Rational analysis of the selection task

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Rational analysis of the selection task

• Oaksford and Chater (1994)
• Presented by
• Bryan C. Russell

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Wason selection task

• Rule if there is a vowel on one side, then there
  is an even number on the other side

K
2
7
A
3
Last time

• Humans are stupid
• Cosmides et al.
• Social contract theory (i.e. innate ability to
  detect cheaters)
• Depends on perspective (enforcer or actor)

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Outline

• Probabilistic account of Wason selection task
• Information-theoretic background
• Application to abstract selection task
• Application to thematic selection task
• Discussion

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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
• Expectation 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

• If a passenger form says ENTERING on one side
  then the other side must include cholera
  information

ENTERING not checked
cholera information
no cholera information
ENTERING checked
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Rule types

• Obligations if action (p), then must condition
  (q)
• Permissions if condition (p), then may action (q)

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Subject perspective for permission rule

• Enforcer
• Pretend you are an immigrant officer
• Actor
• Pretend you are a traveler
• Objective inquirer
• Check the validity of the statement

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Human performance

• Obligation action (p) gt must condition (q)
• Permission condition (p) gt may action (q)

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Utility-based model

• Focus on rule-use, not rule-testing
• Associate cost with turning over a card

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Utility-based model
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Performance of utility-based model
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Andersons (1990) steps for rationality

• Specify precisely the goals of the cognitive
  system
• Develop a formal model of the environment to
  which the system is adapted
• Make minimal assumptions about computational
  limitations

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Andersons (1990) steps for rationality

• Derive the optimal behavior function given the
  previous steps
• Examine the empirical evidence to see whether the
  predictions of the behavioral function are
  confirmed
• Rinse, lather, repeat, and refine the theory

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Conclusions

• Bayesian approach more principled than other
  accounts
• Applies to both abstract and thematic versions of
  the problem (and their variants)
• Behavior is adapted to the environment and does
  not necessarily follow logic/mathematic theory

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Discussion questions

• Is the rarity assumption valid? How do we test
  it?
• Is the selection task representative of
  accounting for rational thought? Is it
  exhaustive?
• How is this model realized?
• Does one learn explicitly the utility costs and
  Pr(p)/Pr(q)?