Cognitive Processes PSY 334 Chapter 11 Judgment and

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

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

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

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

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

Baye’s Theorem P(H) =. 001 P(~H) =. 999 P(E|H) =. 8 P(E|~H) =. 01 from police statistics this is 1. 0 -. 001 Base rate

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

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

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

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

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

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

Judgments of Probability o People can be biased in their estimates when they depend upon memory. o Tversky & Kahneman – differential availability of examples. n n 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 o The idea that over a period of time things will even out. o Fallacy -- If something has not occurred in a while, then it is more likely due to the “law of averages. ” o People lose more because they expect their luck to turn after a string of losses. n Dice do not know or care what happened before.

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

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

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

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

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