intuitive beliefs
play

Intuitive Beliefs Jawwad Noor Boston University 2 Introduction - PowerPoint PPT Presentation

1 Intuitive Beliefs Jawwad Noor Boston University 2 Introduction Economics: rational beliefs described by a prior probability + Bayesian updating Psychology: Beliefs are not monotone let alone additive (conjunction/disjunction


  1. 1 Intuitive Beliefs Jawwad Noor Boston University

  2. 2 Introduction • Economics: rational beliefs described by a prior probability + Bayesian updating • Psychology: – Beliefs are not monotone let alone additive (conjunction/disjunction fallacy) – Updating is not Bayesian (base-rate neglect, gambler’s fallacy, etc) – Intuitive judgements based on heuristics (Kahneman-Tversky 1974) • Field evidence for non-Bayesian updating – over/under updating: Stone (EI 2012) – gambler’s fallacy: Suetens et al (JEEA 2016) – Over-reaction: Debondt and Thaler (JF 1985) – Representativeness heuristic: Ahmed and Safdar (MS 2016)

  3. 3 Introduction • Behavior driven by intuition has economic relevance – incomplete deliberation due to limited time/cognitive resources – gaps filled by gut feeling • Classic reference on choice based on spontaneous feelings rather than deliberation: “[A] large proportion of our positive activities...can only be taken as the result of animal spirits—a spontaneous urge to action rather than inaction, and not as the outcome of a weighted average of quantitative benefits multiplied by quantitative probabilities.” Keynes (1936)

  4. 4 Introduction • This paper: formal theory of intuitive beliefs – Concepually, what is intuition? – How to model mathematically?

  5. 5 Introduction • This paper: formal theory of intuitive beliefs – Concepually, what is intuition? – How to model mathematically? • Inspiration from psychology and philosophy: associations • Activation of a mental image activates/inhibits another – e.g..... – Vocation, ethnicity, religion, etc may bring about the image of a stereotype – Involuntary and costless mental processing • Associations learnable, strength determined by frequency, salience, similarities, etc • Can be strengthened (reinforcement) or weakened (counter-conditioning or decay) • Intuitive beliefs driven by associations triggered by observation of information

  6. 6 Introduction • This paper: formal theory of intuitive beliefs – Concepually, what is intuition? – How to model mathematically? • Inspiration from cognitive science: neural networks • Elements of the model (note: not decision-theoretic): – network of associations, shaped by experience – nodes triggered by an observation generate output at connected nodes – the output of the network is what appears to us as intuition

  7. 7 Outline • Formal Model • Properties: Evidence, Bayesian intersection, Uniqueness • Axiomatization: Preview • Shaping the network • Conclusion

  8. 8 Primitives • A state of the world is a description of the relevant uncertainty: • Γ = {    } = finite index set of elements of uncertainty • Ω  = {           } = abstract set of possible realizations of element  ∈ Γ • Illustration: Agent is on a boat, lost in the open sea, and is uncertain about  = health/survival  = what kind of fish is swimming under the water

  9. 9 Primitives • A state of the world is a description of the relevant uncertainty: • Γ = {    } = finite index set of elements of uncertainty • Ω  = {           } = abstract set of possible realizations of element  ∈ Γ • Illustration: Agent is on a boat, lost in the open sea Γ = {   } Ω  = {     } Ω  = {      }

  10. 10 Primitives • State space: Ω = Q  ∈ Γ Ω  , generic state  = (       ) • Example Ω = { (   )  (   )   } • Large complicated state spaces are not a challenge • Construction and operation of networks is cognitively costless

  11. 11 Primitives • Σ  = { Ω   x   y   z   } ⊂ 2 Ω  = "elementary events" of element  • Example: health/fish in the Yellow Sea... y  ⊂ Ω  = {     } y  ⊂ Ω  = {       } • Event space given by Σ = Q  ∈ Γ Σ  , generic event x = ( x   x    x  ) • Identify Yellow Sea with y = ( y   y  ) ⊂ Ω  × Ω  • Product structure is convenient: each elementary event is a node in a network

  12. 12 Primitives • A belief  ( ·| z ) conditional on z ∈ Σ over the space ( Ω  Σ ) : – set function  : Σ → [0  1] – assigns 1 to the full space – 0 to any event with a null elementary event – Satisfies  ( x | z ) =  ( x ∩ z | z ) – Not necessarily additive or monotone (conjunction/disjunction fallacies) •  ( ·| Ω ) is the prior,  ( ·| z ) for Ω 6 =  ∈ Σ is posterior • Primitive: collection of conditional beliefs p = {  ( ·| z ) : z ∈ Σ and  ( z | Ω )  0 }

  13. 13 Model • Each elementary event is a node of a network • {shark} • z  • y  • {death} • z  • y 

  14. 14 Model • Evaluate  (   | y   y  ) • {shark} • z  • y  • {death} • z  • y 

  15. 15 Model • Evaluate  (   | y   y  ) • {shark} • z  % % • y  − → − → − → − → − → • {death} • z  • y   (  | y  ) ∈ R + ∪ { ∞ }  (  | y  ) ∈ R + ∪ { ∞ }

  16. 16 Model • Evaluate  (   | y   y  ) • {shark} • z  % &- % &- • y  − → − → − → − → − → • {death} • z  • y   (  | y  )   (  |  ) ×  (  | y  )  (  | y  )   (  |  ) ×  (  | y  )

  17. 17 Model • Evaluate  (   | y   y  ) ↑ • z  • {shark} % &- % &- • y  − → − → − → − → − → • {death} − → • z  • y   (  | y  )   (  |  ) ×  (  | y  )  (  | y  )   (  |  ) ×  (  | y  )

  18. 18 Model • Evaluate  (   | y   y  ) ∙ • z  • {shark} % ↑ &- % ↑ &- ⇒ • y  − → − → ↑ − → − → • {death} ↑ % ↑ % • z  • y   (  | y  )   (  |  ) ×  (  | y  )  (  | y  )   (  |  ) ×  (  | y  )  (  | y  )   (  |  ) ×  (  | y  )  (  | y  )   (  |  ) ×  (  | y  )

  19. 19 Model • Expression for beliefs: Based on axioms and on tractability  (   | y   y  ) = ⎡ ⎤  (  | y  )   (  |  ) ×  (  | y  ) ⎢ ⎥  (  | y  )   (  |  ) ×  (  | y  ) ⎢ ⎥ ⎢ ⎥  ⎢ ⎥ ⎣ ⎦  (  | y  )   (  |  ) ×  (  | y  )   (  | y  )   (  |  ) ×  (  | y  )

  20. 20 Model • Expression for beliefs: Based on axioms and on tractability  (   | y   y  ) = ⎡ ⎤  (  | y  )   (  |  ) ×  (  | y  ) ⎢ ⎥  (  | y  )   (  |  ) ×  (  | y  ) ⎢ ⎥ ⎢ ⎥ exp − 1 ⎢ ⎥ ⎣ ⎦  (  | y  )   (  |  ) ×  (  | y  )   (  | y  )   (  |  ) ×  (  | y  ) • Inverse of exp so that  ∈ [0  1]

  21. 21 Model • Expression for beliefs: Based on axioms and on tractability  (   | y   y  ) = ⎡ ⎤  (  |  ) − 1 ×  (  | y  ) − 1  (  | y  ) − 1   (  |  ) − 1 ×  (  | y  ) − 1 ⎢ ⎥  (  | y  ) − 1  ⎢ ⎥ ⎢ ⎥ exp − 1 ⎢ ⎥  (  |  ) − 1 ×  (  | y  ) − 1  ⎣ ⎦  (  | y  ) − 1   (  |  ) − 1 ×  (  | y  ) − 1  (  | y  ) − 1  • Inverse of exp so that  ∈ [0  1] • Inverse of signals so that  is increasing in signals

Recommend


More recommend