Cognitive Processes PSY 334 Chapter 10 – Reasoning & Decision-Making August 21, 2003

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.

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”

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.

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.

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.

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 B -- $3 with a 5/6 probability  Most subjects choose B

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

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.