcome
Copeland, Gunawan, & Bies-Hernandez (2011) part 2
The credibility of a given source influenced how people evaluated syllogisms ◦ Specifically, less credible sources led to participants being more likely to correctly reject invalid syllogisms People's logical reasoning can be influenced by extraneous content ◦ Such as source credibility (e.g., Honest/Dishonest; Expert/Non-expert) ◦ And their prior beliefs (Evans, Barston, & Pollard 1983)
Stevens's Power Law
The empirical relationship between an increased intensity or strength in a physical stimulus and the perceived magnitude increase in sensation created by the stimulus ◦ Changes in our sensation of a stimulus does not linearly increase with changes in the stimulus ◦ Rather, changes in our sensation of a stimulus increase exponentially with changes in the stimulus Smaller JND in terms of physical units for: ◦ Dim lights relative to bright lights ◦ Small objects relative to large objects
Representativeness heuristic
We judge likelihood of uncertain events based on the representativeness of an event an estimate of the probability of an event is determined by one of two features 1. How similar the event is to the population of events in came from 2. Whether the event seems similar to the process that produced it: ◦ What is the probability that object A belongs to class B? ◦ What is the probability that event A originates from process B? ◦ What is the probability that process B will generate event A?
Discriminability Effect - Illusions
The greater the distance or difference between the two stimuli being compared - the faster the decision that the stimuli actually do differ. In this picture, the distance between the Leaning Tower of Pisa and the hand appears much less than it actually is. ◦ It becomes more difficult to make a decision about the size of each object ◦ Tricking into thinking that there similar sizes
Problem solving
The process through which we figure out how to reach our goals, starting from our current state • We solve problems all of the time - Range from trivial problems to consequential ones - Range from applied problems to academic problems
Köhler's insight learning with chimpanzees
The task was to retrieve bananas, Köhler manipulated where bananas were and what objects were given to the chimpanzees • Bananas were hung outside of the cage and two short poles were placed inside the cage. After many unsuccessful attempts, they joined poles together to reach bananas. • Bananas suspended from ceiling with many boxes left around the cage. After many unsuccessful attempts, they stacked boxes and climbed on top to reach bananas Chimpanzees' behavior illustrated perception of relations and the importance of insight in problem solving
Illusion of validity
The tendency to overestimate the ability to accurately predict the outcome when analyzing data ◦ Especially when the data appear to show a consistent or coherent pattern ◦ Confidence in estimate depends on how representative the pattern is ◦ Example: - People are much more confident predicting final GPA of a student who has consistently gotten B's in his first year than for one who has an even number of A's and C's ◦ All B's is a more consistent pattern than a mix of A's and C's ◦ B's are a fairly representative grade
Maier (1931) - Gestalt Problem Solving In Humans
Two strings are suspended from the ceiling, and the goal is to tie them together. • The problem is that the strings are too far apart for a person to hold one, reach the other, then tie them together. • Several other objects are also available: a chair, some paper, and a pair of pliers • Even standing on the chair does not get the person close enough to the two strings
Dual systems approach (Kahneman, 2011)
Two systems involved in reasoning and decision making: ◦ System 1: - Operates automatically and quickly - Little to no sense of voluntary control - Heuristic approach - associative ◦ System 2: - Allocates attention to effortful mental activities - Associated with subjective experience of agency choice and concentration - Algorithm approach - rule-based
Intuition, Reason, and Metacognition (Thompson, Turner, and Pennycook, 2011)
Type 1 processes generate two distinct outputs: ◦ Content of the initial answer ◦ Sense of correctness of that answer - Feelings of Rightness (FOR) Feelings of Rightness ◦ Vary in strength across set of problems ◦Intuitive answers are often accompanied by a sense of correctness ◦ Signal whether the current output suffices or additional Type 2 processes are needed
Well-Defined Problems
Usually have a correct answer, and certain procedures (when applied correctly) will lead to a solution • 4x + 10x = 140 • Most research done on this type
Counterfactual reasoning: blaming the victim
We maintain properties of the main object or focus of the story unless a different focus is provided ◦ Actions are judged based on: ◦ How free the character was to choose what to do ◦ Leaving work at regular hour vs. leaving work early vs. leaving work due to a family emergency ◦ How socially acceptable the choices are
Anchoring
When the subject bases the estimate on an initial piece of information offered when making decisions Example: estimate one of these ◦ 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 ◦ Median estimate: 2,250 ◦ 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 ◦ Median estimate 512 The anchor is the left-most number in this example Different starting points yield different estimates, which are biased toward the initial values Example: subjects were asked to estimate the percentage of African countries in the United Nations ◦ Spin the wheel 0-100 ◦ Determine whether this number is higher or lower than the estimate ◦ These arbitrary numbers had a marked effect on the estimates ◦ Groups that received a 10 estimated 25 ◦ Groups that received a 65 estimated 45
Decision making:
a search for evidence, where the decision depends on some criteria or rule for evaluating the evidence
Probability heuristics theory:
decisions are made based on a collection of heuristics that use the information value of the premises ◦ E.g., atmosphere and illicit conversion. More heuristics in later video. ◦ Rely on superficial characteristics of the information instead of evaluating validity and soundness
Regression to the mean
extreme observations tend to be followed by more moderate ones ◦ If a soccer play scores an average of 2 goals a game throughout his career, then has a two games where they score 4 goals in each ◦ People infer that the player improved, despite it being highly likely that they will return to their average of 2 goals per game Can lead to erroneous causal explanations Can cause us to overestimate effect of punishment and underestimate effect of reward, or training Related to our insensitivity to sample size - regression to the mean is more likely to occur in small samples
Simulation heuristic:
mental construction or imagination of outcome, a forecasting of how some event will turn out or how it might have turned out under another set of circumstances ◦ The ease with which it can be imagined is basis of heuristic ◦ Easy to imagine --> more available and thus seen as being more likely ◦ Difficult to imagine --> hypothetical outcome is seen as being unlikely
Experiment 3: Design
probability judgment task The bios provided could be congruent, incongruent, or neutral with respect to the largest group of individuals.
Heuristic
strategy or approach that works under some circumstances but is not guaranteed to yield the correct answer ◦ Often not systematic and orderly ◦ Informal method or guideline ◦ Often quicker and easier than algorithms
Invalid arguments
◦ P1: Some penguins are swimmers ◦ P2: Some swimmers are Olympic athletes ◦ C: Some penguins are Olympic athletes Despite having a similar appearance to some of the previous syllogisms we discussed: ◦ 'Some' is a modifier means at least one and possibly all ◦ 'No' or 'None' is another common modifier ◦ The inclusion of 'Some' does not lead to an invariably correct conclusion ◦ So the syllogisms do not have a valid form ◦ So therefore they cannot be sound Euler Circles (Venn diagrams) are a useful tool to help us evaluate logical relationships between ideas and concepts ◦ The use of modifiers ('all', 'some', 'no') impacts the difficulty of evaluating the validity of arguments
Measuring Type 1 processes:
◦ Participants are instructed to give the first answer that came to mind ◦Initial response reflect the outcome of Type 1 processing with minimal Type 2 processing ◦ Fast responses are more likely than slow responses to reflect the output of heuristic ◦ Assessed FORs after each response -- Either evaluate certainty or rightness
Measuring Type 2 processes
◦ Participants were allowed as much time as needed ◦ Instructions indicated that participants should be sure that they had taken their time and thought about the problem carefully Measurements: ◦ Probability of change from the first answer to the second answer -- Change of answer would indicate additional analysis ◦ Amount of time spent re-thinking -- Type 2 thinking is directed at rationalizing initial response ◦ Whether the final answer was correct -- Measure of analytic engagement
Friedman & Brown (2000)
◦ Rate latitude (N-S) of North American cities and European/North African cities ◦ Found evidence of a Plausible-reasoning process -- Combining a variety of information from different sources ◦ Specific knowledge of location for some cites, but only a general idea of other ◦ Rome-Chicago Illusion -- We know Chicago is in the north portion of North American -- Rome is in southern Europe -- Think that Chicago is more north than Rome, despite they actually having same latitude -- Based on misconception that North American and Europe are aligned in latitude ◦ Decision making about location is influenced by our prior knowledge
Distance and congruity effects are seen in judgments that include:
◦ Use of imagery -- Example: faster to judge differences between a bear and a squirrel than a rabbit and a squirrel -- Using larger for large animals and smaller for small animals results in faster judgment time ◦ Abstract concepts -- E.g., time, temperature -- Must be mentally represented in similar fashion to quantity-based orderings
