Cognition in Context Understanding Biases in Reasoning, Learning, and Decision Making

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Cognition in ContextUnderstanding Biases in
Reasoning, Learning, and Decision Making

• Craig R. M. McKenzie
• Rady School of Management and
• Department of Psychology
• UC San Diego

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Brief background

• Social scientists often compare how people behave
  with how they ought to behave
• When systematic differences (biases) occur,
  heuristics often invoked as explanation
• Much research has argued that some of these
  conclusions misleading
• Rational analyses can be incomplete or incorrect
• People make assumptions about task structure
• My theme Taking into account real-world
  conditions, combined with normative principles
  that make sense under these conditions, can help
  explain purported biases

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Types of framing effects (Levin et al., 1998)

• Attribute framing
• e.g., 25 fat vs. 75 lean Levin Gaeth,
  1988 Levin, 1987
• Risky choice framing
• e.g., Asian Disease problem Tversky Kahneman,
  1981
• Goal framing
• e.g., breast self-examination Meyerowitz
  Chaiken, 1987

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Traditional view of framing effects

• Framing effects violate description invariance
• Based largely on (risky choice) framing effects,
  Tversky and Kahneman (1986) conclude that . .
  .No theory of choice can be both normatively
  adequate and descriptively accurate

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Equivalence

• But what have people meant by equivalence?
• Objective equivalence
• Formal equivalence
• Logical equivalence
• Information equivalence is what is required
• To make irrational claim, different frames must
  not communicate choice-relevant information (Sher
  McKenzie, 2006)

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Information leakage(Sher McKenzie, 2006
McKenzie Nelson, 2003 McKenzie, 2004
McKenzie, Liersch, Finkelstein, 2006)

• Logical equivalence does not guarantee
  information equivalence
• E.g., passive and active sentence forms
• A speakers choice of frame can be informative
• E.g., 1/2 full vs. 1/2 empty
• Assume exactly 2 frames, F1 and F2, and
  background condition B
• p(F1B) gt p(F1B) ? p(BF1) gt
  p(BF2)
• If knowledge of B relevant to choice, then
  responding differently to F1 and F2 is rational
• Frames information equivalent only if no
  choice-relevant inferences can be drawn from
  speakers choice of frame. Else, information
  leakage is said to occur.

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Why do attribute framing effects occur?

• Traditional explanation Positive frame (e.g.,
  lean) evokes positive associations, negative
  frame (fat) evokes negative associations, which
  influence judgments (Levin, 1987 Levin et al.,
  1998)
• Our explanation Speakers more likely to use
  label (e.g., fat) that has increased relative
  to reference point, thereby leaking information
  about relative abundance

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Information leakage(McKenzie Sher, in
preparation)

• Imagine that all ground beef is about 40 fat, or
  60 lean. Recently, you heard that a new ground
  beef is going to be sold on the market that is
  25 fat, or 75 lean. You happen to be talking
  to a friend about the new beef. Given that most
  ground beef is 40 fat, or 60 lean, what is the
  most natural way to describe the new ground beef
  to your friend? Place a mark next to one
  description
• _____ The new beef is 25 fat
• _____ The new beef is 75 lean
• when other beef 40 fat/60 lean, 53 describe
  new beef as 75 lean
• when other beef 10 fat/90 lean, 23 describe
  new beef as 75 lean
• Speakers choice of frame leaks info about
  relative fat content

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Information absorption and source of frame
(McKenzie Sher, in preparation)
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Similar results

• using medical treatment outcomes ( die vs.
  survive) (McKenzie Nelson, 2003)
• illustrate normative issue
• looking at spontaneous, real behavior (Sher
  McKenzie, 2006)
• describing outcome of flips of coin and rolls of
  die (Sher McKenzie, 2006)
• Findings not explained in terms of associative
  account
• examining default effects (McKenzie, Liersch,
  and Finkelstein, 2006)

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Framing effects conclusions

• Traditional normative view incorrect
• Frames must be information equivalent, not
  logically equivalent, for framing effects to be
  irrational
• Information leakage has psychological, as well as
  rational, implications
• Unclear extent to which information leakage can
  explain all framing effects

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Covariation assessment
Variable Y
Present
Absent
Present
Variable X
Absent
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Cell A bias

• Robust finding Cell A has largest impact and
  Cell D smallest impact Cells B and C fall in
  between
• This bias seen as nonnormative because 4 cells
  equally important in traditional normative models
• ?P A/(AB) C/(CD)
• ? (AD-BC)/(AB)(CD)(AC)(BD)1/2

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Who cares?

• Covariation assessment underlies such fundamental
  behaviors as learning, categorization, and
  judging causation
• People's ability to accurately assess covariation
  allows them to explain the past, control the
  present, and predict the future (Crocker, 1981)

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Bayesian account

• Cell A bias makes normative (Bayesian) sense if
  presence of variables tends to be rarer than
  their absence (Anderson, 1990 McKenzie
  Mikkelsen, 2000, 2007)
• Bayesian perspective assumes subjects approach
  covariation task as one of inference rather than
  statistical summary (see also Griffiths
  Tenenbaum, 2005)
• Trying to discriminate between 2 hypotheses about
  population relationship (H1) vs. no
  relationship (H2)
• Likelihood ratios, e.g., p(Cell AH1)/p(Cell AH2)

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Absolute log-likelihood ratio of cells as
function of p(X) and p(Y). LLR
Abs(logp(jH1)/p(jH2)), j A, B, C, D H1
rho0.1 H2 rho0
When presence of X and Y is rare, Cell A most
informative and Cell D least informative (B C
fall in between)
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Yeah, but

• is it reasonable to assume that the presence of
  variables is rare?
• Well, most people do not have a fever, most
  things are not red, most people are not
  accountants, and so on
• Of categories X and not-X (e.g., red things
  and non-red things), which would be larger?
• Cell A bias reversed when subjects know that
  absence of variables rare (McKenzie Mikkelsen,
  2007)

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Covariation assessment conclusions

• Rarity affects cell impact as predicted by
  Bayesian account
• Cell A vs. D and Cell B vs. C
• Second robust phenomenon Subjects prior beliefs
  about relationship between variables influence
  judgments which is hallmark of Bayesian
  approach
• Normative principles, combined with consideration
  of environment, provide parsimonious account of
  the two most robust phenomena in covariation
  literature
• Different from framing effects, though Not case
  that traditional normative model wrong, but a
  different normative model applies

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Bayesian account of some classic learning
phenomena

• Previous evidence for Bayesian approach comes
  from summary descriptions of data and
  presentation of single cells
• What about trial-by-trial updating
  traditionally the domain of Rescorla-Wagner
  model?
• Will limit ourselves to the 2-variable case 1
  predictor and 1 outcome
• Goal is to show, via computer simulation, that
  Bayes can account for previous updating findings

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The Bayesian Model(adapted from J. R. Anderson,
1990)

• Parameters
• H1, H2
• H1 rho 0.5, H2 rho 0
• p(H1) 1-p(H2)
• alphaX, betaX
• alphaX/(alphaXbetaX) p(X)
• rarity ? alphaX lt betaX
• alphaY, betaY
• alphaY/(alphaYbetaY) p(Y)
• rarity ? alphaY lt betaY

Y
Ab
Pr
Pr
alphaX
X
betaX
Ab
alphaY
betaY
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Trial-by-Trial Updating

• p(H1E) p(H1)p(EH1)/p(H1)p(EH1)p(H2)p(EH2)
  
• alpha and/or beta updated by 1
• FOR EXAMPLE, if Cell A is observed
• p(H1A) p(H1)p(AH1)/p(H1)p(AH1)p(H2)p(AH2)
  
• p(AH2) p(X)p(Y)
• p(AH1) p(AH2)rhosqrt(p(X)1-p(X)p(Y)1-p(Y)
  
• alphaX ? alphaX 1
• alphaY ? alphaY 1
• p(H1A) ? p(H1)

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Density Bias

• Initial rise in conditioning or judgments of
  contingency when presented with uncorrelated data
  (phi 0), especially when outcome is common

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Density Bias
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Density Bias and Rarity
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Rescorla-Wagner Model

• ?VX aß(?-SV)
• perhaps for an increment in associative
  connections to occur, it is necessary that the US
  instigate some mental work on the part of the
  animal. This mental work will occur only if the
  US is unpredictable if it in some sense
  surprises the animal (Kamin, 1969)

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R-W and Density Bias
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Density Bias, R-W, and alpha/beta
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Partial Reinforcement Effect

• Initial learning of weak correlation takes longer
  to extinguish than initial learning of strong
  correlation

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Partial Reinforcement Effect
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Also

• Learned irrelevance/helplessness
• Initial learning of independence between
  variables retards subsequent learning of real
  relationship
• Latent inhibition
• Initial presentations of X (CS) alone retard
  subsequent learning of CS-UCS relationship
• UCS pre-exposure effect
• Initial presentations of Y (UCS) alone retard
  subsequent learning of CS-UCS relationship

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Some advantages of Bayes in this context

• Can explain both trial-by-trial updating and
  responses to summaries of data
• Parsimony
• Local Bayes reduces to counting
• Global Bayes used to explain behavior ranging
  from vision to reasoning
• Speculation R-W mimics Bayesian response
• Marrs levels of analysis?

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What did he say?

• Some important biases can be seen as rational
  which provides more satisfying account
• Important interplay between normative models and
  behavior
• Normative principles combined with
  considerations of the structure of the
  environment can help explain why people behave
  as they do
• Many biases indicate behavior that is not only
  more rational, but also psychologically richer,
  than previously thought

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Thank you!
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Risky Choice Asian Disease Problem(Tversky
Kahneman, 1981)

• Imagine that U.S. is preparing for outbreak of an
  unusual Asian disease, which is expected to kill
  600 people. Two alternative programs to combat
  the disease have been proposed. Assume that the
  exact scientific estimate of the consequences of
  the programs are as follows
• If Program A adopted, 200 people will be saved.
• If Program B adopted, 1/3 probability that 600
  people will be saved, and 2/3 probability that no
  people will be saved.
• If Program C adopted, 400 people will die.
• If Program D adopted, 1/3 probability that nobody
  will die, and 2/3 probability that 600 people
  will die.

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Risky Choice Frame Selection

• Subjects first chose preferred program from
  completely described programs.
• Imagine that your job is to describe the
  situation, and the programs which have been
  proposed, to a committee who will then decide
  which program, A or B, to use. Please complete
  the sentences below as if you were describing the
  programs to the committee.
• be saved
• If Program A is adopted, ________ people will
  .
• (write ) die
• (circle one)
• If Program B is adopted,
• be saved
• there is ________ probability that ________
  people will ,
• (write ) (write
  ) die
• (circle one)
• be
  saved
• and ________ probability that _______ people
  will .
• (write ) (write )
  die
• 
  (circle one)

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Implicit Recommendation Results (unpublished data)

• If prefer sure thing (Program A)
• 81 (83/103) word sure thing in terms of saved
• If prefer gamble (Program B)
• 48 (45/93) word sure thing in terms of saved
• Word gamble same regardless of preference (1/3
  prob that 600 saved and 2/3 prob that 600 die)
• Speakers preferences affect phrasing of risky
  choice option(s) -- which listeners might use to
  infer speakers preference

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Strength of Preference and Choice of Frame
(unpublished data)
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Cell A bias ? Cell D bias

• Condition 3 (Concrete) Sample 1
  Sample 2 (Cell)
• Emotionally disturbed Yes / Drop out Yes
  6 1 (A)
• Emotionally disturbed Yes / Drop out No
  1 1 (B)
• Emotionally disturbed No / Drop out Yes
  1 1 (C)
• Emotionally disturbed No / Drop out No
  1 6 (D)
• Which sample stronger evidence of relation?
  73 27
• --------------------------------------------------
  -------------------------------
• Condition 4 (Concrete) Sample 1
  Sample 2 (Cell)
• Emotionally healthy No / Graduate No
  6 1 (D)
• Emotionally healthy No / Graduate Yes
  1 1 (C)
• Emotionally healthy Yes / Graduate No
  1 1 (B)
• Emotionally healthy Yes / Graduate Yes
  1 6 (A)
• Which sample stronger evidence of relation?
  67 33