Stakeholder Preference Modeling with Probabilistic Inversion
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Transcript of Stakeholder Preference Modeling with Probabilistic Inversion
Stakeholder Preference Modeling with
Probabilistic Inversion
Roger M. CookeResources for the Future
Dept Math, TU DelftJune 16, 2011
• Foundations• Health states• Risks nano-enabled food
Expert Judgment for Uncertainty Quantification: PM2.5
Uncertainty in Mortality Response to Airborne Fine Particulate Matter: Combining European Air Pollution Experts Jouni T. Tuomisto, Andrew Wilson, John S. Evans, Marko Tainio (RESS 2008)
Fundamental Theorem of Decision TheoryFor Rational PreferenceUNIQUE probability P which represents degree of belief:
DegBel(France wins worldcup) > DegBel(Belgium wins worldcup) P(F) > P(B)
AND a Utility function, unique up to 0 and 1, that represents values:
($1000 if F, $0 else) > ($1000 if B, $0 else) Exp’d Utility (($1000 if F, $0 else)) > Exp’d Utility (($9000 if B, $0 else))
BUT….
UNLIKE Expert Judgment: There is no
• Updating utilities on observations
• Convergence of utilities via Observations
• Empirical control on Utilities
• Community of ‘Utility Experts’
• Rational consensus on Utilities
Why is Preference Modeling Impoverished?
AHPMAUTMCDMELECTRAREMBRANTOUTRANKINGTHURSTONE
BRADLEY TERRYPROBITLOGITNESTED LOGITPSYCH’L SCALING
Validation???
What means Validation?
Goal = find ‘true Utility values’ for alternatives?Fools’s Errand
Condorcet’s Paradox of Majority Preference
1/3 prefer Mozart > Hayden > Bach 1/3 prefer Hayden > Bach > Mozart1/3 prefer Bach > Mozart > Hayden
THEN 2/3’s prefer
Bach > MozartMozart > HaydenHayden > Bach
What can we do?
Random Utility Theory
Each (rational) stakeholder has a utility function over alternatives characterize population as distribution over utility functions
Probabilistic Inversion
Domain: utility functionsOf stakeholders
Range: choices of stakeholders
G maps utilities into choices
Invert G at this distribution
Observe Stakeholders Preferences
Used for stakeholder Preference Modeling:
• Risks of Nano enabled foods (Flari, WHO, CIS)• Valuing impaired health states (Flari, FDA)• Valuing fossil fuel policy options (RFF)• Prioritizing ecosystem threats (NCEAS)• Prioritizing zoonose threats (RIVM)• Modeling wiring failure (Mazzuchi)• Prioritizing vCVJ options (Aspinall Health Canada)• UK Research Council (Aspinall)• Aus. Univ. Fac Sci reviews (Aspinall).
steps
1. Get discrete choice data from stakeholders for choice alternatives A1,…An– “Which of (A,B) do you prefer”– “Rank your top 3 of (A, B, C, D, E, F)”
2. Find dist’n over utilities on [0,1]n which reproduces stakeholders preferences
3. If utility is function of covariates, validate out of sample.
Valuation of impaired Health statesFlari et al
17 health states6 criteriaEach criteria has 3 values, described in narrative19 Experts ranked 5 groups of 5 health states
First, find dist’n over utilities for the 17 Health States which recover Observed Frequencies of rankings (i.e. wo criteria)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
f(x) = 0.912874736742624 x + 0.0143452928596942R² = 0.977197926615134
Predicted vs Observed Frequencies of 105 rankings, scale values for the 17 Health States, no MAUT model
RecoveredLinear (Recovered)
Observed
Reco
vere
d
Build MAUT model for HS utilities, based on the 6 criteria
• Each stakeholder has a weight vector that determines his/her preference
• Population of stakeholders = population of weights
• Characterize population based on all rankings involving at least 7 (30%) experts (= 28 rankings).
• Validate on remaining rankings (= 77 rankings)
Average weights
12%
29%
8%27%
10%
15%
Mean Weights
MobilitySelf CareUsual ActivitiesPain DiscomfortAnxiety DepressionCognitive Functioning
Preference dependence emerges from fitting
Average weights per group of 5 health states
Predict out-of-sample rankings
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.800
0.1
0.2
0.3
0.4
0.5
0.6
0.7
f(x) = 0.879511080111118 x + 0.0210766294292423R² = 0.5721455934275
Predicted vs Observed % rankings, 28 fitted, 77 Out-of-Sample
PredictedLinear (Predicted)
Observed Percentage Ranks
pred
icted
per
cent
ages
Ran
ks
First time in HISTORY that a multi attribute model has been WRONG!!!
Average of predictions vs Out-of-Sample observed rankings, Not SOOO bad
0.00 0.05 0.10 0.15 0.20 0.25 0.30-0.05
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Out-of-sample:average predicted versus observed
observed percentages for out-of-sample rankings (less than 30% of experts)
pred
icte
d pe
rcen
tage
s fo
r ou
t-of
-sam
-pl
e ra
nkin
gs
Risks of Nano-Enabled Foods
Flari et al
Nano enabled food risks (VLARI) rank top and bottom 5
Correlation of criteria weights
Conclusion
• Stakeholder preference modeling is empirical science
• ‘preference for criteria’ inferred from data, not elicited
• (in) dependence in choices inferred from data, not assumed
THANK YOU