Cognitive Processes PSY 334 Chapter 11 – Judgment & Decision-Making

Inductive Reasoning  Processes for coming to conclusions that are probable rather than certain.  As with deductive reasoning, people’s judgments do not agree with prescriptive norms.  Baye’s theorem – describes how people should reason inductively. Does not describe how they actually reason.

Baye’s Theorem  Prior probability – probability a hypothesis is true before considering the evidence.  Conditional probability – probability the evidence is true if the hypothesis is true.  Posterior probability – the probability a hypothesis is true after considering the evidence. Baye’s theorem calculates posterior probability.

Burglar Example  Numerator – likelihood the evidence (door ajar) indicates a robbery.  Denominator – likelihood evidence indicates a robbery plus likelihood it does not indicate a robbery.  Result – likelihood a robbery has occurred.

Burglary Probabilities

Baye’s Theorem Hlikelihood of being robbed ~Hlikelihood of no robbery E|Hlikelihood of door being left ajar during a robbery E|~Hlikelihood of door ajar without robbery

Baye’s Theorem P(H) =.001from police statistics P(~H) =.999this is P(E|H) =.8 P(E|~H) =.01 Base rate

Base Rate Neglect  People tend to ignore prior probabilities.  Kahneman & Tversky: 70 engineers, 30 lawyers vs 30 engineers, 70 lawyers No change in.90 estimate for “Jack” with description.  Effect occurs regardless of the content of the evidence: Estimate of.5 regardless of mix for “Dick”

Description of Jack  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 spare time on his many hobbies, which include home carpentry, sailing and mathematical puzzles.

Cancer Test Example  A particular cancer will produce a positive test result 95% of time. If a person does not have cancer this gives a 5% false positive rate.  Is the chance of having cancer 95%?  People fail to consider the base rate for having that cancer: 1 in 10,000.

Cancer Example P(H) =.0001likelihood of having cancer P(~H) =.9999likelihood of not having it P(E|H) =.95testing positive with cancer P(E|~H) =.05testing positive without cancer Base rate

Conservatism  People also underestimate probabilities when there is accumulating evidence.  Two bags of chips: 70 blue, 30 red 30 blue, 70 red Subject must identify the bag based on the chips drawn.  People underestimate likelihood of it being bag 2 with each red chip drawn.

Probability Matching  People show implicit understanding of Baye’s theorem in their behavior, if not in their conscious estimates.  Gluck & Bower – disease diagnoses: Actual assignment matched underlying probabilities. People overestimated frequency of the rare disease when making conscious estimates.

Gluck & Bower’s Results Implicit JudgmentsExplicit Judgments

Frequencies vs Probabilities  People reason better if events are described in terms of frequencies instead of probabilities.  Gigerenzer & Hoffrage – breast cancer description: 50% gave correct answer when stated as frequencies, <20% when stated as probabilities.  People improve with experience.

Judgments of Probability  People can be biased in their estimates when they depend upon memory.  Tversky & Kahneman – differential availability of examples. Proportion of words beginning with k vs words with k in 3 rd position (3 x as many). Sequences of coin tosses – HTHTTH just as likely as HHHHHH.

Gambler’s Fallacy  The idea that over a period of time things will even out.  Fallacy -- If something has not occurred in a while, then it is more likely due to the “law of averages.”  People lose more because they expect their luck to turn after a string of losses. Dice do not know or care what happened before.

Chance, Luck & Superstition  We tend to see more structure than may exist: Avoidance of chance as an explanation Conspiracy theories Illusory correlation – distinctive pairings are more accessible to memory.  Results of studies are expressed as probabilities. The “person who” is frequently more convincing than a statistical result.

Recognition Heuristic  Gigerenzer says use of availability of info in memory is not a fallacy but helpful.  Recognition heuristic – people attach greater importance to what they recognize than what they don’t. They say Heidelberg is bigger because they recognize the name, not Bamberg. This works because size and familiarity are correlated, but may not work in other areas

Decision Making  Choices made based on estimates of probability.  Described as “gambles.”  Which would you choose? $400 with a 100% certainty $1000 with a 50% certainty

Utility Theory  Prescriptive norm – people should choose the gamble with the highest expected value.  Expected value = value x probability.  Which would you choose? A -- $8 with a 1/3 probability$2.67 B -- $3 with a 5/6 probability$2.50  Most subjects choose B

Deal or No Deal?  CVX-t3o CVX-t3o  Which would you choose? A -- 1 million dollars with a probability of 1 B million dollars with a probability of ½  Utility theory predicts B but people pick A

Subjective Utility  The utility function is not linear but curved. It takes more than a doubling of a bet to double its utility ($8 not $6 is double $3).  The function is steeper in the loss region than in gains: A – Gain or lose $10 with.5 probability B -- Lose nothing with certainty People pick B because enough is enough.

Subjective Utility  Doubling the amount of money does not double the value to people: For $1 million, U = 1 Then 2.5 million x ½ = 1.25 million  If people value the chance to win $2.5 instead of $1 only slightly more than getting $1 million for sure, U=1.2 not 2.5  So, $1 million = U, but $2.5 million =.6 (1.2 x ½), so choosing $1 million wins.

Subjective Utility The value we place on money is not linear to the face value of money.

Framing Effects  Behavior depends on where you are on the subjective utility curve. A $5 discount means more when it is a higher percentage of the price. $15 vs $10 is worth more than $125 vs $120.  People prefer bets that describe saving vs losing, even when the probabilities are the same.

Greater Weight on Losses  Someone has lost $140 at the races but can now bet $10 with 15:1 odds. A – refuse the bet and accept $140 loss B – Make the bet and face losing $150 or breaking even.-140 point on subjective curve  If expressed differently the decision changes: A – Refuse the bet and stay the same B – Make the bet and lose $10 more with a poor chance of gaining $140.0 point on subjective curve

Odds of Living vs Dying Change Decision-making A – Save 200 people. B – 1/3 probability 600 saved, 2/3 probability no one saved C – 400 people will die D – 1/3 probability nobody will die 2/3 probability 600 people will die  72% preferred A but only 22% preferred C (equivalent to A). D is the same as B.

Impersonal vs Personal Dilemmas A – A runaway trolley will kill 5 people unless it is switched to a different track where it will kill 1 person. Do you do it? B – The trolley will kill 5 people unless you push a stranger off a bridge into the path of the trolley, killing him. Do you do it?  Most people say yes to A but no to B.  Different brain regions are active in the two choices (B is emotional).

Evidence from Neuroscience  Dopamine neurons in the nucleus acumbens (basal ganglia) respond to reward size.  Probability of reward is evaluated in the ventromedial prefrontal cortex (which also integrates probabilities & utilities). People with damage have trouble with gambling tasks (such as Iowa gambling task with good/bad decks).