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Rational Analysis of Selection Task: Probability-Based Model in Human Decision-Making

This analysis by Bryan C. Russell delves into human decision-making through a probabilistic framework, focusing on the selection task. The study explores rules, hypotheses, assumptions, card probabilities, and model behaviors, examining how humans compare and decide based on information values. The rarity assumption is validated, showcasing the utility-based model for thematic selection tasks. Discussion points ponder using such a framework for rationality and if the selection task adequately represents rational thought.

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Rational Analysis of Selection Task: Probability-Based Model in Human Decision-Making

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  1. Rational analysis of the selection task Bryan C. Russell 9.012

  2. Wason selection task • Rule: if there is an A on one side, then there is a 2 on the other side K 2 7 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)

  4. 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

  5. Card probabilities

  6. Card probabilities • Task: Select card that maximally reduces hypothesis uncertainty

  7. Entropy/uncertainty

  8. Entropy/uncertainty

  9. Entropy/uncertainty

  10. Another experiment… • Suppose you observe: • TTHTHHTHHHHTHHTHTHHT

  11. Another experiment… • Suppose you observe: • TTHTHHTHHHHTHHTHTHHT • HTHHTTHTHHTTTTTTTTTH

  12. Another experiment… • Suppose you observe: • TTHTHHTHHHHTHHTHTHHT • HTHHTTHTHHTTTTTTTTTH

  13. Mutual information

  14. Application to selection task a = Pr(p)

  15. Application to selection task a = Pr(p)

  16. Model behavior

  17. 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

  18. Model behavior R

  19. 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

  20. How do humans compare?

  21. Analysis • Both humans and model accounts for the following information relationship: • choose p > choose q > choose not-q > choose not-p

  22. Thematic selection task

  23. Utility-based model

  24. Validity of the rarity assumption

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

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