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From cognitive principles to decision making

From cognitive principles to decision making. Nick Chater Behavioural Science Group, Warwick Business School With input from discussions with Gordon Brown, Graham Loomes, Robert Mackay , Chris Olivola & Daniel Read, Neil Stewart, Ivo Vlaev. OVERVIEW. COGNITIVE VS RATIONAL PRINCIPLES

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From cognitive principles to decision making

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  1. From cognitive principles to decision making Nick Chater Behavioural Science Group, Warwick Business School With input from discussions with Gordon Brown, Graham Loomes, Robert Mackay, Chris Olivola & Daniel Read, Neil Stewart, Ivo Vlaev...

  2. OVERVIEW • COGNITIVE VS RATIONAL PRINCIPLES • CANDIDATE COGNITIVE PRINCIPLES • AN OVERSIMPLE MODEL • TWO TYPES OF ELABORATION

  3. 1. COGNITIVE VS RATIONAL PRINCIPLES

  4. Rational vs cognitive principles • Cognitive • Origins of un/partially constrained “intuitions;” constraints from: • Perception • Attention • Memory • ... • Rational • Local coherence constraints between “intuitions” • Logic (coherence between beliefs) • Probability (coherence between degrees of belief) • Decision theory (coherence between values, degrees of belief, actions) • ... Justification Mechanism

  5. Both rational and cognitive principles required • Coherence of intuitions needed to produce integrated representation of world/plan of action etc • But coherence is not enough... • Coherence constraints are often very loose • Mere coherence is not enough • What are the elements that we are bringing into to coherence? Fitting together pieces of a puzzle Seeing what shape the individual pieces are

  6. 2. CANDIDATE COGNITIVE PRINCIPLES

  7. Some candidate principles... • Principle 1: Ratios, not absolute values, are cognitively basic. • Principle 2: Comparisons are made withindimensions. • Principle 3: “Opponent” processes. • Principle 4: Scale-invariance (e.g., Chater & Brown, 1999)

  8. Value £ Qualitative consequence 1 • Principle 1: Ratios, not absolute values, are cognitively basic.  no value functions! Prospect theory Kahneman & Tversky 1979 Expected Utility

  9. Qualitative consequence 2 • Principle 1: Ratios, not absolute values, are cognitively basic. • Principle 2: Comparisons are made withindimensions. • principle 2 almost follows from Principle 1, as ratios are ill-defined across different units (e.g., seconds vs $)  Comparison- not value-based theories of multi-attribute choice

  10. Multiattribute value-based choice f2=1 f2=3 A B f3=3 f1=2 f3=1 f1=3 Value(A) = g(f1...fn) = 6 Value(B) = g(f1...fn) = 9 Value(A)=6 < Value(B)=9 Choose B

  11. Multiattributecomparison-based choice f2=1 f2=3 A B f3=3 f1=2 f3=1 f1=3 B ‘wins’ on f1 A ‘wins’ on f2 B ‘wins’ on f3 B wins overall (Loomes, 2010; Scholten & Read, 2010; Stewartet al, 2006; Brandstatter, et al, 2006) Choose B

  12. Qualitative consequence 3 • Principle 1: Ratios, not absolute values, are cognitively basic. • Principle 2: Comparisons are made withindimensions. • Principle 4: Scale-invariance  Dimensions have “independent” influence

  13. What is scale-invariance? • In a nutshell: • Throw away “units” • Can you reconstruct them from your data? • If not, phenomenon is scale-invariant Only power laws yx are scale invariant

  14. Scale-invariance of ratios Requires that choice of an option is a generalized power function of g(r1,...,rn), where g(r1,r2,...,rn) = c.(r1)α1.(r2)α2...(rn)αn ln[g(r1, r2,...,rn)] = ln(c) + α1(ln(r1)) + α2(ln(r2))+...+αn(ln(rn)) • Dimensions have independent (“additive”) influence

  15. Specific implications: • Constant relative risk aversion (scale-up prizes, choices invariant) $5 preferred to ½ chance of $12 just when $10 preferred to ½ chance of $24 • Hyberbolic discounting (scale-up times, choices invariant) $5 in 1 day preferred to $6 in 2 days just when $5 in 2 day preferred to $6 in 4 days Nb: independence is sometimes violated…

  16. Qualitative consequence 4 • Principle 1: Ratios, not absolute values, are cognitively basic. • Principle 2: Comparisons are made within dimensions. • Principle 3: “Opponent” processes.  Choice between items of similar overall value can be very different...

  17. An example • V(A)≈ V(B) ≈ V(D) • But {A, D} is easy: A is always, and rapidly, preferred to D • And {A, B} is hard: A is unreliably and slowly compared with B ...a serious problem for value-based theories of choice

  18. Why one comparison is easy, one hard The difference is an immediate consequence of feature-by-feature comparison... A D A B vs economy economy quality quality

  19. 3. AN OVERSIMPLE MODEL

  20. Decision under risk... • Principle 1: compare ratios, e.g., • RISKY has 4 times the “prize”; • SAFE is 2 times more likely to win • Principle 2: within dimension comparison only • No comparison of transforms U($10), U($40). Only ratios between “raw” numbers SAFE: $10 for sure RISKY: ½: $40 for sure ½: $0

  21. Opponent processes (Principle 3) SAFE: $10 for sure RISKY: ½: $40 ½: $0 Ratio = 2 Ratio = 4 • PROB OF WINNING: ratio, for SAFE • MAGNITUDE OF PRIZE: ratio of 4 for RISKY

  22. Scale invariance (Principle 4) SAFE: $10 for sure RISKY: ½: $40 ½: $0 β α vs • The “pull” of probability of winning • The “pull” of the big prize Scale invariance demands a power function of the ratios...

  23. Scale invariance (Principle 4) Pr(choose SAFE) = α β α +

  24. 4. TWO TYPES OF ELABORATION

  25. Elaboration Type 1: What ratios are represented? Do we represent a probability like this? 1 0 Or should it be...

  26. Representing the probability and its complement? 1 0

  27. The common ratio effect • .9 chance of $5000 vscertain $4000 • .45 chance of $5000 vs.5 chance of $4000 EU predicts identical responses... But if we consider both ratios of probabilities, these are very different...

  28. The common ratio effect • Ratios for prob of winning: 1:.9 = .5:.45 • Ratios of prob of losing: .1:0 >> .55:.5 So people “irrationally” reluctant to give up certainty...  Common-ratio effect (Allais’ Paradox)

  29. Elaboration Type 2: When the cognitive principles break down... Too big to care Scale invariance violated Scale invariant region Too small to care! Implies insensitivity to very large (bias to safe), very small (bias to safe or risky) sum of money.

  30. Finding cognitive and rational principles as a research strategy in cognitive science • Cognitive principles determine isolated judgements/choices as a function of the task • But rational coherence constraints with background knowledge/preferences will continually intrude • Splitting between the two may be crucial to creating the right set of cognitive and rational principles

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