utility aggregation in temporally extended experiences: what´s in representative moments?

Utility Aggregation in Temporally Extended Experiences: What´s in

Representative Moments?

Irina Cojuharenco*Dmitry Ryvkin**

*Department of Economics and ManagementUniversitat Pompeu Fabrairina.cojuharenco@upf.edu

**Department of Economics, Florida State University

Temporally Extended Experiences

• MBA programs• Medical procedures• Meals• Music• Job performance

All can be translated into the language of Utility!

Definitions

time

utility

Experienced Utility – measurable states of satisfaction experienced by people (moment utility – experienced utility measured at a particular moment)

Remembered Utility – subjective report of total utility, found to be the average of Peak and End experienced utility

Total Utility – an objective measure summarizing the utility of all moment within an experience, e.g., average of moment utilities

Research Question

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

How different is remembered utility based on Peak-End versus Average experienced utility?

Will experiences be ranked differently: what´s the correlation between Peak-End and Average utility?

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

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

Random Experiences

Assumptions:

Utility, ut, is derived from hedonic stimuli st

Stimuli, st, are drawn from uniform [0,1]ut= st

t=1, …, T where T is the length of experienceCorrelation between Peak-End and Average utility, r(T):

. . . . . . . .

Random Experiences

r(T) and simulations for N=1000, 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.

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

The Data (54 Data Sets)T, Length of N, r, Correlation

Data set Experience Participants estimate 95% Conf. Interval1 30 26 0.87 0.73 - 0.942 30 27 0.97 0.94 - 0.993 30 27 0.93 0.85 - 0.974 30 27 0.93 0.85 - 0.975 30 27 0.84 0.68 - 0.926 30 27 0.91 0.81 - 0.967 30 27 0.95 0.89 - 0.988 30 27 0.91 0.81 - 0.969 30 27 0.92 0.83 - 0.96

10 30 27 0.61 0.30 - 0.8011 42 23 0.93 0.84 - 0.9712 45 27 0.91 0.81 - 0.9613 45 27 0.90 0.79 - 0.9514 45 26 0.95 0.89 - 0.9815 50 27 0.94 0.87 - 0.9716 50 27 0.95 0.89 - 0.9817 52 24 0.92 0.82 - 0.9718 57 22 0.98 0.95 - 0.9919 60 26 0.96 0.91 - 0.9820 60 27 0.86 0.71 - 0.9321 60 26 0.97 0.94 - 0.9922 60 27 0.92 0.83 - 0.9623 60 27 0.86 0.71 - 0.9324 60 27 0.96 0.91 - 0.9825 60 27 0.89 0.77 - 0.9526 60 27 0.94 0.87 - 0.9727 60 27 0.95 0.89 - 0.98

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 DataT, Length of N, r, Correlation

Data set Experience Participants estimate 95% Conf. Interval28 60 27 0.93 0.85 - 0.9729 73 25 0.88 0.74 - 0.9530 75 27 0.66 0.37 - 0.8331 90 26 0.94 0.87 - 0.9732 90 27 0.87 0.73 - 0.9433 90 27 0.88 0.75 - 0.9434 90 26 0.93 0.85 - 0.9735 30 23 0.50 0.11 - 0.7636 30 23 0.73 0.46 - 0.8837 3 20 0.72 0.44 - 0.8938 3 21 0.82 0.60 - 0.9239 18 42 0.80 0.66 - 0.8940 7 36 0.80 0.64 - 0.8941 7 46 0.77 0.62 - 0.8742 4 42 0.81 0.67 - 0.8943 6 28 0.78 0.40 - 0.8344 11 37 0.84 0.71 - 0.9145 10 35 0.89 0.79 - 0.9446 10 36 0.83 0.69 - 0.9147 10 36 0.90 0.81 - 0.9548 10 35 0.88 0.77 - 0.9449 10 36 0.91 0.83 - 0.9550 10 36 0.62 0.37 - 0.7951 10 36 0.74 0.54 - 0.8652 10 36 0.67 0.44 - 0.8253 10 36 0.67 0.44 - 0.8254 10 36 0.80 0.64 - 0.89

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).

. . . . . . . .

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

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].

t=1, …, T where T is the length of experience.α determines the transmission of “information” from one moment utility to the other.

or

. . . . . . . .

Correlation between Peak-End and Average utility, r(T):examined in simulations for α=0, 0.1, 0.2,…,1 and t=2, 3, …, 100.

Anchoring-and-Adjustment

T

r(T)

. . . . . . . .

The variability in Average utility helps explain 25% of variability in Peak-End utility for experiences

characterized by α= 0.9 and T = 100.

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

AdaptationAssumptions:

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].

t=1, …, T where T is the length of experience.β determines the transmission of “information” from one moment utility to the other.

and

or

or

. . . . . . . .

Correlation between Peak-End and Average utility, r(T):examined in simulations for β=0, 0.1, 0.2,…,1 and t=2, 3, …, 100.

Adaptation

T

r(T)

. . . . . . . .

The variability in Average utility helps explain 49% of variability in Peak-End utility for experiences

characterized by β= 1 and T = 100.

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

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.

. . . . . . . .

Between and Within Variability in the Data

Standard Deviations in Utility Reports Between and Within Inividuals

Data sets

. . . . . . . .

Simulations

We examine individual heterogeneity distributed normally and uniformly with variance large (between>>within), medium (between=within) and small (between<<within).

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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

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.

. . . . . . . .

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

. . . . . . . .

. . . . . . . .

Strength of Dynamics

Estimation ResultsData Set T,Length of N, Participants α=1-β 95% Conf. Interval

Experience1 30 26 0.36 [0.07 - 0.65]2 30 27 0.55 [0.38 - 0.72]3 30 27 0.70 [0.47 - 0.93]4 30 27 0.59 [0.34 - 0.84]5 30 27 0.48 [0.00 - 0.95]6 30 27 0.03 [-0.41 - 0.48]7 30 27 0.66 [0.41 - 0.92]8 30 27 -0.39 [-0.88 - 0.10]9 30 27 0.69 [0.40 - 0.98]10 30 27 -0.07 [-0.79 - 0.66]11 42 23 0.37 [-0.04 - 0.78]12 45 27 0.48 [0.08 - 0.89]13 45 27 -0.09 [-0.44 - 0.27]14 45 26 0.08 [-1.08 - 1.25]15 50 27 0.71 [0.25 - 1.18]16 50 27 0.64 [0.35 - 0.93]17 52 24 0.42 [0.08 - 0.77]18 57 22 0.19 [-0.39 - 0.77]19 60 26 0.63 [0.08 - 1.18]20 60 27 0.12 [-0.17 - 0.42]21 60 26 -0.30 [-0.82 - 0.23]22 60 27 0.18 [-1.09 - 1.46]23 60 27 0.75 [0.40 - 1.10]24 60 27 0.52 [0.16 - 0.87]25 60 27 -0.63 [-2.67 - 1.41]26 60 27 1.01 [0.06 - 1.95]27 60 27 0.47 [0.17 - 0.76]

. . . . . . . .

Estimation Results. . . . . . . .

Data Set T,Length of N, Participants α=1-β 95% Conf. IntervalExperience

28 60 27 0.66 [0.47 - 0.84]29 73 25 0.31 [-0.08 - 0.70]30 75 27 0.33 [0.12 - 0.54]31 90 26 0.39 [-0.01 - 0.80]32 90 27 0.57 [0.25 - 0.89]33 90 27 0.56 [0.32 - 0.80]34 90 26 0.38 [-0.08 - 0.84]35 30 23 0.22 [0.07 - 0.38]36 30 23 0.21 [0.02 - 0.40]39 18 42 -0.03 [-0.18 - 0.12]40 7 36 0.25 [-0.17 - 0.67]41 7 46 0.25 [-0.15 - 0.65]43 6 28 0.1 [-0.21 - 0.41]44 11 37 -0.08 [-0.37 - 0.21]45 10 35 -0.1 [-0.32 - 0.13]46 10 36 0.35 [-0.07 - 0.77]47 10 36 0.02 [-0.35 - 0.39]48 10 35 -0.24 [-0.67 - 0.19]49 10 36 0.08 [-0.26 - 0.42]50 10 36 0.15 [-0.12 - 0.42]51 10 36 -0.11 [-0.45 - 0.24]52 10 36 0.08 [-0.15 - 0.30]53 10 36 0.19 [-0.07 - 0.45]54 10 36 0 [-0.25 - 0.26]

. . . . . . . .

Hedonic Stimuli

Hedonic Stimuliare 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

Individual Heterogeneityare 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

Predicting Correlation between Peak-End and Average Experienced Utility

r(data)

r(anch.and adj.)

r(adapt.)

r(alpha=0)

r(beta=0)

Correlation observed in the data

Correlation predicted based on anchoring-and-adjustment given α and individual heterogeneity as estimated

Correlation predicted based on adaptation given β and individual heterogeneity as estimated

Correlation predicted based on individual heterogeneity alone (assuming the underlying model is anchoring-and-adjustment)Correlation predicted based on individual heterogeneity alone (assuming the underlying model is adaptation)

. . . . . . . .

Data sets for which was statistically significant

r(data)

r(anch.and adj.)

r(adapt.)

r(alpha=0)

r(beta=0)

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1 2 3 4 5 7 9 11 12 15 16 17 19 23 24 26 27 28 29 30 31 32 33 34 35 36 46 53

Predicting Correlation between Peak-End and Average experienced utility

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Predicting Correlation between Peak-End and Average Experienced Utility

r(anch.and adj.)

r(adapt.)

r(alpha=0)

r(beta=0)

Mean absolute deviation 0.09, correlation with actual r(data) 0.57*** (Spearman rank-order).

. . . . . . . .

Mean absolute deviation 0.09, correlation with actual r(data) 0.42*** (Spearman rank-order).

Mean absolute deviation 0.10, correlation with actual r(data) 0.19 (Spearman rank-order).

Mean absolute deviation 0.11, correlation with actual r(data) -0.03 (Spearman rank-order).

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

Conclusion

• We have helped quantify the similarity/dissimilarity 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@upf.edu