PSYC 345 Exam 4; Ch. 10-11
Probabilistic judgment
- Ppl can make this when they can see all info available - However, can be biased in their estimates of probabilities when they must rely on factors such as memory and similarity judgments
Conservatism
- Ppl frequently underestimate the cumulative force of evidence in making probability judgements - Edwards (1968) presented ppl with two bags of 100 poker chips - One 70 blue/30 red, the other 30 blue/70 red - He then picked one bag and drew a chip - If red, the probability of the bag being the red-dominant bag jumps from /5 to .7, according to Bayes' rule
Decision making
- Ppl make decisions under uncertainty in terms of subjective utilities and subjective probabilities - There is little consensus in the field about how to construct a realistic subjective probability function
Affirmation of the Consequent
it asserts that if a conditional statement is true and if the consequent is true, then the antecedent must also be true (i.e., given that If A, then B is true and that B is true, it is a fallacy to conclude that A must be true) - Given B is true, infer A is true
prescriptive model
(normative) A model that specifies how people ought to behave to be considered rational
attribute identification
Determining which attributes are relevant to the formation of a hypothesis
syllogisms
Logical arguments consisting of two premises and a conclusion.
What is a permission schema?
The antecedent specifies a situation in which the consequent is not allowed.
Green et al., 2001
- A runaway trolley is headed for five ppl who will be killed if it proceeds on its current course. The only way to save them is to hit the switch that will turn the trolley onto an alternate set of tracks where it will skill on person instead of five - A runaway trolley is headed for five ppl who will be killed if it proceeds on its current course. The only way to save them is to hit the switch that will turn the trolley onto an alternate set of tracks where it will skill on person instead of five In the first case, the moral dilemma is less personal than the second case - Ppl more likely to hit the switch, vs push another person, even with the same outcome - Under fMRI- parietal regions more active0 associated with "cold calculation- hitting the switch - In case of having to push another person on the tracks, brain regions associated with emotional processes, like the ventromedial prefrontal cortex were active
Phineas Gage
- Accident involving a metal railroad spike - survived; his personality changed - Tore through his ventromedial prefrontal cortex
Somatic marker hypothesis
- Bechara and colleagues posited than an emotional "marker" caused by the large losses from the bad decks registers before conscious awareness - Maia and McCelland 2004 questions whether these somatic markers were really implicit
Earlier standard theory
- Decision making is concerned with eh ebay in which ppl make choices - Ppl should choose alternative with highest expected value (von Neumann and Morgenstern, 1944)- normative or prescriptive theory of decision making and economics - Expected value of an alternative is its probability of paying off times the amount that can be won - For example, in a lottery its the probability of winning times the size of the jackpot Also called expected utility
Oaksford and Chater 1994
- Developed a mathematical analysis of optimal behavior that explains why typical errors in the original Wason task can be sensible - Argued that ppl tend to interpret statements as probabilistic statements about the world rather than strict logical statements- bayesian interpretation - Suggested behavior in the Wason card selection task can be explained if it is assumed that participants select cards that will be informative under a probabilistic model
Bayes nets
- Graphical formalism used in work on AI for reasoning about real-world knowledge - This network shows that both viral pneumonia cause headache, cough, and fever (generative causes) - Antibiotics are given to cure bacterial pneumonia, and aspirin is administered to relieve headache (preventative causes)
Bruner, goodnow, and austin 1956- classic set of experiments
- Hypothesis formation - Ppl were told that they were to discover some concept that described a particular subset of boxes - Ppl have to work with present and not present instances
Groups of stimuli
- In each column, a plu sign (+) signals that the stimulus is an instance of the concept and a minus sign (-) signals that the stimulus is not an instance of the concept - Had to identify relevant features and how they are related - Concept 1- must contain two stars - Concept 2- must have either two borders or two diamonds - Concept 3- number of objects must equal the number of borders
Inductive reasoning and hypothesis testing
- In inductive reasoning, the conclusion does not necessarily follow from the premises with certainty - A general inductive inference is that each number is twice the previous number - Concept identification tasks are particularly difficult
What can we believe with high confidence?
- Knowing what to believe is impacted by a host of highly confident assertions - Evaluating such assertions aided by strategies used by professional face checkers: - Reading laterally- confer with multiple quantitatively different sources - Research the background of each source - Making smart selections from results that come back from google search - Using wikipedia wisely- visit the talk tab
Why are adolescents more likely to make bad decisions?
- Knowledge and experience. They lack some of the info and experiences adults have - Different values and situations, they are more likely to weigh the benefits of risky behavior in the context of their peers
Don, Worthy, and Livesey 2011
- Midosis- more common- headache and nausea - Coralgia- rare headache and fever - New patient has nausea and fever- do they have midosis or coralgia?
Iowa gambling task
- Normal ppl eventually learn to avoid decks with bad decks with higher payoffs, but also larger losses - Ppl with ventromedial damage keep returning to high-paying decks and do not show measures of emotional engagement when selecting these decks - Normal ppl show a galvanic skin response when selecting the bad decks; patients with vmPFC damage do not
Process explanations
- One class of explanations is that ppl do not do what the experimenters think they are doing - It has been argued that it is not natural for ppl to judge the logical validity of a syllogism. Rather, ppl tend to judge the truth of the conclusion in the real world
How do computers use Bayes's rule
- One technique called Markov Chain Monte Carlo (MCMC) can be used to estimate the posterior distribution for a given problem - MCMC involves using a decision-rule- one such rule is the Metropolis Algorithm to directly estimate the posterior distribution - Some have argued that humans use MCMC-like
Don et al., 2019
- Option A- 65% chance of reward - Option C- 75% chance of reward - AB- shown 100 trials - CD- shown only 50 trials - Option A was preferred more often than C, even though it had a lower probability of reward - A was more available in memory due to being shown more often
Evaluation of conditional arguments
- People rarely fail to accept a modus ponens inference - Ppl are only able to show high levels of logical reasoning with modus ponens - The frequency with which they accept the valid modus tollens is only slightly greater than the frequencies with which they accept the invalid inferences
Wason 1960
- People seem to test their hypothesis less than optimally - 2-4-6 task - Told the 2,4,6 is an instance of arule, and are asked to find what rule is by asking whether other triads are instances of that rule - Ppl propose many rules, and are told yes or no, than they can guess a rule - The rule is eventually announced as "any three numbers in order of magnitude"
Base-rate neglect
- Ppl often fail to take base rates into account in making probability judgements - Often ignore prior probabilities - Ppl tend to weigh other evidence when they ignore base rates (Kahneman and Tversky 1973) - Despite their display of probability matching, ppl showed this by systematically over estimating the frequency with which the rarer disease was associated with each of the four symptoms considered
Knutson et al., 2005
- Ppl shown many uncertain outcomes - 50% change of winning $5 - The nucleus accumbens shows greater activity in response to a 50% chance of $5 reward than to a 50% chance of a $1 reward - The ventromedial prefrontal cortex shows greater activity in response to an 80% chance of a $5 reward than to a 20% chance of a $5 reward
fMRI study- Goel, Buchel, Frith, and Dolan 2000
- Ppl solved syllogisms - Consist of two premises and a conclusion- valid/unvalid - All poodles are pets - All pets have names - Therefore, all poodles have names Incongruent but valid - All pets are poodles - All poodles are vicious - Therefore, all pets are vicious Only 74% responded valid for incongruent, 84% for congruent
Gluck and Bower 1988
- Probability matching might be considered implicit Bayesian behavior - Ppl looked at the medical records of hypothetical patients, and diagnosed which of two diseases was present in each patient - Given feedback on the correctness of their diagnoses - One disease occurred three times more often than the other
In the process of discovery a new theory, scientists
- Search possible theories and possible experiments to understand these theories - Make inductive inferences about possible hypothesis for new research studies - Probabilistic assertions based on prior knowledge
Gigerenzer and Hoffrage 1995
- Showed that base-rate neglect decreases if events are stated in terms of frequencies rather then in terms of probabilities - Argued that people reason better with frequencies than with probabilities because they experience frequencies of events in daily life
Neural representation of subjective utility and probability
- Subjective utility of an outcome appears to be related to the activity of dopamine neurons in the basal ganglia - Drugs like nicotine and cocaine can increase dopamine levels in the basal ganglia - Basal ganglia: important for motivation (Olds and Milner 1954) - Nucleus accumbens- represents info on the magnitude of reward - Ventromedial prefrontal region (Knutson et al., 2005)- responsive to magnitude, as well as the probability or likelihood of reward
In studies of scientific discovery, ppl
- Tend to focus on experiments consistent with their favorite hypothesis - Show a reluctance to search for alternative hypothesis - Confirmation bias- technology to seek evidence that is consistent with one's current hypothesis (NIckerson 1998) - Bias to defend one's hypothesis, ignore contrary evidence
Shafir 1993
- Two patients are described in a divorce case and ppl played the role of judge who must choose who is to be awarded custody The question can be framed in positive or negative terms - Awards custody, deny custody Factors in custody decisions - Parents are similar, but parent B has more extreme positive and negative factors - Choice depends on the frame
O'bryan et al., 2018
- Used fMRI and MVPA- found that people show activation for the common feature when selecting the rare response - Suggests ppl use eliminative inference where they eliminate the more common disease when the rare symptom is present
Errors in mental models
- come from ppl overlooking possible explanations of the premises - Counterexamples are particularly easy to overlook - may establish that a conclusion is possible, but not that it is necessary or valid in all cases
Fugelsand and Dunbar 2005
- fMRI study of ppl trying to integrate data with specific hypothesis - Anterior cingulate cortex (ACC) active when processing info inconsistent with prior views - ACC often active when monitoring conflict
Dopamine activity in the nucleus accumbens reflects the magnitude of reward
- spikes correspond to reward prediction errors- the difference between observed and expected reward - Positive prediction errors- from unexpectedly large reward - Negative prediction errors- from less than expected - Human ventromedial prefrontal cortex is involved in integrating probabilities of rewards with magnitudes of rewards
recognition heuristic
A heuristic that applies in cases where people recognize one item and not another, leading them to believe that the recognized item has a higher value than the unrecognized item with respect to a specified criterion. - Gigerenzer and colleagues have argued that heuristics are often good, or adaptive to use - Kahneman and Tversky had shown that heuristics often lead to irrational decisions
denial of the antecedent
A logical fallacy: it asserts that, if a conditional statement is true and if the antecedent is false, then the consequent must also be false (i.e., given that If A, then B is true and that A is false, it is a fallacy to conclude that B must be false). - Given A is false, infer B is false
descriptive model
A model that describes how people actually behave. Contrast with prescriptive model.
Modus Tollens
A rule of logic: if a conditional statement is true and if its consequent is false, then its antecedent must be false (i.e., if the conditional statement If A, then B is true, and if the consequent B is false, we can infer that the antecedent A is false. - Given B is false, infer A is false - method for denying ot abolishing
categorical syllogism
A syllogism in which logical quantifiers relate categories A to B in one premise, relate B to C in the other premise, and relate A to C in the conclusion. - No pittsburgher is a browns fan - All browns fans live in cleveland - Therefore, no pittsburgher lives in cleveland - Research on reasoning with quantifiers has focused on trying to understand why people accept many invalid of these
Wason selection task
A task in which participants must decide which of four cards need to be turned over to check the validity of a conditional statement; the cards represent the four possibilities of antecedent and consequent of the conditional being true or false. - Used to demonstrate human inability to reason correctly - ppl have particular difficulty in recognizing the importance of exploring whether the consequent is false
Bayes's theorem
A theorem that prescribes how to combine the prior probability of a hypothesis with the conditional probability of the evidence, given the hypothesis, to assess the posterior probability of the hypothesis, given the evidence
Brain Activation during meaningful content
Activation in left ventral prefrontal and left parietal-temporal areas
conditional statement
An assertion that, if an antecedent is true, then a consequent must be true: a statement of the form If A, then B.
Penelope is part of a research study where she must guess the probability of pulling m&ms from a bag of blue and red m&ms. She is trying to guess the probability of pulling another blue m&m, given she already pulled one earlier. The true probability is 75%, but she thinks she has a 10% chance. What is this an example of?
Conservatism
permission schema
An interpretation of a conditional statement in which the antecedent specifies the situations in which the consequent is permitted.
probability matching
Choosing among alternatives in proportion to the success of previous choices. - The frequency with which ppl correctly diagnosed the rarer of the two diseases corresponds closely to the Bayesian probabilities
Describe this logical syllogism: If this is a dog, then it is an animal. This is not a dog. Therefore it is not an animal.
Denial of the antecedent
rule learning
Determining what kind of rule (conjunctive, disjunctive, or relational) connects the features when forming a hypothesis.
Evans 2007, Stanovich 2011
Dual process theories - Argue that human reasoning both does and does not correspond to normative prescriptions - Suggests human reasoning is governed by two different types of processes: - Type 1: rapid, automatic, and rely on associations between situations and actions - Type 2: slow, deliberative, and may follow prescriptions of the normative models criticisms - Theories are set to accommodate any result and so can predict none - If ppl display normatively irrational behavior, this is because their type 1 processes dominate - If they display normatively rational behavior, this is because their type 2 processes dominate
framing effects
Effects whereby people make different choices among equivalent alternatives depending on how the alternatives are stated. - Tendency for ppl to make different choices among the same alternatives, depending on the statement of the alternatives (Kahneman and Tversky 1984) Ppl tend to be risk-averse with gains, and risk-seeking with losses - Sure gains are enticing- low risk - Sure losses are aversive- better to take the risk of having no losses at all
logical quantifiers
Elements such as all, no, some, and some ... not that appear in statements like All A are B and Some C are not D.
True or False. Humans are able to make accurate predictions based on their memory.
False
People are better at making judgments if rates are described in terms of...
Frequencies
Tversky and Kahneman 1974
Judgements of probabilities - asked to estimate the proportion of english words that start with k vs the number of words that have k as the third letter - Theorized that ppl would remember more words that start with k - Ppl estimated twice as many words start with k - Actual ration is twice as many letters have k as the third letter
inductive reasoning
Reasoning in which the conclusions follow only probabilistically from the premises. - Is it going to rain today? - Probabilistic
deductive reasoning
Reasoning in which the conclusions follow with certainty from the premises. - valid/invalid syllogisms - Deterministic - often tested by asking people to state whether conditional statements (if-then) are valid/invalid - Limitations of the atmosphere hypothesis - Tells about what ppl are thinking and why - Ppl only approximate the predictions of the atmosphere hypothesis and are often more accurate than it would predict
Paradox
Human reasoning is judged to be deficient when compared against the standards of logic and math AI systems built on these same standards are judged deficient when compared against the standards of humans
posterior probability
In Bayes's theorem, the probability that a hypothesis is true after consideration of the evidence.
prior probability
In Bayes's theorem, the probability that a hypothesis is true before consideration of the evidence.
conditional probability
In the context of Bayes's theorem, the probability that a particular piece of evidence will be found if a hypothesis is true
What is the issue with the Dual-Processing theory?
It is not falsifiable.
Kahneman and Tversky 1973
Jack has been chosen at random from a group of 70 lawyers and 30 engineers - Jack is a 45-year old man. He is married and has four children. He is generally conservative, careful, and ambitious. He shows no interest in political and social issues and spends most of his free time on his many hobbies, which includes home carpentry, sailing, and math puzzles - How likely is it that Jack is an engineer versus a lawyer? - Ppl gave a .90 estimate that Jack was an engineer Another group told there wer 70 engineers and 30 lawyers
mental model theory
Johnson-Laird 1983 The theory that participants judge the validity of a syllogism by imagining a world that satisfies the premises and seeing whether the conclusion is satisfied in that world
People use different problem-solving operators, depending on their interpretation of the logical connective if
Logical interp Causal interp Probabilistic interp Permission interp
Type 1 processes
Rapid and automatic processes, relying on associations between situations and actions.
Why is Bayesian statistics relevant for reasoning?
People treat logical statements as probabilistic; evidence must be gathered before drawing conclusions.
Choosing among many alternatives
Ppl get overwhelmed by large amounts of info and take various shortcuts - Simpler strategies- satisficing- stopping as soon - Older adults prefer to choose among fewer options than younger adults (Reed et al., 2014; Worthy et al., 2014)
Bayes's theorem is an example of a prescriptive model. How are they different from descriptive models?
Prescriptive models are normative, meaning they predict sample values.
Estes (1976)
Probability learning is a misnomer - showed that ppl don't necessarily learn probabilities - Probability judgements are reconstructed from memory of past events, dependent on frequency or familiarity in memory, rather than average probability of reward - Don et al., 2019- showed similar results
Brain activation while content free
Similar activation when solving algebra problems
Type 2 processes
Slow and deliberative processes that may follow normative prescriptions.
universal statements
Statements—often involving logical quantifiers such as all and none—that logicians interpret as blanket claims with no exceptions
particular statements
Statements—often involving the logical quantifiers some and some ... not—that logicians interpret as being true about at least some members of a category. Contrast with universal statements.
Cosmides 1989, Gigerenzer and Hug 1992
efficiency with social contract rules and cheater detection - Gave ppl a wason-like task where they had to determine if students were following school district boundary rules- school on one side, place of residence on the other - Cheating condition- goal was to find ppl not attending the right school (80% accuracy) - Non cheating condition- asked to take the perspective of a visiting official from germany (45% accuracy)
gambler's fallacy
The belief that the likelihood of an event increases with the amount of time since the event last occurred. "law of averages" - If heads up has been flipped five times in a row ppl think tails is more likely - In reality coin flips are independent of results from previous flips - Always going to be 50/50
Antecedant
The condition of a conditional statement; that is, the A in If A, then B
ventromedial prefrontal cortex
The portion of the cortex in the front center of the brain. It seems to be involved in decision making and self-regulation, including activities like gambling behavior
subjective probability
The probability that people associate with an event, which need not be identical to the event's objective probability - Much human decision making can be explained assuming that ppl are responding in terms of these subjective utilities and subjective probabilities Kahnerman and Tversky 1984 - Not according to normative economics - This function relates the subjective probability of events to their objective probability. The downward bowing shows that low probabilities are overweighted relative to higher probabilities, especially at the lower end
consequent
The result of a conditional statement; the B in If A, then B.
subjective utility
The value that someone places on something. - Value placed on money is not linear with the face value of money - Negative subjective value of losses is greater than the positive subjective utility of gains - "Losses loom larger"
Atmosphere hypothesis
proposes that the logical quantifiers (some, all, no, and some...not) used in the premises of a syllogism create an "atmosphere" that predisposes participants to accept conclusions having the same quantifiers
Michael-Angelo is playing Poker with his friends and he notices he has a bad hand, but he goes all in anyway. When his friend, Raphael, gets a bad hand, it shows on his face, and he usually folds. What region of Michael-Angelo's brain may be at fault for his lack of emotional mediation?
Ventromedial prefrontal cortex
confirmation bias
When trying to determine whether a hypothesis is correct, the tendency to look only at evidence that is consistent with the hypothesis
In scientific experiments, people tend to...
focus on experiments consistent with their favorite hypothesis.
Modus Ponens
if a conditional statement is true and if its antecedent is true, then its consequent must be true (i.e., if the conditional statement If A, then B is true, and if the antecedent A is true, we can infer that the consequent B is true). - Given A is true, infer B is true - method for affirming
Attraction effect
if the third option is dominated on an attribute by one of the existing options, we are more likely to choose that dominating option
Similarity effect
if the third option is similar to one apartment, we'd be more likely to choose the other
Compromise effect
if the third option makes one option seem like a compromise between the third option and the other option, we are more likely to choose the compromise option
Sandborn et al., 2010
noted that human inference may have similarities to MCMC inference
Cheng and Holyoak 1985
permission schemas are social norms or social contract rules - shows that this version of the Wason task induced a permission schema, that helped ppl solve the task- ppl good at applying social rules
Platt 1964
says the strongest inference in science comes from denying invalid causes or hypothesis
Evolutionary explanation
that we do well with permission schemas because detecting cheaters is adaptive
Griggs and Cox 1982
used the modified Wason task where beer, coke, 16, and 22 were on cards (drink/age), and ppl had to judge whether the drinking law was being violated
