1. Rational analysis of the selection task Oaksford and Chater (1994) Presented by Bryan C. Russell

2. Wason selection task Rule: if there is an A on one side, then there is a 2 on the other side A K27

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 –M D : p,q are dependent (rule is true) –M I : 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 | M D ) = P(p | M I ) = a P(q | not-p,M D ) = P(q | not-p,M I ) = b

5. Card probabilities

6. Task: Select card that maximally reduces hypothesis uncertainty

7. Entropy/uncertainty

10. Another experiment… Suppose you observe: –TTHTHHTHHHHTHHTHTHHT

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

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

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(M I ) 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?

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

24. Thematic selection task If a person is drinking beer, then they must be over 20 years old drinking sprite 25 years old 16 years old drinking beer

25. Thematic selection task If a person is over 20 years old, then they may drink a beer drinking sprite 25 years old 16 years old drinking beer

26. Rule types Obligations: if action (p), then must condition (q) Permissions: if condition (p), then may action (q)

27. Subject perspective for permission rule Enforcer –Pretend you are a bouncer at the R&D pub… Actor/inquirer –A guy walks into a bar…

28. Utility-based model Focus on rule-use, not rule-testing Associate cost with turning over a card

29. Utility-based model

30. Performance of utility-based model

31. Comparison with humans

32. Anderson’s (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

33. Anderson’s (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

34. Discussion questions Why use a probabilistic framework for rationality? Is the rarity assumption valid? Is the selection task representative of accounting for rational thought? Is it exhaustive? How does one learn the utility costs? How does one learn Pr(p) and Pr(q)?