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

A K 2 7 Wason selection task Rule: if there is a vowel on one side, then there is an even number on the other side A K 2 7

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

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

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)

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

Card probabilities

Card probabilities Task: Select card that maximally reduces hypothesis uncertainty

Entropy/uncertainty

Entropy/uncertainty

Entropy/uncertainty

Another experiment… Suppose you observe: TTHTHHTHHHHTHHTHTHHT

Another experiment… Suppose you observe: TTHTHHTHHHHTHHTHTHHT HTHHTTHTHHTTTTTTTTTH

Another experiment… Suppose you observe: TTHTHHTHHHHTHHTHTHHT HTHHTTHTHHTTTTTTTTTH

Mutual information

Application to selection task a = Pr(p)

Application to selection task a = Pr(p)

Model behavior

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

Model behavior R

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

How do humans compare?

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

Thematic selection task If a passenger form says “ENTERING” on one side then the other side must include cholera information “ENTERING” checked “ENTERING” not checked cholera information no cholera information

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

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…

Human performance Obligation: action (p) => must condition (q) Permission: condition (p) => may action (q)

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

Utility-based model

Performance of utility-based model

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

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

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

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)?