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Decision Making Under Uncertainty: Risk, Ambiguity, SSI and Conflict

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Decision Making Under Uncertainty: Risk, Ambiguity, SSI and Conflict Helen Pushkarskaya, Xun Liu, Michael Smithson, Jane Joseph University of Kentucky – PowerPoint PPT presentation

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Title: Decision Making Under Uncertainty: Risk, Ambiguity, SSI and Conflict


1
Decision Making Under Uncertainty Risk,
Ambiguity, SSI and Conflict
  • Helen Pushkarskaya,
  • Xun Liu,
  • Michael Smithson,
  • Jane Joseph
  • University of Kentucky
  • The Australian National University

2
Plan of the presentation
  • Background different types of uncertainty, SEU
    framework and prior experimental evidence
  • Research question
  • Methodology and experimental design
  • Testable hypotheses
  • Results
  • Discussion/ Conclusions

3
Background Uncertainty
  • Knight, 1921 Risk, Uncertainty and Profit
  • quantifiable uncertainty
  • unquantifiable uncertainty

4
Uncertainty Known outcomes
  • Risk (von Neumann Morgenstern, 1944)
  • probabilities known
  • Ambiguity, when there are questions of
    reliability and relevance of information, and
    particularly where there is conflicting opinions
    and evidence about probabilities (Ellsberg,
    1961, p. 659)
  • probabilities unknown/vague

5
Uncertainty Known outcomes
  • Conflict (Smithson,1999)
  • equally reliable sources provide conflicting
    information about probabilities associated with
    known outcomes

6
Uncertainty Unknown outcomes
  • Unawareness (Modica Rustichini, 1994)
  • decision makers are unaware that some unknown
    outcomes are possible
  • Sample Space Ignorance (SSI) (Smithson, 1996
    Smithson, Bartos, Takemura, 2000)
  • i.e., decision makers are aware that some
    unknown outcomes are possible

7
Subjective Expected Utility
  • SEU (Savage, 1954)
  • Risk choose a prospect with the highest expected
    value (von Neumann and Morgenstern, 1944).
  • Ambiguity ignorance prior average probabilities
    over the range of possible values, then treat as
    risk

8
Subjective Expected Utility
  • SEU (Savage, 1954)
  • Conflict ignorance prior--weight estimates of
    probability of the events from each source
    equally, then treat as risk
  • SSI form a subjective partition of the sample
    space, follow the ignorance prior idea and assign
    subjective probabilities to each event from the
    subjective partition, then treat as risk (An
    everything else outcome is included in the
    partition and is treated the same way as others.)

9
Subjective Expected Utility
  • SEU reduces all types of uncertainty (ambiguity,
    conflict, and SSI)
  • to risk environment.

10
Experimental evidence Risk
  • risk-aversion/seeking individuals vary in their
    risk attitudes (Dohmen et al., 2005)
  • risk-aversion/seeking individuals are more
    likely to demonstrate risk aversion in the domain
    of gains and risk seeking in the domain of losses
    (Tversky Kahneman, 1992).

11
Experimental evidence Ambiguity
  • ambiguity aversion exists, especially in the
    gain domain (Camerer Weber, 1992 Lauriola
    Levin, 2001).
  • ambiguity aversion in the loss domain usually
    decreases (e.g. Cohen et al., 1987 Viscusi
    Chesson, 1999), but still present.

12
Experimental evidence Conflict and SSI
  • conflict aversion conflicting unambiguous
    messages from two equally believable sources are
    less preferred then two informatively equivalent,
    ambiguous, but agreeing messages from the same
    sources (Smithson, 1999 Cabantous, 2006)
  • conflict aversion conflicting unambiguous
    sources are perceived as less credible than
    ambiguous but agreeing sources. (Smithson, 1999
    Cabantous, 2006)
  • ignorance aversion individuals prefer risk or
    ambiguity to SSI (Smithson, 1996 Smithson et
    al., 2000).

13
Research question
  • Do preferences toward different types of
    uncertainty (Ambiguity, Conflict, SSI) correlate?
  • Correlated? Possibly have similar psychological
    bases, i.e. recognition of computational
    limitations (Huettel et. al., 2006)
  • Or not correlated? Possibly have distinct
    psychological bases.

14
Methodology and experimental design
  • Simple gambles that model four uncertain
    environments Risk, Ambiguity, Sample Space
    Ignorance and Conflict.
  • Within-subjects analysis of three types of data
  • behavioral parameters -- (dis)preferences toward
    Ambiguity, Conflict and SSI
  • personality and attitude scales
  • response time

15
Method subjects and tasks
  • 42 subjects (21 female and 21 males) were given
    four series of gambles (8 min each) with every
    series constructed from all four types of gambles
    mixed in random order (32 gambles from each
    condition total).
  • Subjects had to choose between certainty payoff
    and a three-card gamble, one card of known type
    and known quantity, and two other cards forming
    risky, ambiguous, conflicting or ignorance
    gambles (see Figures a-d).
  • All four kinds of gambles were matched on the
    variance of the probabilities as well as on
    expected payoffs.
  • 38 (19 males and 19 females) subjects agreed to
    complete surveys with personality and attitudes
    scales.

16
a) Risk
b) Ambiguity
c) Conflict
d) Sample Space Ignorance
17
Method behavioral parameters
  • Follow Congdon (2003)
  • Sure payoff
  • Card 2 or 3 -
  • Card 1 -
  • Where for ambiguity k1, for conflict k2, for
    SSI k3, and for risk k4. Note that

18
Method behavioral parameters
  • g1 -- subjects' preferences for ambiguity
  • g2 -- subjects' preferences for conflict
  • g3 subjects preference for SSI
  • g1 (g2, g3)gt 1 implies pessimism because it
    deflates the probabilities, whereas g1 (g2, g3)lt
    1 implies optimism.

19
Method behavioral parameters
  • li- the sensitivity of choice probability to the
    utility difference, or the amount of randomness
    in the participants choices
  • l 0 means choices are random as l increases
    the choices are less random.

20
Method behavioral parameters
  • qi-- a curvature of the subjects utility
    functions.
  • q 1 - the monetary utility function is linear,
  • q lt 1 - the monetary utility function is
    concave (discounting larger values)
  • q gt 1- the monetary utility function is convex
  • (inflating larger values).
  • Pratt (1964) suggested that q describes
    individual risk-attitudes. Rabin (2000) argued
    that diminishing marginal utility of wealth (i.e.
    concavity) cannot explain risk aversion. We treat
    q as individual (in)sensitivity to monetary
    rewards.

21
Method behavioral parameters
22
Method behavioral parameters
  • For 36 out of 42 subjects ,confirms that
    utility functions are concave
  • Values of are considerably dispersed, but
    all of them greater than 0 choices are not
    random.
  • In both Ambiguity and Ignorance conditions
    probabilities are weighted optimistically (
    ), while under Conflict probabilities
    are weighted pessimistically ( ).

23
Method Personality/attitudes measures
  • Ten Item Personality Inventory (TIPI, Gosling,
    S.D., Rentfrow, P.J., Swann, W.B. Jr., 2003),
    Big-5 Openness, conscientiousness,
    extraversion, neuroticism and agreeableness.
  • Weber, Blais, and Betzs (2002) domain-specific
    risk inventory (DSRI), which elicits
    self-reported tendencies to take risks in six
    domains Recreation, social, ethical, health,
    gambling and investment.
  • Need for Certainty (NFCrt) and Need for Discovery
    (NFD), (Schuurmans-Stekhoven and Smithson, 2008),
    measuring a desire to bolster current beliefs and
    a desire for novel information, respectively.
  • Functional and dysfunctional impulsivity
    (Dickman, 1990). FI people tend to engage in
    rapid, error-prone processing, more accurate
    under time-pressure (Dickman,1990), FI is a
    significant predictor of increased responding to
    rewards (Smillie and Jackson, 2003).

24
Method Personality/attitudes measures
  • The reliabilities for the attitude scales ranged
    from .60 (dysfunctional impulsivity and total
    risk-taking) to .91 (need for certainty).
  • Reliabilities were not computed for the TIPI
    scales because they consist of only two items
    each.
  • Excluded The gambling risk-taking (insufficient
    variability in scores) extraversion and
    conscientiousness (not normally distributed in
    our sample).

25
Method Response time
  • Computed average response time (RT) for each
    subject for each condition
  • Compared RT across conditions
  • Correlated RT with behavioral parameters

26
Testable hypothesis
  • H0 (Dis)preferences toward different types of
    uncertainty have common psychological bases
  • H01. Behavioral parameters are correlated
  • H02. Behavioral parameters correlate with the
    same personality and attitude measures
  • H03. Behavioral parameters correlate with
    corresponding response time in the same manner.

27
H01 Correlation among behavioral measures
28
H01 Correlation among behavioral measures
  • g1 and g3 were highly correlated (.85), which
    suggested a common psychological base for
    ignorance and ambiguity aversion/seeking
  • g2 was not correlated with either g1 or g3, which
    suggested a distinct psychological base for
    conflict aversion

29
H02 Correlation between behavioral parameters
and personality/attitudes measures
  • We predicted ln(g1) ln(g3) as a composite
    variable because both parameters have skewed
    distributions and are strongly positively
    correlated. This composite variable is predicted
    (negatively) only by social risk-taking (a-.108,
    adjusted R2 .134, p .016).
  • Potentially this might suggest that social
    risk-taking scale relates not to a specific
    domain of risk, but to different types of
    uncertainty (environments with missing
    information)

30
H02 Correlation between behavioral parameters
and personality/attitudes measures
  • g2 has two predictors Openness and Need for
    Discovery (adjusted R2 .244, p .004).
  • Oddly, in the regression model Need for Discovery
    is a positive (a.071, p .012) predictor and
    Openness is a negative (a-.30, p .001)
    predictor, despite the fact that Openness and
    Need for Discovery are positively correlated (r
    .508).

31
H02 Correlation between behavioral parameters
and personality/attitudes measures
  • Overall, the behavioral parameters in the choice
    model are not strongly predicted by the
    personality and attitude scales. These findings
    underscore the potential importance of
    ascertaining the relationship between the
    behavioral parameters and the attitude/personality
    scales.

32
H03 Correlation between RT and behavioral
parameters
  • RT in different conditions were positively
    correlated, with exception of ambiguity

33
H03 Correlation between RT and behavioral
parameters
  • g1 (.41) and g3 (.437) positively correlated
    with RT under ambiguity.
  • g2 (-.332) negatively correlated with RT under
    conflict, and under sure gain (-.335).
  • g3 (-.10) did not correlated with RT under SSI.

34
Summary of results
  • Correlation across parameters
  • g1 and g3 are highly correlated (on average lt1)
  • g2 is not correlated with g1 or g3 (on average
    gt1)
  • Correlation with behavioral and attitude scales
  • ln(g1) ln(g3) was predicted by social
    risk-taking
  • g2 has two predictors Openness (negative) and
    Need for Discovery (positive)
  • Correlation with response time
  • g1 correlated positively with RT under ambiguity
  • g2 correlated negatively with RT under conflict
  • g3 was not correlated with RT under ignorance

35
Conclusions
  • (dis)preference toward conflict seems to be
    significantly different from (dis)preferences
    toward ambiguity and sample space ignorance
  • (dis)preferences toward ambiguity and sample
    space ignorance seem to have at least some common
    components since g1 and g3 are strongly
    correlated. However, results of the analysis of
    RTs suggest existence of distinct psychological
    contributors.

36
Conclusion
  • Recognition of computational limitations cannot
    be the common base for attitudes toward
    ambiguity, sample space ignorance and conflict.
  • While the literature is clear in understanding of
    importance of ambiguity in decision making, this
    study strongly suggests that sample space
    ignorance and conflict play distinctive roles
    that have yet to be well understood.

37
  • THANK YOU!
  • QUESTIONS?

38
Appendices
  • A1. Economic significance of correlations between
    behavioral parameters and psychological
    /attitudes measures
  • A2. Methodology/Study Design
  • A3. Correlations of q and l with each other,
    psychological/attitudes measures, RT

39
A1. Economic significance of correlations with
personality measures
40
A1. Economic significance of correlations with
personality measures
41
A2. Method statistical model
  • Where
  • - describes a bias toward or away from
    the jth alternative, not determined by money or
    probability
  • - sensitivity parameter (l0 random
    choices)
  • - the ith person monetary parameter
  • (lt1 convex, gt1 concave)
  • - the probability of the jth
    alternative payoff
  • - the ith person probability
    weighting parameter for the jth alternative (gt1
    pessimistic about the probabilities, lt1
    optimistic about the probabilities)

42
A2. Method Parameterization of subjective
monetary and probabilistic judgment of
alternatives
43
A2. Method statistical model
44
A2. Method Statistical model fit
  • Predicted probabilities (Chi square (80)272.13,
    plt.0001)
  • Observed probabilities

45
A2. Method Card distributions
46
A3. q and l. H01 Correlation among behavioral
measures
  • q and l estimates have a strong negative
    correlation of -.84, suggesting that those with
    low q values compensated by being more sensitive
    to other properties of the alternatives when
    comparing them.

47
A3. q and l. H02 Correlation with
personality/attitudes measures
  • Functional impulsivity alone predicts q and l,
    the monetary utility and sensitivity parameters
    (for both parameters, adjusted R2 091, p
    .041). This scale is correlated -.342 and .342
    with q and l respectively.
  • Functional impulsive people might be more
    sensitive to non-monetary differences between
    alternatives (use heuristics ?????)

48
A3. q and l. H03 Correlation with RT.
  • l (-.599) negatively and q (.568) positively
    correlated with RT under sure gain
  • Individuals more sensitive to non-monetary
    differences among alternative choose not to bet
    more quickly
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