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
• 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

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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

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Uncertainty Known outcomes

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

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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

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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

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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.)
  

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Subjective Expected Utility

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

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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).

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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.

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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).

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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.

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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

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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.

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a) Risk
b) Ambiguity
c) Conflict
d) Sample Space Ignorance
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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

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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.

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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.

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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.

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Method behavioral parameters
Parameter Mean Sd
3.375 .239
.515 .271
-.083 .267
5.65 .218
.377 .019
.964 .06
1.673 .1
.882 .053
.709 .106
.082 .07
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Method behavioral parameters

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

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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).

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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).

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Method Response time

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

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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.

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H01 Correlation among behavioral measures
l
-0.841 q
0.090 -0.073 g1
0.412 -0.266 0.162 g2
-0.095 0.026 0.850 0.070 g3
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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

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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)

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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).

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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.

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H03 Correlation between RT and behavioral
parameters

• RT in different conditions were positively
  correlated, with exception of ambiguity

RT Risk
0.136 RT Ambiguity
.804 0.162 RT SSI
.919 0.084 .827 RT Conflict
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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.

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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

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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.

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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.

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• THANK YOU!
• QUESTIONS?

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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

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A1. Economic significance of correlations with
personality measures
mean g1 p.5 perceived as mean g3 p.5 perceived as
Low Social Risk- Taking (scorelt28.5) 1.1475 0.451 1.0464 0.484
High Social Risk- Taking (scoregt28.5) 0.8978 0.537 0.7950 0.576
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A1. Economic significance of correlations with
personality measures
mean g2 p.5 perceived as
Need for Discovery low (lt40) 1.7643 0.294
Need for Discovery high (gt40) 1.7604 0.295
Openness low (lt7.5) 1.9576 0.257
Openness high (gt7.5) 1.5473 0.342
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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)

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A2. Method Parameterization of subjective
monetary and probabilistic judgment of
alternatives
Alternative Risk Ambiguity Conflict SSI
Sure payoff
Card 1
Card 2 or 3
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A2. Method statistical model
Card 1 Card 2 or 3 Sure Payoff
SEU model .49 .49 .02
Actual .53 .24 .23
Male .57 .23 .20
Female .50 .24 .26
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A2. Method Statistical model fit

• Predicted probabilities (Chi square (80)272.13,
  plt.0001)

• Observed probabilities

Card 1 Card 2 or 3 Sure Payoff
A .51 .29 .21
C .56 .17 .27
I .51 .30 .19
R .56 .19 .24
Card 1 Card 2 or 3 Sure Payoff
A .53 .28 .19
C .57 .19 .25
I .53 .29 .18
R .56 .23 .21
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A2. Method Card distributions
Card 1 Card 2 Card 3 Card 2 Card 3 Total cards
Risk Risk Risk Risk Risk
6 47 47 94 100
94 3 3 6 100
Ambiguity Ambiguity Ambiguity Ambiguity Ambiguity
6 N/A N/A 94 100
94 N/A N/A 6 100
Ignorance Ignorance Ignorance Ignorance Ignorance
6 N/A N/A 94 100
94 N/A N/A 6 100
Conflict Conflict Conflict Conflict Conflict
6 58 (36) 36 (58) 94 100
94 4 (2) 2 (4) 6 100
Averages Averages Averages Averages Averages
50.25 24.87, 30.58 (19.16) 24.87, 19.16 (30.58) 49.75 100
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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.

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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 ?????)

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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