Rational analysis of the selection task

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Rational analysis of the selection task

• Bryan C. Russell
• 9.012

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Wason selection task

• Rule if there is an A on one side, then there is
  a 2 on the other side

K
2
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A
3
Another view of the task

• Let rule be if p then q
• Four types of cards
• (p,q), (not-p,q), (p,not-q), (not-p,not-q)
• Two hypotheses
• MD p,q are dependent (rule is true)
• MI p,q are independent (rule is false)

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Assumptions

• We can assign probabilities to the cards
• Should reflect natural statistics of if p then
  q statements in nature
• P(p MD) P(p MI) a
• P(q not-p,MD) P(q not-p,MI) b

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Card probabilities
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Card probabilities

• Task Select card that maximally reduces
  hypothesis uncertainty

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Entropy/uncertainty
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Entropy/uncertainty
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Entropy/uncertainty
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Another experiment

• Suppose you observe
• TTHTHHTHHHHTHHTHTHHT

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Another experiment

• Suppose you observe
• TTHTHHTHHHHTHHTHTHHT
• HTHHTTHTHHTTTTTTTTTH

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Another experiment

• Suppose you observe
• TTHTHHTHHHHTHHTHTHHT
• HTHHTTHTHHTTTTTTTTTH

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Mutual information
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Application to selection task
a Pr(p)
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Application to selection task
a Pr(p)
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Model behavior
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Observations

• If Pr(q) is low, then choosing p card is
  informative
• If Pr(p) and Pr(q) is low, then choosing q card
  is informative
• If Pr(p) is high, then choosing not-q card is
  informative
• not-p card is not informative (results in zero
  information)
• P(MI) only scales information values

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Model behavior
R
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Rarity assumption

• For selection task, in humans Pr(p) and Pr(q) are
  low
• Expected information over region R
• choose p 0.76
• choose q 0.20
• choose not-q 0.09
• choose not-p 0

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How do humans compare?
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Analysis

• Both humans and model accounts for the following
  information relationship
• choose p gt choose q gt choose not-q gt choose not-p

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Thematic selection task
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Utility-based model
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Validity of the rarity assumption
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Discussion questions

• Why use a probabilistic framework for
  rationality?
• Is the selection task representative of
  accounting for rational thought? Is it
  exhaustive?