Cognitive Processes PSY 334

1. Cognitive ProcessesPSY 334 Chapter 11 – Judgment and Decision-Making

2. 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.

3. 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.

4. 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.

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

6. Baye’s Theorem P(H) = .001 from police statistics P(~H) = .999 this is 1.0 - .001 P(E|H) = .8 P(E|~H) = .01 Base rate

7. 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”. • Effect occurs regardless of the content of the evidence: • Estimate of .5 regardless of mix for “Dick”

8. 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.

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

10. 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.

11. 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.

12. 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.

13. 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 3rd position (3 x as many). • Sequences of coin tosses – HTHTTH just as likely as HHHHHH.

14. 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.

15. 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.

16. 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

17. 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 • B -- $3 with a 5/6 probability • Most subjects choose B

18. 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

19. 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.