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The 3rd London Reasoning Workshop 18-19/08/2007

Matching heuristic cannot explain matching bias in conditional reasoning. In honour of Jonathan Evans ’ 60 th Birthday. The 3rd London Reasoning Workshop 18-19/08/2007. Akira Nakagaki (Waseda University). What is matching bias in propositional reasoning?.

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The 3rd London Reasoning Workshop 18-19/08/2007

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  1. Matching heuristic cannot explain matching bias in conditional reasoning. In honour of Jonathan Evans’ 60th Birthday The 3rd London Reasoning Workshop18-19/08/2007 Akira Nakagaki (Waseda University)

  2. What is matching bias in propositional reasoning? • The phenomenon known as “matching bias” consists of a tendency to see cases as relevant in logical reasoning tasks when the lexical content of a case matches that of a propositional rulewhich applies to that case (Evans, 1998). • The matching effect has been first demonstrated in the truth table task (Evans, 1972) and then the Wason’s selection task (Evans & Lynch, 1966). • Matching bias is a robust phenomenon which has for many years presented a challenge to various theories of propositional reasoning (Evans, 1998).

  3. Statement: If a card has E on the face, then it has 7 on the back. (p ⇒ q） Task: Which card or cards do you have to turn over in order to decide whether the statement is true or false? Hypothetico-deductive reasoning Very difficult task (usually around 10% correct) Selection patterns: selection p, q (46%), selection p (33%), selection p,q, ￢q (7%), selection p, ￢q (4%) （Johnson-Laird & Wason 1970） E K 7 5 （￢ｑ） （ｐ） （￢ｐ） （ｑ） Four Cards presented in AST Wason’s Selection Tasks(Wason, 1966)

  4. E K 7 5 （￢ｑ） （ｐ） （￢ｐ） （ｑ） Four cards presented in AST Wason’s Selection Tasks using negations paradigm (Evans & Lynch 1973) • Negation is introduced into an affirmative conditional p ⇒ q (If a card has E on the face, then it has 7 on the back). • StatementⅠ: p ⇒ q StatementⅡ: p ⇒ ￢q StatementⅢ: ￢p ⇒ q StatementⅣ: ￢p ⇒ ￢q • Task: Which card or cards do you have to turn over in order to decide whether the statement is true or false?

  5. Tasks that examine truth conditions of a conditional. Statement: If a card has A on the left, then it has 8 on the right. (p ⇒ q） Task: Participants are asked to decide for each card whether it conforms or contradicts the statement. Truth Table Tasks(Evans, 1972,1983, Nakagaki, 1998) Card presentation in TTT

  6. What isa matching-heuristic in logical reasoning? • The heuristic-analytic theory proposed by Evans (1989) is based on the ideathat people reason analytically about problem information that ispre-consciously selectedas relevant at a prior heuristic stage. • In order to explain matching bias, Evans (1999) has proposed a matching-heuristic which works at the heuristic stage and directs attention to cases explicitly stated in the rules regardless of the presence of negations.

  7. Howdoesa matching-heuristicexplain matching bias? • In the WST, participant tend to select only p or p & q cards regardless of the presence of negations in the rule, because the matching-heuristic directs attention to the p and q cards that are explicitly stated in the rules.Responses reflect only heuristic judgments of relevance and analytic reasoning processes do not comein to play. • The TTT requires both ajudgement of relevance and, for relevant cases, further judgement ofwhether such cases are true or false. The TTT requires analyticreasoning also.

  8. Evidences against the matching-heuristic theory • Evans’ own experiment by which he tried to demonstrate the matching heuristic (Evans, Experiment 1, 1995). • Results of disjunctive reasoning tasks (Evans & Johnson-Laird 1969; Evans, & Newstead, 1980; Roberts, 2002). • Results of Wason’s selection task with two rules(Feeney & Handly, 2000). • Results of non-standard Wason’s selection task(Nakagaki, 2000). • Developmental study of Wason’s selection task (Nakagaki, 1992).

  9. EvidenceⅠ： The matching-heuristic theory was refuted by his own experiment • Evans conducted an experiment by which he tried to demonstrate the matching heuristic (Evans, Experiment 1, 1995). • In WST, participants were asked to decide to which of the four cards the rule appears to be relevant. • Contrary to his expectation, participants did not show any matching bias in his critical experiment. • Nevertheless, Evans interpreted this result not as a refutation of his theory but as a change of what is relevant to the task.

  10. EvidenceⅡ： Results of disjunctive reasoning tasks • There is no matching bias in disjunctive selection tasks (Wason & Johnson-Laird 1969; Nakagaki, 1990; Roberts, 2002). • There is no matching bias in disjunctive truth table tasks (Evans, & Newstead, 1980, Experiment 1). • They described themselves their experiment as “providing a powerful test of the matching bias hypothesis (matching-heuristic)”. • But they found no evidence of the matching bias.

  11. EvidenceⅢ： Suppression of q card selections in WST • What will happen if participants are presented with the WST with two rules, p⇒q and r⇒q. • Since the matching heuristic is preconscious and non-logical, it is predicted that this WST would increase participants’ selections of the q card due to its enhanced relevance. • In spite of this prediction, the introduction of the additional rule in WST suppressed q card selections substantially (Feeney & Handly, 2000).

  12. EvidenceⅣ： Anti-matching bias in non-standard WST. • What will happen if participants are asked to select cards which verify or falsify the rule in WST. This task is called “non-standard WST”. • Since the matching heuristic is preconscious and non-logical, it is predicted that this instruction would not change participants’ card selection. • In spite of this prediction, they showed anti-matching biasin non-standard WST using negation paradigm (Nakagaki, 2000).

  13. EvidenceⅤ： Anti-matching bias in prescriptive WST • A developmental study of prescriptive WST revealed different patterns of card selection in junior high school students (Nakagaki, 1992). • Since the matching heuristic is a very simple one, it is predicted that younger generation would be more prone to matching bias than adults. • In spite of this prediction, they tended to select not-p and not-q cards even in WST with p⇒q，and showed anti-matching biasin prescriptive WST using negation paradigm.

  14. Conclusion: Doesthe matching-heuristicreally explain matching bias? • The matching-heuristic directs attention to cases explicitly stated in the rule. However, no explanation is found why people judge these cases as relevant to the task. • If the matching heuristic includes relevance judgment as well, it is a re-description of the phenomenon. In other words, it is a tautological explanation of matching bias. • Matching bias is not a non-logical response (Evans1998 p.48) at all, but it is the best possible logical solution for the participant’s system of propositional operations (Nakagaki, 2005).

  15. Thank you for your attention. End of my presentation Presenter: Akira Nakagaki (Waseda University)

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