Cognitive Processes PSY 334

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Cognitive ProcessesPSY 334

• Chapter 11 Judgment and Decision-Making

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Inductive Reasoning

• Processes for coming to conclusions that are
  probable rather than certain.
• As with deductive reasoning, peoples judgments
  do not agree with prescriptive norms.
• Bayes theorem describes how people should
  reason inductively.
• Does not describe how they actually reason.

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Bayes 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.
• Bayes theorem calculates posterior probability.

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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.

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Bayes Theorem

• H likelihood of being robbed
• H likelihood of no robbery
• EH likelihood of door being left ajar during a
  robbery
• EH likelihood of door ajar without robbery

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Bayes Theorem

• P(H) .001 from police statistics
• P(H) .999 this is 1.0 - .001
• P(EH) .8
• P(EH) .01

Base rate
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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

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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.

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Cancer Example
Base rate

• P(H) .0001 likelihood of having cancer
• P(H) .9999 likelihood of not having it
• P(EH) .95 testing positive with cancer
• P(EH) .05 testing positive without cancer

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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.

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Probability Matching

• People show implicit understanding of Bayes
  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.

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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, lt20 when stated as probabilities.
• People improve with experience.

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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.

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Gamblers 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.

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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.

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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

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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

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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

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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.