cognition in context understanding biases in reasoning, learning, and decision making craig r. m....
TRANSCRIPT
Cognition in Cognition in ContextContextUnderstanding “Biases” in Understanding “Biases” in Reasoning, Learning, and Reasoning, Learning, and Decision MakingDecision Making
Craig R. M. McKenzieCraig R. M. McKenzie
Rady School of Management and Rady School of Management and
Department of PsychologyDepartment of Psychology
UC San DiegoUC San Diego
Brief background…Brief background…
Social scientists often compare how people Social scientists often compare how people behave with how they ought to behavebehave with how they ought to behave
When systematic differences (biases) occur, When systematic differences (biases) occur, heuristics often invoked as explanation heuristics often invoked as explanation
Much research has argued that some of Much research has argued that some of these conclusions misleadingthese conclusions misleading– Rational analyses can be incomplete or incorrectRational analyses can be incomplete or incorrect– People make assumptions about task structurePeople make assumptions about task structure
My theme: Taking into account real-world My theme: Taking into account real-world conditions, combined with normative conditions, combined with normative principles that make sense under these principles that make sense under these conditions, can help explain purported biasesconditions, can help explain purported biases
Types of framing Types of framing effects effects (Levin et al., 1998)(Levin et al., 1998)
Attribute framingAttribute framing– e.g., “25% fat” vs. “75% lean”; Levin & e.g., “25% fat” vs. “75% lean”; Levin &
Gaeth, 1988; Levin, 1987Gaeth, 1988; Levin, 1987
Risky choice framingRisky choice framing– e.g., Asian Disease problem; Tversky & e.g., Asian Disease problem; Tversky &
Kahneman, 1981Kahneman, 1981
Goal framingGoal framing– e.g., breast self-examination; Meyerowitz e.g., breast self-examination; Meyerowitz
& Chaiken, 1987& Chaiken, 1987
Traditional view of Traditional view of framing effectsframing effects
Framing effects violate Framing effects violate “description invariance”“description invariance”
Based largely on (risky choice) Based largely on (risky choice) framing effects, Tversky and framing effects, Tversky and Kahneman (1986) conclude that Kahneman (1986) conclude that “. . .[N]o theory of choice can be “. . .[N]o theory of choice can be both normatively adequate and both normatively adequate and descriptively accurate”descriptively accurate”
EquivalenceEquivalence
But what have people meant by But what have people meant by “equivalence”?“equivalence”?– Objective equivalenceObjective equivalence– Formal equivalenceFormal equivalence– Logical equivalenceLogical equivalence
Information equivalenceInformation equivalence is what is is what is requiredrequired– To make “irrational” claim, different To make “irrational” claim, different
frames must not communicate choice-frames must not communicate choice-relevant information relevant information (Sher & McKenzie, 2006)(Sher & McKenzie, 2006)
Information leakageInformation leakage(Sher & McKenzie, 2006; McKenzie & Nelson, 2003; (Sher & McKenzie, 2006; McKenzie & Nelson, 2003;
McKenzie, 2004; McKenzie, Liersch, & Finkelstein, 2006)McKenzie, 2004; McKenzie, Liersch, & Finkelstein, 2006)
Logical equivalence does not guarantee Logical equivalence does not guarantee information equivalenceinformation equivalence– E.g., passive and active sentence formsE.g., passive and active sentence forms
A speaker’s A speaker’s choice of framechoice of frame can be informative can be informative– E.g., “1/2 full” vs. “1/2 empty”E.g., “1/2 full” vs. “1/2 empty”
Assume exactly 2 frames, F1 and F2, and Assume exactly 2 frames, F1 and F2, and background condition B: background condition B:
p(“F1”|B) > p(“F1”|~B) p(“F1”|B) > p(“F1”|~B) ↔↔ p(B|“F1”) > p(B|“F1”) > p(B|“F2”)p(B|“F2”)
If knowledge of B relevant to choice, then If knowledge of B relevant to choice, then responding differently to F1 and F2 is rationalresponding differently to F1 and F2 is rational
Frames information equivalent only if no Frames information equivalent only if no choice-relevant inferences can be drawn from choice-relevant inferences can be drawn from speaker’s choice of frame. Else, “information speaker’s choice of frame. Else, “information leakage” is said to occur.leakage” is said to occur.
Why do attribute Why do attribute framing effects occur?framing effects occur?
Traditional explanation: Traditional explanation: Positive frame (e.g., “lean”) Positive frame (e.g., “lean”) evokes positive associations, evokes positive associations, negative frame (“fat”) negative frame (“fat”) evokes negative evokes negative associations, which influence associations, which influence judgmentsjudgments (Levin, 1987; Levin et al., 1998)(Levin, 1987; Levin et al., 1998)
Our explanation: Speakers Our explanation: Speakers more likely to use label (e.g., more likely to use label (e.g., “fat”) that has increased “fat”) that has increased relative to reference point, relative to reference point, thereby leaking information thereby leaking information about relative abundanceabout relative abundance
Information leakageInformation leakage(McKenzie & Sher, in preparation)(McKenzie & Sher, in preparation)
Imagine that all ground beef is about 40% fat, or 60% lean. Imagine that all ground beef is about 40% fat, or 60% lean. Recently, you heard that a new ground beef is going to be Recently, you heard that a new ground beef is going to be sold on the market that is 25% fat, or 75% lean. You sold on the market that is 25% fat, or 75% lean. You happen to be talking to a friend about the new beef. happen to be talking to a friend about the new beef. Given that most ground beef is 40% fat, or 60% lean, Given that most ground beef is 40% fat, or 60% lean, what is the most natural way to describe the new ground what is the most natural way to describe the new ground beef to your friend? Place a mark next to one description:beef to your friend? Place a mark next to one description:
_____ The new beef is 25% fat_____ The new beef is 25% fat_____ The new beef is 75% lean_____ The new beef is 75% lean
when other beef 40% fat/60% lean, when other beef 40% fat/60% lean, 53%53% describe describe new beef as “75% lean”new beef as “75% lean”
when other beef 10% fat/90% lean, when other beef 10% fat/90% lean, 23%23% describe describe new beef as “75% lean” new beef as “75% lean”
Speaker’s choice of frame leaks info about relative Speaker’s choice of frame leaks info about relative fat contentfat content
Information absorption Information absorption and source of frame and source of frame (McKenzie & Sher, in preparation)(McKenzie & Sher, in preparation)
ContextConversation Advertisement
% In
ferr
ing
Th
at B
eef
is
L
ean
er T
han
Mo
st
0
20
40
60
80
100
0
20
40
60
80
100
"75% Lean""25% Fat"
……using medical treatment outcomes (% using medical treatment outcomes (% die vs. % survive) die vs. % survive) (McKenzie & Nelson, 2003)(McKenzie & Nelson, 2003)
– illustrate normative issueillustrate normative issue ……looking at spontaneous, real behavior looking at spontaneous, real behavior
(Sher & McKenzie, 2006)(Sher & McKenzie, 2006)
……describing outcome of flips of coin and describing outcome of flips of coin and rolls of die rolls of die (Sher & McKenzie, 2006)(Sher & McKenzie, 2006)
– Findings not explained in terms of associative Findings not explained in terms of associative accountaccount
……examining default effects examining default effects (McKenzie, Liersch, (McKenzie, Liersch, and Finkelstein, 2006)and Finkelstein, 2006)
Similar results…
Framing effects Framing effects conclusionsconclusions Traditional normative view incorrectTraditional normative view incorrect
– Frames must be information equivalent, Frames must be information equivalent, not logically equivalent, for framing effects not logically equivalent, for framing effects to be irrationalto be irrational
Information leakage has psychological, Information leakage has psychological, as well as rational, implicationsas well as rational, implications
Unclear extent to which information Unclear extent to which information leakage can explain all framing effectsleakage can explain all framing effects
Cell ACell A Cell BCell B
Cell CCell C Cell DCell D
Present
Absent
Variable X
Present Absent
Variable Y
Covariation assessment
Robust finding: Cell A has largest Robust finding: Cell A has largest impact and Cell D smallest impact; impact and Cell D smallest impact; Cells B and C fall in betweenCells B and C fall in between
This bias seen as nonnormative This bias seen as nonnormative because 4 cells equally important in because 4 cells equally important in traditional normative modelstraditional normative models P = A/(A+B) – C/(C+D)P = A/(A+B) – C/(C+D) = (AD-BC)/[(A+B)(C+D)(A+C)= (AD-BC)/[(A+B)(C+D)(A+C)
(B+D)](B+D)]1/21/2
Cell A “bias”Cell A “bias”
Who cares?Who cares?
Covariation assessment underlies Covariation assessment underlies such fundamental behaviors as such fundamental behaviors as learning, categorization, and learning, categorization, and judging causationjudging causation
People's ability to accurately assess People's ability to accurately assess covariation allows them to explain covariation allows them to explain the past, control the present, and the past, control the present, and predict the future predict the future (Crocker, 1981)(Crocker, 1981)
Cell A “bias” makes normative Cell A “bias” makes normative (Bayesian) sense if presence of variables (Bayesian) sense if presence of variables tends to be rarer than their absencetends to be rarer than their absence (Anderson, 1990; McKenzie & Mikkelsen, 2000, 2007)(Anderson, 1990; McKenzie & Mikkelsen, 2000, 2007)
Bayesian perspective assumes subjects Bayesian perspective assumes subjects approach covariation task as one of approach covariation task as one of inferenceinference rather than statistical rather than statistical summarysummary (see also Griffiths & Tenenbaum, 2005)(see also Griffiths & Tenenbaum, 2005)
– Trying to discriminate between 2 hypotheses Trying to discriminate between 2 hypotheses about population – relationship (H1) vs. no about population – relationship (H1) vs. no relationship (H2)relationship (H2)
– Likelihood ratios, e.g., p(Cell A|H1)/p(Cell A|Likelihood ratios, e.g., p(Cell A|H1)/p(Cell A|H2)H2)
Bayesian accountBayesian account
Absolute log-likelihood ratio of cells as function of p(X) and p(Y).
|LLR| = Abs(log[p(j|H1)/p(j|H2)]), j = A, B, C, D; H1: rho=0.1; H2: rho=0
When presence of X and Y is rare, Cell A most informative and Cell D least informative (B & C fall in between)
0.0
0.2
0.4
0.6
0.8
1.0
0.00.2
0.40.6
0.81.0
0.00.20.40.60.8Cel
l A L
og L
ikel
ihoo
d R
atio
p(X)
p(Y)
0.00.51.01.52.02.53.03.5
0.00.2
0.40.6
0.81.0
0.00.20.40.60.8Cel
l B L
og L
ikel
ihoo
d R
atio
p(X)
p(Y)
0.00.51.01.52.02.53.03.5
0.00.2
0.40.6
0.81.0
0.00.20.40.60.8Cel
l C L
og L
ikel
ihoo
d R
atio
p(X)
p(Y)
0.0
0.2
0.4
0.6
0.8
1.0
0.00.2
0.40.6
0.81.0
0.00.20.40.60.8Cel
l D L
og L
ikel
ihoo
d R
atio
p(X)
p(Y)
……is it reasonable to assume that the is it reasonable to assume that the presence of variables is rare? presence of variables is rare?
Well, most people do not have a fever, Well, most people do not have a fever, most things are not red, most people most things are not red, most people are not accountants, and so onare not accountants, and so on– Of categories “X” and “not-X” (e.g., red Of categories “X” and “not-X” (e.g., red
things and non-red things), which would be things and non-red things), which would be larger?larger?
Cell A “bias” reversed when subjects Cell A “bias” reversed when subjects know that know that absenceabsence of variables rare of variables rare (McKenzie & Mikkelsen, 2007)(McKenzie & Mikkelsen, 2007)
Yeah, but…Yeah, but…
Rarity affects cell impact as predicted by Bayesian Rarity affects cell impact as predicted by Bayesian accountaccount– Cell A vs. D Cell A vs. D andand Cell B vs. C Cell B vs. C
Second robust phenomenon: Subjects’ prior beliefs Second robust phenomenon: Subjects’ prior beliefs about relationship between variables influence about relationship between variables influence judgments – which is hallmark of Bayesian approachjudgments – which is hallmark of Bayesian approach
Normative principles, combined with consideration Normative principles, combined with consideration of environment, provide parsimonious account of of environment, provide parsimonious account of the two most robust phenomena in covariation the two most robust phenomena in covariation literatureliterature
Different from framing effects, though: Not case Different from framing effects, though: Not case that traditional normative model wrong, but a that traditional normative model wrong, but a different normative modeldifferent normative model applies applies
Covariation Covariation assessment assessment conclusionsconclusions
Bayesian account of Bayesian account of some classic learning some classic learning phenomenaphenomena
Previous evidence for Bayesian Previous evidence for Bayesian approach comes from summary approach comes from summary descriptions of data and presentation descriptions of data and presentation of single cellsof single cells
What about trial-by-trial updating – What about trial-by-trial updating – traditionally the domain of Rescorla-traditionally the domain of Rescorla-Wagner model?Wagner model?
Will limit ourselves to the 2-variable Will limit ourselves to the 2-variable case: 1 predictor and 1 outcomecase: 1 predictor and 1 outcome
Goal is to show, via computer Goal is to show, via computer simulation, that Bayes can account for simulation, that Bayes can account for previous updating findingsprevious updating findings
The Bayesian ModelThe Bayesian Model(adapted from J. R. Anderson, 1990)(adapted from J. R. Anderson, 1990)
Parameters:Parameters: H1, H2 H1, H2
– H1: rho = 0.5, H2: rho = 0H1: rho = 0.5, H2: rho = 0 p(H1) = 1-p(H2)p(H1) = 1-p(H2) alphaX, betaX alphaX, betaX
– alphaX/(alphaX+betaX) = alphaX/(alphaX+betaX) = p(X)p(X)
– rarity rarity alphaX < betaX alphaX < betaX alphaY, betaY alphaY, betaY
– alphaY/(alphaY+betaY) = alphaY/(alphaY+betaY) = p(Y)p(Y)
– rarity rarity alphaY < betaY alphaY < betaY
AA BB
CC DD
Pr
Ab
Pr AbY
X
alphaX
betaX
alphaY
betaY
Trial-by-Trial UpdatingTrial-by-Trial Updating
p(H1|E) = p(H1)p(E|H1)/[p(H1)p(E|H1)+p(H2)p(E|H2)]p(H1|E) = p(H1)p(E|H1)/[p(H1)p(E|H1)+p(H2)p(E|H2)] alpha and/or beta updated by 1alpha and/or beta updated by 1
FOR EXAMPLE, if Cell A is observed:FOR EXAMPLE, if Cell A is observed: p(H1|A) = p(H1)p(A|H1)/[p(H1)p(A|H1)+p(H2)p(A|H2)]p(H1|A) = p(H1)p(A|H1)/[p(H1)p(A|H1)+p(H2)p(A|H2)] p(A|H2) = p(X)p(Y)p(A|H2) = p(X)p(Y) p(A|H1) = p(A|H2)+rho[sqrt(p(X)*1-p(X)*p(Y)*1-p(Y)]p(A|H1) = p(A|H2)+rho[sqrt(p(X)*1-p(X)*p(Y)*1-p(Y)] alphaX alphaX alphaX + 1 alphaX + 1 alphaY alphaY alphaY + 1 alphaY + 1 p(H1|A) p(H1|A) p(H1) p(H1)
Density BiasDensity Bias
Initial rise in conditioning or Initial rise in conditioning or judgments of contingency when judgments of contingency when presented with uncorrelated data presented with uncorrelated data (phi = 0), especially when (phi = 0), especially when outcome is commonoutcome is common
Density BiasDensity Bias
H1: rho = 0.5, H2: rho = 0P(H1) = P(H2) = 0.5P(X) = 0.5alphaX = alphaY = 1beta X = betaY = 19Observed data: Phi = 0
Trial
0 10 20 30 40 50 60 70 80 90 100
P(H
1|E
)
0.0
0.2
0.4
0.6
0.8
1.0
P(Y) = 0.3P(Y) = 0.5P(Y) = 0.7
Density Bias and Density Bias and RarityRarity
H1: rho = 0.5, H2: rho = 0P(H1) = P(H2) = 0.5P(X) = 0.5, P(Y) = 0.7Observed data: phi = 0
Trial
0 10 20 30 40 50 60 70 80 90 100
P(H
1|E
)
0.0
0.2
0.4
0.6
0.8
1.0
Alpha = 1, Beta = 19Alpha = Beta = 10
Rescorla-Wagner Rescorla-Wagner ModelModel ΔVΔVXX = αβ(λ- = αβ(λ-ΣΣV)V) “…“…perhaps for an increment in perhaps for an increment in
associative connections to occur, it is associative connections to occur, it is necessary that the US instigate some necessary that the US instigate some mental work on the part of the mental work on the part of the animal. This mental work will occur animal. This mental work will occur only if the US is unpredictable – if it only if the US is unpredictable – if it in some sense ‘surprises’ the in some sense ‘surprises’ the animal” animal” (Kamin, 1969)(Kamin, 1969)
R-W and Density BiasR-W and Density Bias
P(X) = 0.5alphaX = 0.9betaX = alphaY = betaY = 0.2Observed data: phi = 0
Trial
0 20 40 60 80 100 120 140 160 180 200
VX
0.0
0.2
0.4
0.6
0.8
1.0
P(Y) = 0.3P(Y) = 0.5P(Y) = 0.7
Density Bias, R-W, and Density Bias, R-W, and alpha/betaalpha/beta
P(X) = 0.5, P(Y) = 0.7betaY = 0.2Observed data: phi = 0
Trial
0 20 40 60 80 100 120 140 160 180 200
VX
0.0
0.2
0.4
0.6
0.8
1.0
alphaX = 0.9alphaX = 0.2alpha~X = 0.9alpha~X, beta~Y = 0.9
Partial Reinforcement Partial Reinforcement EffectEffect Initial learning of weak correlation Initial learning of weak correlation
takes longer to extinguish than takes longer to extinguish than initial learning of strong initial learning of strong correlationcorrelation
Partial Reinforcement Partial Reinforcement EffectEffect
H2: rho = 0P(H1) = 0.9P(X) = P(Y) = 0.5Alpha = Beta = 10Observed data: phi = 0
Trial
0 20 40 60 80 100
P(H
1|E
)
0.0
0.2
0.4
0.6
0.8
1.0
H1: rho = 0.4H1: rho = 0.7H1: rho = 1.0
Also…Also…
Learned irrelevance/helplessnessLearned irrelevance/helplessness– Initial learning of independence between Initial learning of independence between
variables retards subsequent learning of variables retards subsequent learning of real relationshipreal relationship
Latent inhibitionLatent inhibition– Initial presentations of X (CS) alone retard Initial presentations of X (CS) alone retard
subsequent learning of CS-UCS relationshipsubsequent learning of CS-UCS relationship UCS pre-exposure effectUCS pre-exposure effect
– Initial presentations of Y (UCS) alone retard Initial presentations of Y (UCS) alone retard subsequent learning of CS-UCS relationshipsubsequent learning of CS-UCS relationship
Some advantages of Some advantages of Bayes in this contextBayes in this context
Can explain both trial-by-trial updating Can explain both trial-by-trial updating and responses to summaries of dataand responses to summaries of data
ParsimonyParsimony– Local: Bayes reduces to countingLocal: Bayes reduces to counting– Global: Bayes used to explain behavior Global: Bayes used to explain behavior
ranging from vision to reasoningranging from vision to reasoning Speculation: R-W mimics Bayesian Speculation: R-W mimics Bayesian
responseresponse– Marr’s levels of analysis?Marr’s levels of analysis?
What did he say?What did he say?
Some important “biases” can be seen as rational Some important “biases” can be seen as rational – which provides more satisfying account– which provides more satisfying account
Important interplay between normative models Important interplay between normative models and behaviorand behavior
Normative principles – Normative principles – combined with combined with considerations of the structure of the considerations of the structure of the environmentenvironment – can help explain why people – can help explain why people behave as they dobehave as they do
Many “biases” indicate behavior that is not only Many “biases” indicate behavior that is not only more rational, but also psychologically richer, more rational, but also psychologically richer, than previously thoughtthan previously thought
Thank you!Thank you!Context
Conversation Advertisement
% I
nfe
rrin
g T
ha
t B
ee
f is
L
ea
ne
r T
ha
n M
os
t
0
20
40
60
80
100
0
20
40
60
80
100
"75% Lean""25% Fat"
0.0
0.2
0.4
0.6
0.8
1.0
0.00.2
0.40.6
0.81.0
0.00.20.40.60.8Cel
l A L
og L
ikel
ihoo
d R
atio
p(X)
p(Y)
0.00.51.01.52.02.53.03.5
0.00.2
0.40.6
0.81.0
0.00.20.40.60.8Cel
l B L
og L
ikel
ihoo
d R
atio
p(X)
p(Y)
0.00.51.01.52.02.53.03.5
0.00.2
0.40.6
0.81.0
0.00.20.40.60.8Cel
l C L
og L
ikel
ihoo
d R
atio
p(X)
p(Y)
0.0
0.2
0.4
0.6
0.8
1.0
0.00.2
0.40.6
0.81.0
0.00.20.40.60.8Cel
l D L
og L
ikel
ihoo
d R
atio
p(X)
p(Y)
H1: rho = 0.5, H2: rho = 0P(H1) = P(H2) = 0.5P(X) = 0.5, P(Y) = 0.7Observed data: phi = 0
Trial
0 10 20 30 40 50 60 70 80 90 100
P(H
1|E
)
0.0
0.2
0.4
0.6
0.8
1.0
Alpha = 1, Beta = 19Alpha = Beta = 10
H2: rho = 0P(H1) = 0.9P(X) = P(Y) = 0.5Alpha = Beta = 10Observed data: phi = 0
Trial
0 20 40 60 80 100
P(H
1|E
)
0.0
0.2
0.4
0.6
0.8
1.0
H1: rho = 0.4H1: rho = 0.7H1: rho = 1.0
H1: rho = 0.5, H2: rho = 0P(H1) = P(H2) = 0.5P(X) = 0.5alphaX = alphaY = 1beta X = betaY = 19Observed data: Phi = 0
Trial
0 10 20 30 40 50 60 70 80 90 100
P(H
1|E
)
0.0
0.2
0.4
0.6
0.8
1.0
P(Y) = 0.3P(Y) = 0.5P(Y) = 0.7
P(X) = 0.5, P(Y) = 0.7betaY = 0.2Observed data: phi = 0
Trial
0 20 40 60 80 100 120 140 160 180 200
VX
0.0
0.2
0.4
0.6
0.8
1.0
alphaX = 0.9alphaX = 0.2alpha~X = 0.9alpha~X, beta~Y = 0.9
Risky Choice: Asian Risky Choice: Asian Disease ProblemDisease Problem(Tversky & Kahneman, 1981)(Tversky & Kahneman, 1981)
Imagine that U.S. is preparing for outbreak of an Imagine that U.S. is preparing for outbreak of an unusual Asian disease, which is expected to kill 600 unusual Asian disease, which is expected to kill 600 people. Two alternative programs to combat the people. Two alternative programs to combat the disease have been proposed. Assume that the exact disease have been proposed. Assume that the exact scientific estimate of the consequences of the scientific estimate of the consequences of the programs are as follows:programs are as follows:
If Program A adopted, 200 people will be saved.If Program A adopted, 200 people will be saved. If Program B adopted, 1/3 probability that 600 people If Program B adopted, 1/3 probability that 600 people
will be saved, and 2/3 probability that no people will be will be saved, and 2/3 probability that no people will be saved.saved.
If Program C adopted, 400 people will die.If Program C adopted, 400 people will die. If Program D adopted, 1/3 probability that nobody will If Program D adopted, 1/3 probability that nobody will
die, and 2/3 probability that 600 people will die.die, and 2/3 probability that 600 people will die.
Risky Choice Frame Risky Choice Frame SelectionSelectionSubjects first chose preferred program from completely described Subjects first chose preferred program from completely described
programs.programs.
Imagine that your job is to describe the situation, and the 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 have been proposed, to a committee who will then decide which program, A or B, to use. Please complete the sentences which program, A or B, to use. Please complete the sentences below as if you were describing the programs to the committee.below as if you were describing the programs to the committee.
be savedbe savedIf Program A is adopted, ________ people willIf Program A is adopted, ________ people will . .
(write #) (write #) diedie (circle one)(circle one)
If Program B is adopted, If Program B is adopted, be savedbe saved
there is ________ probability that ________ people will ,there is ________ probability that ________ people will , (write #)(write #) (write #) (write #) die die
(circle one)(circle one) be savedbe saved
and ________ probability that _______ people willand ________ probability that _______ people will . . (write #)(write #) (write #) (write #) die die
(circle one)(circle one)
Implicit Implicit Recommendation Recommendation Results Results (unpublished data)(unpublished data)
If prefer sure thing (Program A):If prefer sure thing (Program A):– 81% (83/103) word sure thing in terms of 81% (83/103) word sure thing in terms of
“saved”“saved” If prefer gamble (Program B):If prefer gamble (Program B):
– 48% (45/93) word sure thing in terms of “saved”48% (45/93) word sure thing in terms of “saved” Word gamble same regardless of preference Word gamble same regardless of preference
(“1/3 prob that 600 saved and 2/3 prob that (“1/3 prob that 600 saved and 2/3 prob that 600 die”)600 die”)
Speakers’ preferences affect phrasing of Speakers’ preferences affect phrasing of risky choice option(s) -- which listeners risky choice option(s) -- which listeners might use to infer speaker’s preferencemight use to infer speaker’s preference
Strength of Preference Strength of Preference and Choice of Frame and Choice of Frame (unpublished data)(unpublished data)
Strength of Preference
Weak Moderate Very Strong% W
ord
ing
Su
re T
hin
g in
Ter
ms
of
"Sav
ed"
40
50
60
70
80
90
100Prefer Sure Thing (Prog. A)Prefer Gamble (Prog. B)
Cell A “bias” Cell A “bias” Cell D Cell D “bias”“bias”
Condition 3 (Concrete)Condition 3 (Concrete) Sample 1 Sample 2 (Cell) Sample 1 Sample 2 (Cell)Emotionally disturbed: Yes / Drop out: Yes 6 1 (A)Emotionally disturbed: Yes / Drop out: Yes 6 1 (A)Emotionally disturbed: Yes / Drop out: No 1 1 (B)Emotionally disturbed: Yes / Drop out: No 1 1 (B)Emotionally disturbed: No / Drop out: Yes 1 1 (C)Emotionally disturbed: No / Drop out: Yes 1 1 (C)Emotionally disturbed: No / Drop out: No 1 6 (D)Emotionally disturbed: No / Drop out: No 1 6 (D)
““Which sample stronger evidence of relation?” 73% 27%Which sample stronger evidence of relation?” 73% 27%------------------------------------------------------------------------------------------------------------------------------------------------------------------Condition 4 (Concrete)Condition 4 (Concrete) Sample 1 Sample 2 (Cell) Sample 1 Sample 2 (Cell)Emotionally healthy: No / Graduate: No 6 1 (D)Emotionally healthy: No / Graduate: No 6 1 (D)Emotionally healthy: No / Graduate: Yes 1 1 (C)Emotionally healthy: No / Graduate: Yes 1 1 (C)Emotionally healthy: Yes / Graduate: No 1 1 (B)Emotionally healthy: Yes / Graduate: No 1 1 (B)Emotionally healthy: Yes / Graduate: Yes 1 6 (A)Emotionally healthy: Yes / Graduate: Yes 1 6 (A)
““Which sample stronger evidence of relation?” 67% 33%Which sample stronger evidence of relation?” 67% 33%