Utility Aggregation in Temporally Extended Experiences: What

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Utility Aggregation in Temporally Extended
Experiences Whats in Representative Moments?

• Irina Cojuharenco
• Dmitry Ryvkin

Department of Economics and Management Universita
t Pompeu Fabra irina.cojuharenco_at_upf.edu Depart
ment of Economics, Florida State University
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Temporally Extended Experiences

• MBA programs
• Medical procedures
• Meals
• Music
• Job performance
• All can be translated into the language of
  Utility!

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Definitions
Experienced Utility measurable states of
satisfaction experienced by people (moment
utility experienced utility measured at a
particular moment)
Total Utility an objective measure summarizing
the utility of all moment within an experience,
e.g., average of moment utilities
Remembered Utility subjective report of total
utility, found to be the average of Peak and End
experienced utility

utility
time
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Research Question
How different is remembered utility based on
Peak-End versus Average experienced
utility? Will experiences be ranked differently
whats the correlation between Peak-End and
Average utility?

• Experiences
• 4-5-1-8-9-6-9-4-7-7-2
• 8-2-1-5-1-0-3-3-2-7-8
• 3-0-2-3-1-1-4-2-8-9-4

• End
• 2
• 8
• 4

Peak 7 8 9
Average 6 4 3
Peak-End 5 8 6
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Presentation Plan

• The case of random experiences
• What experimental and field data tells
• When experienced utility evolves by
  anchoring-and-adjustment
• When adaptation underlies experienced utility
• Individual heterogeneity in the reports of
  utility
• Estimation of dynamics and individual
  heterogeneity
• Predicting correlation between Peak-End and
  Average experienced utility given estimation
  results
• Conclusion

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Presentation Plan

• The case of random experiences
• What experimental and field data tells
• When experienced utility evolves by
  anchoring-and-adjustment
• When adaptation underlies experienced utility
• Individual heterogeneity in the reports of
  utility
• Estimation of dynamics and individual
  heterogeneity
• Predicting correlation between Peak-End and
  Average experienced utility given estimation
  results
• Conclusion

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Random Experiences
. . . . . . . .
Assumptions Utility, ut, is derived from
hedonic stimuli st Stimuli, st, are drawn from
uniform 0,1 ut st t1, , T where T is the
length of experience Correlation between Peak-End
and Average utility, r(T)
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Random Experiences
. . . . . . . .
r(T) and simulations for N1000, the number of
experiences summarized by Peak-End versus Average
experienced utility
r(T)
T
In summarizing long random experiences little
correlation can be expected between Peak-End and
Average experienced utility.
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Presentation Plan

• The case of random experiences
• What experimental and field data tells
• When experienced utility evolves by
  anchoring-and-adjustment
• When adaptation underlies experienced utility
• Individual heterogeneity in the reports of
  utility
• Estimation of dynamics and individual
  heterogeneity
• Predicting correlation between Peak-End and
  Average experienced utility given estimation
  results
• Conclusion

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The Data (54 Data Sets)
. . . . . . . .
Data sets 1-34 Baumgartner, Sujan, and Padget
(1997), per-second evaluations of advertisements.
Data set 44 Ariely and Car- mon (2003), hourly
reports of pain in a day-long hospital field
study. Data sets 35-38, 39-43, 45-54 our
unpublished research, evaluations of images in
image-viewing experiments, evaluations of
classroom explanations and discussions in
classroom field studies, evaluation of life
aspects in a month-long life satisfaction study.
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The Data
. . . . . . . .
Correlation between Peak-End and Average
experienced utility is high and significant,
almost uniformly across data sets (variation in
population correlations controlling for sampling
error 0.008).
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Presentation Plan

• The case of random experiences
• What experimental and field data tells
• When experienced utility evolves by
  anchoring-and-adjustment (Hogarth Einhorn,
  1992)
• When adaptation underlies experienced utility
• Individual heterogeneity in the reports of
  utility
• Estimation of dynamics and individual
  heterogeneity
• Predicting correlation between Peak-End and
  Average experienced utility given estimation
  results
• Conclusion

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Anchoring-and-Adjustment
. . . . . . . .
Assumptions Utility, ut, is derived from
hedonic stimuli st and past period utility ut-1.
Stimuli, st, are drawn from uniform 0,1.
or
t1, , T where T is the length of
experience. a determines the transmission of
information from one moment utility to the
other.
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Anchoring-and-Adjustment
. . . . . . . .
Correlation between Peak-End and Average utility,
r(T) examined in simulations for a0, 0.1,
0.2,,1 and t2, 3, , 100.
r(T)
T
The variability in Average utility helps explain
25 of variability in Peak-End utility for
experiences characterized by a 0.9 and T 100.
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Presentation Plan

• The case of random experiences
• What experimental and field data tells
• When experienced utility evolves by
  anchoring-and-adjustment
• When adaptation underlies experienced utility
  (Frederick Loewenstein, 1999)
• Individual heterogeneity in the reports of
  utility
• Estimation of dynamics and individual
  heterogeneity
• Predicting correlation between Peak-End and
  Average experienced utility given estimation
  results
• Conclusion

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Adaptation
. . . . . . . .
Assumptions Utility, ut, is derived from
hedonic stimuli st adjusted by the adaptation
level (the level of utility due to previous
experience that leaves one hedonically neutral).
Stimuli, st , uniform 0,1.
and
or
or
t1, , T where T is the length of
experience. ß determines the transmission of
information from one moment utility to the
other.
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Adaptation
. . . . . . . .
Correlation between Peak-End and Average utility,
r(T) examined in simulations for ß0, 0.1,
0.2,,1 and t2, 3, , 100.
r(T)
T
The variability in Average utility helps explain
49 of variability in Peak-End utility for
experiences characterized by ß 1 and T 100.
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Presentation Plan

• The case of random experiences
• What experimental and field data tells
• When experienced utility evolves by
  anchoring-and-adjustment
• When adaptation underlies experienced utility
• Individual heterogeneity in the reports of
  utility
• Estimation of dynamics and individual
  heterogeneity
• Predicting correlation between Peak-End and
  Average experienced utility given estimation
  results
• Conclusion

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Individual Heterogeneity
. . . . . . . .

• Due to
• initial moods (initial condition u0i)
• individual-specific effects (ci added to
  equation for ut)

Variance in u0i or ci may make variability in
individual-specific means of reported utility
(between variability) greater than variability in
experience-specific moment utilities (within
variability). This may explain high and
significant correlation between Peak-End and
Average experienced utility.
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Between and Within Variability in the Data
. . . . . . . .
Data sets
Standard Deviations in Utility Reports Between
and Within Inividuals
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Simulations
. . . . . . . .

• We examine individual heterogeneity distributed
  normally and uniformly with variance large
  (betweengtgtwithin), medium (betweenwithin) and
  small (betweenltltwithin).

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. . . . . . . .
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. . . . . . . .
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. . . . . . . .
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. . . . . . . .
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Presentation Plan

• The case of random experiences
• What experimental and field data tells
• When experienced utility evolves by
  anchoring-and-adjustment
• When adaptation underlies experienced utility
• Individual heterogeneity in the reports of
  utility
• Estimation of dynamics and individual
  heterogeneity
• Predicting correlation between Peak-End and
  Average experienced utility given estimation
  results
• Conclusion

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Estimating Dynamics and Individual Heterogeneity
in the Data
. . . . . . . .
Population model
Describes the strength of dynamics
anch.-a-adj.
adapt.
Stands for unobserved hedonic stimuli
for anch.-a-adj.
and
for adaptation.
Individual-specific unobserved effect.
Error-term satisfying sequential exogeneity
conditional on unobserved effect.
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Estimation Strategy
. . . . . . . .

• Step 1. Time differencing to exclude the
  unobserved effect

Step 2. Time dummies
Step 3. Instrumental variables
Obtain
on time
Step 4. Regress new variable
and individual dummies to obtain and
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. . . . . . . .
Strength of Dynamics
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Estimation Results
. . . . . . . .
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Estimation Results
. . . . . . . .
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. . . . . . . .
Hedonic Stimuli
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Hedonic Stimuli
. . . . . . . .
are informative about the distribution of
in case of anchoring-and-adjustment and
in case of adaptation.
Sample distribution in 3 first and 3 last data
sets
For later purposes, we assume normality and
characterize hedonic stimuli in terms of sample
mean and standard deviation of .
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. . . . . . . .
Individual Heterogeneity
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Individual Heterogeneity
. . . . . . . .
are informative about the distribution of
individual heterogeneity, in 34 of 51 data sets
we cannot reject normality.
Sample distribution in 3 first and 3 last data
sets
For later purposes, we characterize individual
heterogeneity as normally distributed with
sample mean and standard deviation of .
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Presentation Plan

• The case of random experiences
• What experimental and field data tells
• When experienced utility evolves by
  anchoring-and-adjustment
• When adaptation underlies experienced utility
• Individual heterogeneity in the reports of
  utility
• Estimation of dynamics and individual
  heterogeneity
• Predicting correlation between Peak-End and
  Average experienced utility given estimation
  results
• Conclusion

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Predicting Correlation between Peak-End and
Average Experienced Utility
. . . . . . . .
Correlation observed in the data
r(data)
Correlation predicted based on anchoring-and-adjus
tment given a and individual heterogeneity as
estimated
r(anch.and adj.)
Correlation predicted based on adaptation given ß
and individual heterogeneity as estimated
r(adapt.)
Correlation predicted based on individual
heterogeneity alone (assuming the underlying
model is anchoring-and-adjustment)
r(alpha0)
Correlation predicted based on individual
heterogeneity alone (assuming the underlying
model is adaptation)
r(beta0)
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Predicting Correlation between Peak-End and
Average experienced utility
. . . . . . . .
Data sets for which was statistically
significant
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Predicting Correlation between Peak-End and
Average Experienced Utility
. . . . . . . .
Mean absolute deviation 0.09, correlation with
actual r(data) 0.57 (Spearman rank-order).
r(anch.and adj.)
Mean absolute deviation 0.09, correlation with
actual r(data) 0.42 (Spearman rank-order).
r(adapt.)
Mean absolute deviation 0.10, correlation with
actual r(data) 0.19 (Spearman rank-order).
r(alpha0)
Mean absolute deviation 0.11, correlation with
actual r(data) -0.03 (Spearman rank-order).
r(beta0)
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Presentation Plan

• The case of random experiences
• What experimental and field data tells
• When experienced utility evolves by
  anchoring-and-adjustment
• When adaptation underlies experienced utility
• Individual heterogeneity in the reports of
  utility
• Estimation of dynamics and individual
  heterogeneity
• Predicting correlation between Peak-End and
  Average experienced utility given estimation
  results
• Conclusion

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Conclusion
. . . . . . . .

• We have helped quantify the similarity/dissimilari
  ty due to selective versus comprehensive
  aggregation of utility in the comparison of
  equal-length experiences.
• Even few representative moments can potentially
  rank experiences similarly to average experienced
  utility.
• The high and significant correlation between
  Peak-End and Average experienced utility can be
  due to
• Dynamics of experienced utility
• Individual heterogeneity in utility reports

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Conclusion
. . . . . . . .

• We have contributed to the studies of unit
  weighting schemes for decision-making (Einhorn
  Hogarth, 1975). Simple one-parameter dynamic
  processes have been shown to induce a particular
  structure of intercorrelation between
  components of a composite variable. The value
  of the parameter has been related to the
  similarity between the selective and the
  comprehensive aggregation of components.
• Even if experienced utility does not evolve by
  anchoring-and-adjustment or adaptation,
  correlation between Peak-End and Average
  experienced utility can be built into the data
  on experiences by the experimenter if he follows
  the scripts of anchoring-and-adjustment or
  adaptation in the choice of hedonic stimuli.

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Thank You for Your Attention!
For any questions regarding this work, please,
contact Irina Cojuharenco at irina.cojuharenco_at_upf
.edu