Cognition 7-10 Lecture Notes PDF

**LECTURE 7: PROBABILITIES** Probability judgments often deviate from the dictates of probability theory 1. Heuristics = simplifying strategies that reduce effort but are prone to bias/error. 2. Ecological rationality = Apparent biases may be rational responses given the ecology of the...

**LECTURE 7: PROBABILITIES** Probability judgments often deviate from the dictates of probability theory 1. Heuristics = simplifying strategies that reduce effort but are prone to bias/error. 2. Ecological rationality = Apparent biases may be rational responses given the ecology of the human decision-maker **Heuristics and Biases:** 1. **Availability** **Estimating causes of death -** People: overestimate rare events, and underestimate common events. **Effect of memory** Listen to list of 39 names including: 19 famous women and 19 famous men\ 20 less famous men 20 less famous women - 12.3 names recalled from famous group vs 8.4 from less famous group - 81% judged that gender with famous names was more frequent **Conjunction fallacy =** in four pages of a novel (about 2,000 words), how many words would you expect to find that have the form: \_ \_ \_ \_ i n g? \_ \_ \_ \_ \_ n \_?. 2. **Representativeness --** judgements of probability are based on assessments of similarity. Base rate neglect = "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 include home carpentry, sailing, and mathematical puzzles." - Business administration - Computer science - Engineering - Humanities and education - Law - Library science - Medicine - Physical and life sciences - Social science and social work Three groups judged: - Rank each subject by likelihood Tom is specializing in it - Rank each subject by how representative Tom is of a typical student - Estimate what percentage of all students study this topic 3. **Anchoring** Is the percentage of African countries in the United Nations... - More or less than 65%? Best estimate? - More of less than 10%? Best estimate? **Chapman & Johnson (1999)** Is the likelihood of the Republicans winning the next election more or less than 34%? Your best estimate? Estimates correlated with anchor (r = 0.45) **Anchor and adjust** However...Incentives, warnings and cognitive capacity have little effect on accuracy (Epley & Gilovich, 2005) Many other mechanisms produce the same effect. **Part 1 Summary** - Some researchers treat bias as error that results from "lazy" processing - The Availability, Representativeness, and Anchor-and-Adjust heuristics are three examples of this **Ecological rationality** 1. **Natural frequencies** **Example 1: Natural Frequencies** "For a woman at age 40 who participates in routine screening, the probability of breast cancer is 1%. If a woman has breast cancer, the probability is 80% that she will have a positive mammogram. If a woman does not have breast cancer, the probability is 10% that she will still have a positive mammogram." Imagine a woman from this age group with a positive mammogram. What is the probability that she actually has breast cancer?" **Bayes** \ [\$\$p\\left( H \\middle\| D \\right) = \\frac{p\\left( D \\middle\| H \\right)\\ \\times \\ p(H)}{\\left( p\\left( D \\middle\| H \\right) \\times \\ p\\left( H \\right) \\right) + (p\\left( D \\middle\| \\neg H \\right) \\times \\ p\\left( \\neg H \\right))}\$\$]{.math.display}\ P(cancer) = 0.01 P(no cancer) = 0.99 P(positive\|cancer) = 0.80 P(positive\|no cancer) = 0.10 P(cancer\|positive) = 0.075 **Gigerenzer and colleagues:** - Probability theory and normalised probabilities are recent. - We are much better at tracking natural frequencies. 2. **Misperception of randomness** **Gambler's fallacy =** "Even money" bets after streaks of length 1, 2, 3... Proportion of bets that are "with" and "against" the streak. **Gambler's Fallacy -- Representativeness** **Tversky & Kahneman (1971) =** People expect a local sequence to have properties of generating process (long sequence). So HHHHHT is not as representative as HTHTTH. **Past Experience:** - Inappropriate generalization of past experience - Random mechanical outcomes = Sampling without replacement **Memory constraints** Look at the properties of fair coin under realistic conditions: - People only ever see finite sequences - People can only hold a short subsection of a sequence in memory (e.g., the last 4 outcomes) **Week 8: Reasoning** **Two types of reasoning:** **Inductive =** Sarah has fallen asleep in all Psychology lectures so far. Therefore, sarah will always fall asleep in psychology lectures. **Deductive =** Sarah always falls asleep in psychology lectures. Sarah is in a psychology lecture, therefore, sarah will fall asleep. **Syllogisms:** ALL NONE SOME SOME...NOT First premise: A and B Second premise: B and C Conclude something about: A and C **Examples:** ALL Psychologists (A) are Comedians (B) ALL Comedians (B) are Tap-Dancers (C) What can we conclude? ALL Psychologists (A) are Tap-dancers (C) ALL Psychologists (B) are Poets (A) ALL Psychologists (B) are Acrobats (C) What can we conclude? SOME Poets (A) are Acrobats (C) **Heuristics:** - "Atmosphere" (quality and quantity) of premises shape conclusions. Evidence: - 45 problems with "no valid conclusion" -- -- -- -- -- -- -- -- - **BUT** doesn't explain why people sometimes correctly infer "no valid conclusion". **Comprehension:** "All A are B..." "Some A are B" "All A are B, and vice versa" "Some, but not all, A are B" Clarifying premises greatly reduces the "error" rates (Ceraso & Provitera, 1971) **Mental Models:** - Premises: all psychologisrs are comedians, all comedians are psychopaths. - **Step 1:** construct a mental model of world implied by premises. Psychologist Comedian Psychologist Comedian... Comedian Psychopath Comedian Psychopath... - **Step** **2** Make a composite model and draw a conclusion - Composite: - Psychologist Comedian Psychopath - Conclusion: All psychologists are psychopaths - **Step 3** Validate by searching for alternative models and checking they don't contradict the conclusion - Conclusion: All psychologists are psychopaths. In this case there are no other models consistent with the premises, so accept the conclusion Premises: No Artists are Bakers, All Bakers are Candlestick-makers. - The more alternative models are considered, the more likely one is to draw the correct conclusion. - Requires more time, effort, and mental capacity. - Working memory test, then: All cyclists are coffee-drinkers, All coffee-drinkers are surgeons. Choose from 9 possible conclusions - More possible models = less accurate + slower - Higher working memory = faster and more accurate - But not direct evidence for model construction/validation 1. Participants given syllogism 2. Write down conclusion 3. Indicate all considered Multiple-model problems harder......but people didn't try to construct more models And no correlation between N considered and accuracy "reasoners are *able* to construct alternative models...but \[they\] normally construct only one" **Framing & Experience:** +-----------------------+-----------------------+-----------------------+ | | **Believable** | **Unbelievable** | +=======================+=======================+=======================+ | **Valid** | No cigarettes are | No addictive things | | | inexpensive | are inexpensive | | | | | | | Some addictive things | Some cigarettes are | | | are inexpensive | inexpensive | | | | | | | Therefore, some | Therefore, some | | | addictive things are | cigarettes are not | | | not cigarettes | addictive | +-----------------------+-----------------------+-----------------------+ | **Invalid** | No addictive things | No cigarettes are | | | are inexpensive | inexpensive | | | | | | | Some cigarettes are | Some addictive things | | | inexpensive | are inexpensive | | | | | | | Therefore, some | Therefore, some | | | addictive things are | cigarettes are not | | | not cigarettes | addictive | +-----------------------+-----------------------+-----------------------+ **Propositional Reasoning:** **"If it is raining, then I take the bus"** Raining = took the bus = valid modus ponens = 97% Not bus = not raining = valid modus tollens = 74% Took bus = raining = invalid affirmation of consequent = 64% Not raining = not bus = invalid denial of antecedent = 56%. **Four card selection task:** - "If there is a D on one side of any card, then there is a 3 on its other side" - One out of 34 participants chose the correct cards **Heuristics:** - If there is an S on one side, then there will be a 9 on the other - If there is an S on one side, then there will not be a 9 on the other **Comprehension:** - Many people misunderstand the rule, but reason consistently after that (Gebauer & Laming, 1997; Wagner-Egger, 2007) - "If there is a D on one side...", "then there is a 3 on the other" - If there is a D on top...""then there is a 3 on the other, and vice versa". **Mental Models:** - "If there is a Circle, then there is a Triangle" **Model**: - Circle Triangle **Conclusions:** - Given Circle - conclude Triangle (MP) - Given Triangle- conclude Circle (AC) - Given no Triangle- no conclusion possible (failure to draw Modus Tollens) **Model:** Circle Triangle No Circle Triangle No Circle No Triangle **...** **Conclusions:** - Given Circle : Conclude Triangle (MP) - Given Triangle: Conclude may not be circle (Avoid AC) - Given no Triangle: Conclude no Circle (Modus Tollens) **Framing and Experience:** If a person is drinking beer, then the person must be over 19 years of age Abstract version: 0% chose p, not-q Underage drinking version: 73% chose p, not-q **Deontic Reasoning** **Cuing of relevant prior experiences?** - But: "If a man eats cassava root, then he must have a tattoo on his face" (Cosmides, 1989) **Evolved "cheater detection" algorithm?** - But: "If you clear up spilt blood, then you must wear rubber gloves" (Manktelow & Over, 1990) **Relevance/Expected Utility of the various cards** **Relevance / Expected Utility** **Matching heuristic:** Items mentioned in rule seem relevant **"Cheater detection":** High utility to finding took-benefit-didn't-pay **Relevance** - You work in a travel agency in 1979, and you need to check that customers have followed the rule: "If a person travels to any East African country, then that person must be immunized against cholera" (62%) - Your boss is worried that she may have mis-informed customers. Check whether customers have followed the rule "If a person travels to any East African country, then that person must be immunized against cholera" (71%) - "Relevance-guided comprehension processes tend to determine participants' performance and pre-empt the use of other inferential capacities. Because of this, the value of the selection task as a tool for studying human inference has been grossly overestimated." (Sperber & Girotto, 2002). **Summary:** - People sometimes solve reasoning problems by relying on simple heuristics - They may also reason correctly but have a different interpretation of the terms than that intended by the experimenter - Mental Models theory is an ambitious, imperfect description of the process by which people reason - Any successful account of reasoning must incorporate the effects of experience and the "real world" use of reasoning as a tool for decision-making and communication **Week 9: Decision making** **Expected value =** the expected value of an option is the sum of each possible outcome weighted by its probability. EV = p~1~a~1~ + p~2~a~2~ + p~3~a~3~ +... p~n~a~n~ a = the value of the outcome p = the probability of the outcome n = the total number of outcomes Option A: An 80% chance of £4000 Option B: £3000 for sure What would you choose? EV(A) = 0.8 x £4000 + 0.2 x £0 = £3200 EV(B) = 1.0 x £3000 = £3000 80% of people choose option B. This means they are 'risk averse' for gains **[Expected Utility]** Option A: An 80% chance of £4000 Option B: £3000 for sure What would you choose? EV(A) = 0.8 x 4000 + 0.2 x £0 = 3200 EV(B) = 1.0 x 3000 = 3000 EU(A) = 0.8 x u(4000) + 0.2 x u(0)= 0.8 x 145 = 116 EU(B) = 1.0 x u(3000) = 1.0 x 122 = 122 **[Expected Utility Theory]** A rational, prescriptive account of choice, but... A poor description of reality **[Violations of Expected Utility]** In addition to whatever you own you have been given: £1000 Now choose: A: 50% chance of £1000 (16%) B: £500 for sure (84%) £2000 Now choose: C: 50% chance of -£1000 (69%) D: -£500 for sure (31%) Violations of Expected Utility Imagine you are choosing between programs to combat a deadly disease which is expected to kill 600 people: Program A: (72%) 200 people will be saved Program B: (28%) 1/3 probability that 600 people will be saved 2/3 probability that no people will be saved Program A: (22%) 400 people will die Program B: (78%) 1/3 probability that nobody will die 2/3 probability that 600 people will die **[Reference-dependence]** - Outcomes are considered as gains or losses with respect to a reference point. - Often the status quo **Risk attitudes** - Risk-averse for (perceived) gains - Risk seeking for (perceived) losses **Loss aversion** Would you take a bet with a 50% chance of winning £1000 and a 50% chance of losing £1000? **Probability - "Certainty effect"** Option 1: (67%) 5% chance to win a 3-week tour of England, France, and Italy Option 2: 10% chance to win a 1-week tour of England Option 1: 50% chance to win a 3-week tour of England, France, and Italy Option 2: (78%) 1-week tour of England, with certainty Changes in probability will have a much bigger impact when they approach certainty (0% or 100%). Non-linear probabilities You have two lotteries to win \$250. One offers a 5% chance to win the prize and the other offers a 30% chance to win the prize. Option A: You can improve the chances of winning the first lottery from 5 to 10%. Option B: You can improve the chances of winning the second lottery from 30 to 35%. Which of these seems like a more significant change? 75% CHOSE A You have two lotteries to win \$250. One offers a 65% chance to win the prize and the other offers a 90% chance to win the prize. Option C: You can improve the chances of winning the first lottery from 65 to 70%. Option D: You can improve the chances of winning the second lottery from 90 to 95%. Which of these seems like a more significant change? 63% CHOSE D Prospect Theory -- Problems 1. **Limited scope -- Valuation vs Choice** A 95% chance to win \$2.50 and a 5% chance to lose \$0.75 (P-bet). A 40% chance to win \$8.50 and a 60% chance to lose \$1.50 (\$-bet). An hour later... You own a ticket for this bet. What is your minimum selling price? 73% of people who choose the P-bet sell the \$-bet for a higher price **Limited Scope -- Attraction Effect** Online only \$59.99 Print only \$125.00 Print & Online \$125.00 Online only \$59.99 Print & Online \$125.00 Option A. 40% chance of \$25 Option B. 30% chance of \$33 Option C. 40% chance of \$20 - 60% CHOOSE A Option A. 40% chance of \$25 Option B. 30% chance of \$33 Option C. 25% chance of \$33 - 75% CHOOSE B Imagine you are going to buy an electric bike, and you have the following information: Price in pounds (£) Range in miles when battery full  A. £460, 59 miles B. £707, 104 miles C. £471, 52 miles 2. **Purely descriptive** Prospect theory is *descriptive*. Where do the curves come from? **Purely Descriptive -- Decision by sampling** Bank Credits  Graph showing the ranks of deposits and withdrawls together. Similar shape to the prospect theory value function. **Purely Descriptive** **Summary** - Decisions and choices are often "irrational" - Prospect theory explains these effects by invoking reference points, the value function, and probability weighting - Prospect Theory is enormously influential, but we need to understand cognitive processes Week 10: Emotion and decision making Part 1 The nature of emotions and their relation to bodily states Two (related) core issues 1 Are there universal "basic emotions"? 2 What is the role of physiological change? Basic emotions? Darwin (1872) Anger -- Fear -- Surprise Sadness -- Disgust - Enjoyment Ekman (1992) Criteria for "basic" emotions, including: - Rapid onset - Brief duration - Unbidden occurrence - Distinctive universal signals Specific physiological correlates Universal Expression? "People are active perceivers who categorize facial movements using culturally learned emotion concepts" (p.211) The James-Lange view Stimulus -- Percept -- Physiological changes -- Emotion "the bodily changes follow directly the perception of the exciting fact, and that our feeling of the same changes as they occur is the emotion" Emotions not dependent on physiology - People without peripheral inputs still experience emotion (but perhaps not as strongly?) - Peripheral arousal doesn't recreate emotion - Peripheral states not sufficiently differentiated Predicting emotions from physiology - "the most robust finding...was the observation of substantial variation in ANS responding during instances of the same emotion category" - "an emotion category is a population of context-specific, highly variable instances that need not share an ANS fingerprint" Interpretation of the physiology [\[CHART\]]{.chart} Where are we now? Part 2 An account of the links between brain, body, emotion, and decision-making Amygdala & Emotion Lesions - Reduced fear conditioning (Blanchard & Blanchard, 1972) - Selective recognition of fear from face photos (Calder et al., 1996) - Lack enhanced memory for emotional components of narrative (Adolphs et al., 1997) Recall of emotional information predicted by amygdala activation at encoding (Hamann et al., 1999) vmPFC & Emotion Damage: No elevated SCR for emotional stimuli with "social significance" (Damasio et al., 1990) More likely to "overcome an emotional response" during moral dilemma (Koenigs et al., 2007) Heightened emotional reactivity and hypoemotionality (Anderson et al., 2006) Patient EVR Following a tumour and lesion to the vmPFC, EVR had normal intellect, impulsiveness, memory and reasoning ability, but lacked emotional reactions and engaged in poor real-world decision-making The Iowa Gambling Task (IGT) Task a: Win \$100 Lose \$0 Win \$100 Lose \$0 Win \$100 Lose \$150 Win \$100 Lose \$0 Win \$100 Lose \$300 Win \$100 Lose \$0 Win \$100 Lose \$200 Win \$100 Lose \$0 Win \$100 Lose \$250 Win \$100 Lose \$350 Task B: Win \$100 Lose \$0 Win \$100 Lose \$0 Win \$100 Lose \$0 Win \$100 Lose \$0 Win \$100 Lose \$0 Win \$100 Lose \$0 Win \$100 Lose \$0 Win \$100 Lose \$0 Win \$100 Lose \$1250 Win \$100 Lose \$0 Task C: Win \$50 Lose \$0 Win \$50 Lose \$0 Win \$50 Lose \$50 Win \$50 Lose \$0 Win \$50 Lose \$50 Win \$50 Lose \$0 Win \$50 Lose \$50 Win \$50 Lose \$0 Win \$50 Lose \$50 Win \$50 Lose \$50 Task D: Win \$50 Lose \$0 Win \$50 Lose \$0 Win \$50 Lose \$0 Win \$50 Lose \$0 Win \$50 Lose \$0 Win \$50 Lose \$0 Win \$50 Lose \$0 Win \$50 Lose \$0 Win \$50 Lose \$0 Win \$50 Lose \$250 IGT and vmPFC damage [\[CHART\]]{.chart} IGT time course [\[CHART\]]{.chart} [\[CHART\]]{.chart} IGT: vmPFC Damage IGT: Amygdala & vmPFC Damage IGT: What are people conscious of? Six vmPFC patients and 10 controls Every 10 trials after trial 20: "Tell me all you know about what is going on in this game" "Tell me how you feel about this game" IGT: What are people conscious of?  The somatic marker hypothesis Part 3 The problems with this view 1 We may not need somatic cues [\[CHART\]]{.chart} 2 Somatic cues may not signal outcomes 3 No need to posit unconscious knowledge "Tell me all you know about what is going on in this game" Not a good instruction! Instead. For each deck: - Rate from -10 to +10 - Estimate average net result - Estimate average winning amount - Estimate frequency of losses - Estimate average loss - Which single deck would you pick? 4 An alternative explanation for patient data Progress... A prime example of how psychology research "works" Some ideas jettisoned and methodologies refined Some ideas retained/developed: Sensitivity to somatic signals; Key role of vmPFC/orbitofrontal cortex and amygdala Summary There are complex links between somatic states, cognitive appraisals, and experienced emotions The somatic marker hypothesis is a bold attempt to link physiology, brain structures, and real-world decision making The story of this idea exemplifies how we make progress in cognitive science **Week 11 -- Group Decision Making** 1\. The downsides Conformity = why line is the same length as the standard?  Authority In 1977 KLM and Pan-Am jumbo jets collided on a runway in Tenerife. The worst ever aviation accident on land. An investigation into the incident found that the engineer did not challenge the captain's decision to proceed with take-off despite doubting the runway was clear. When officers of different rank occupied cockpits together accidents increased. 40% of junior co-pilots reported not relaying concerns about safety to senior pilots. Crew resource management Polarization 10 groups of 6 people Procedure: 1. Rate 8 traffic felony cases (4 high guilt and 4 low guilt) 2. Discuss half the cases 3. Rate all 8 cases again Assume guilty and punish Groupthink Characteristics: Cohesive groups striving for unanimity and avoiding conflict or criticism. Exacerbated in homogenous teams, where members are, or become, too similar A close-up of a text Description automatically generated 2\. The benefits Medical diagnosis - 101 Radiologists - Reviewed mammograms - Decided whether they would recall a patient for further investigation - Groups of doctors **with similar levels of diagnostic accuracy** will outperform the best doctor in the group  Wisdom of the crowd -\ Surprisingly Popular  **Wisdom of the crowd (within)** Dialectical bootstrapping: First, assume that your first estimate is off the mark. Second, think about a few reasons why that could be. Which assumptions and considerations could have been wrong? Third, what do these new considerations imply? Was the first estimate rather too high or too low? Fourth, based on this new perspective, make a second, alternative estimate. A graph of a number of indicators Description automatically generated with medium confidence  Effective at cancelling out random errors Not so effective at systematic errors (e.g., anchoring) Irrational Individuals With Collective Rationality T. Rugatulus ants like their nests to be dark and have small entrances Individual Ants  Colony **Improved reasoning** If a card has a vowel on one side, it has an even number on the other side **Cards Turned** **Individuals** ------------------ ----------------- P, ¬Q 9.4% P, Q, ¬Q 0% P 15.6% P, Q 43.8% All 6.3% Other 25% **A B C D E F G H I J** **3 5 8 2 1 6 4 7 0 9** 1. Guess: A + D = ? Answer: B 2. Hypothesis: B = 3 Answer: False \ A math equation with a white background Description automatically generated with medium confidence Groups do better than the best individual in a group could have done alone \* except for groups of 2 **Summary** There are several pitfalls to be aware of in group decision-making, including the effects of **conformity**, **authority,** **polarization** and **groupthink**. There are also many benefits to group decision-making including **wisdom of the crowd** and **improved reasoning.** Common themes are independence and diversity. These are the qualities that are overridden when decision-making fails in groups, and they are the qualities that are necessary for the success of wisdom of the crowd phenomena.