Presentation at the Third Conference of International Consortium for Social Well-Being Studies, held at Plataran Hotel & Convention Center, Magelang, Indonesia, March 4, 2018

1. Search for Collective Preference on Statuses of Society:
Aggregating Individual Evaluations
based on Equality and Economic Growth
Koji YAMAMOTO
(Hylab LLP)
Presentation at the Third Conference of International Consortium for Social
Well‐Being Studies, held at Plataran Hotel & Convention Center, Magelang,
Indonesia, March 4, 2018

2. Introduction
2

3. Introduction
• How can we measure the well‐being of a whole society?
• The popular methods to do so are:
– (i) To utilize objective indices about a society, such as indices for
economic production and equality (e.g. GDP, GNI, Gini)
– (ii) To utilize simple aggregated values of subjective evaluations
by individuals, who live in the society, of themselves, such as the
percentage of those who feel happy
• Possible Drawbacks
– Method (i) can be criticized for not considering how ordinary
people feel.
– Method (ii) may also be criticized because there can be people
who tend to feel satisfied even in very difficult life situations,
and such people can more likely be ignored by policy makers, if
they only base their policy on simple subjective indices.
3

4. Introduction
• In the present study, we are to show an alternative method to
measure the well‐being of a society.
• The proposed method
– Based on objective information about the society.
– Conducted in a democratically more legitimate way,
considering how ordinary people think. This avoids
dogmatic judgments by an only limited number of
observers, for example, researchers or policy makers.
4

5. Introduction
• Our method consists of the following steps:
– (1) Estimating Individual Evaluation Function
• Based on real data
• We estimate the individual evaluation criteria with which
each of ordinary people evaluates a society
• Obtain the criteria with which an individual "subjectively"
evaluates a society using "objective" information.
– (2) Aggregating IEF into Collective Preference Order
• Aggregate the individual evaluations into a collective
preference order with respect to multiple statuses of a
society
• Conducted with a particular rule, i.e. in a transparent and
well‐defined way. In this sense, this aggregation is
"objectively" done.
5

6. Introduction
• Our method needs survey data from a set of questionnaire items.
• We show the results of sample analyses about evaluation based on
economic growth and equality.
• Related: Better Life Index (BLI)
– The website of BLI offers an interactive interface for users to set
weights on respective measurements of countries to obtain an
overall ranking of countries.
– BLI very clearly and explicitly assumes that the individual
evaluation criteria on statuses of a society vary among different
people.
– Conceptually speaking, this idea is similar to that of our present
study.
• In addition to this idea, we shall also present the attempt to
aggregate such various individual evaluations.
6

7. Concepts
7

8. Concepts
• Figure 1:
the idea of
Individual
Evaluation
Function, IEF
8
Figure 1. Individual Evaluation Function on Status of Society
Status A
Gini=0.30
Growth=0%
Status B
Gini=0.40
Growth=2%
Individual Evaluation Function
(IEF) represents individuals'
subjective evaluation on status
of society
Status of society is
described by
Objective Indices

9. Concepts
• Figure 2:
How we
aggregate
individual
preferences
into
Collective
Preference
Order, CPO
9
Figure 2. Collective Preference Order
Status A
Gini=0.30
Growth=0%
Status B
Gini=0.40
Growth=2%
Collective Preference Order (CPO)
reflects all individuals' evaluations
collectively, in a well‐defined and
transparent way (= objectively)
CPO:
A is more
desirable
than B!
Status of society is
described by
Objective Indices

10. Step 1: Estimating IEF
10

11. Step 1: Estimating IEF
• Model:
– Each person has IEF, and one prefers the policy which
maximizes the evaluation under perceived restriction.
– Based on this model, we can estimate the parameters of
IEF for different individuals using real data.
– IEF is evaluated with the equality, EQ, and the economic
growth, GR, and also with parameters of normative criteria
– After knowing the estimated set of parameters for each
individual, we can know how each person evaluates a real
or fictional status of a society, using the IEF formula, with
the indices for equality and growth.
11
  GREQIEF iiii  )1()( 2


12. Step 1: Estimating IEF
• Data
– JHPS: Japan’s nationwide panel survey
• not SWB data
– Use responses in 2011 and 2012
• Item: asked concrete amounts of money for desired
redistribution in “a fictional society” and the perceived
external effect on economic growth
– Using this set of questionnaire items, we can estimate the
parameters with which people evaluates “objective”
indices on a whole society.
12

13. Step 1: Estimating IEF
• Questionnaire Item
13
Fictional society:
The society includes households A, B, and C. Each household has
4 persons. The government collects taxes and social insurance,
and uses them to ensure one’s living. If the government does not
collect taxes or social insurance, household A’s income would be
3.5 million yen, B’s 7 million yen, C’s 12.5 million yen per annum.
(1) How much in taxes and social insurance premiums do you
think should be collected, and paid as benefits to the
households? Answer each question in 10,000 yen units. Do not
separate taxes and social insurance premiums, and answer the
total amount. If you think no collection or payment is necessary,
write 0.

14. Step 1: Estimating IEF
• Questionnaire Item (Cont.)
14
(2) If someone from one of the households in this society became
unemployed, and the income became 0, how much should the
government pay the household per year to ensure their living? Write
your answer in 10,000 yen units.
(3) Some may think that if the government collects taxes, or pay
benefits to every household, it affects economical growth. If the
government in this fictional society decided to introduce the policy
that you suggested in (1) and (2), compared with the government not
taking any action, what would happen to economical growth?
[Alternatives: 1. It would worsen dramatically. / 2. It would worsen
slightly. / 3. It would not change. / 4. It would improve slightly. / 5. It
would improve dramatically. / 6. Not sure. ]

15. Step 2: Showing CPO
15

16. Step 2: Showing CPO
• How do Japanese citizens rank the statuses of the society?
– Figure 3: Japan’s real status of each of ten years, from 2005
to 2014
• Real Gini coefficients of disposable income
• GNI growth rates
16

17. Step 2: Showing CPO
17
Figure 3. Gini and Growth, Japan, 2005-2014
Data Source: JHPS2011-2012; World Bank; Solt (2009; 2016)
Note: Shown are Japan's Gini coefficients (post-transfer Gini) and growth rates
(annual growth in real GNI per capita) for respective years.
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
‐6%
‐4%
‐2%
0%
2%
4%
6%
0.298 0.299 0.300 0.301 0.302 0.303 0.304 0.305
Growth Rate
Gini

18. Step 2: Showing CPO
• Pair‐wise majority comparison to find Condorcet ordering
– Table 2: The resulted round‐robin table
– In each cell, we show whether the ROW status is winning
or not, and also, the support rate for the ROW status.
– The number of wins against other statuses:
• When this value is larger, the status of the year is more
preferred, ranked higher, collectively.
18

19. 19
Table 2. Round-Robin Table: Collective Preference Order on Actual Statuses of Japan, 2005-2014
Year Gini Growth 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014
Win Win Win Win Win Win Win --- ---
(98%) (98%) (100%) (100%) (59%) (98%) (98%) (1%) (4%)
--- --- Win Win --- Win Win --- ---
(2%) (1%) (99%) (100%) (11%) (99%) (98%) (1%) (4%)
--- Win Win Win --- Win Win --- ---
(2%) (99%) (100%) (100%) (29%) (99%) (98%) (1%) (4%)
--- --- --- Win --- Win Win --- ---
(0%) (1%) (0%) (100%) (4%) (87%) (60%) (0%) (2%)
--- --- --- --- --- --- --- --- ---
(0%) (0%) (0%) (0%) (0%) (0%) (0%) (0%) (0%)
--- Win Win Win Win Win Win --- ---
(41%) (89%) (71%) (96%) (100%) (100%) (100%) (11%) (12%)
--- --- --- --- Win --- --- --- ---
(2%) (1%) (1%) (13%) (100%) (0%) (1%) (1%) (3%)
--- --- --- --- Win --- Win --- ---
(2%) (2%) (2%) (40%) (100%) (0%) (99%) (1%) (3%)
Win Win Win Win Win Win Win Win ---
(99%) (99%) (99%) (100%) (100%) (89%) (99%) (99%) (14%)
Win Win Win Win Win Win Win Win Win
(96%) (96%) (96%) (98%) (100%) (88%) (97%) (97%) (86%)
Data Source: JHPS2011-2012; World Bank; Solt (2009; 2016)
2014 0.2989 0.71% 9
Note: Shown in rows are Japan's Gini coefficients (post-transfer Gini) and growth rates (annual growth in real GNI per capita) for respective years.
Each cell corresponds to each of two-party comparisons between the row statuses and the column statuses. In each cell, the winning/losing and the
support rate of the ROW status is shown. Estimated parameters based on JHPS for 2011 and 2012 are utilized in determining individuals' evaluation,
but the above support rates etc. are calculated only in the 2011 sample, to avoid voting with "unequal-weights".
2012 0.3039 1.50% 2
2013 0.3014 2.80% 8
2010 0.3040 4.30% 6
2011 0.3042 0.28% 1
2008 0.3032 -1.55% 3
2009 0.3038 -5.53% 0
2006 0.3034 1.79% 4
2007 0.3032 1.91% 5
Japan's Status Target of Comparison N of
Wins
2005 0.3027 1.94% 7

20. Step 2: Showing CPO
• Figure 4‐1:
– The resulted rank value for each year in the square
brackets. For example, [R1] stands for the year is ranked at
No. 1.
• Generally speaking, smaller Gini tends to be preferred
collectively.
20

21. Step 2: Showing CPO
21
Figure 4-1. How Statuses are Ranked (1)
Data Source: JHPS2011-2012; World Bank; Solt (2009; 2016)
Note: Shown are Japan's Gini coefficients (post-transfer Gini) and growth rates
(annual growth in real GNI per capita) for respective years. In the square
brackets with "R" letter are the rank values of the status among ten periods
compared.
2005 [R3]
2006 [R6]
2007 [R5]
2008 [R7]
2009 [R10]
2010 [R4]
2011 [R9]
2012 [R8]
2013 [R2]
2014 [R1]
‐6%
‐4%
‐2%
0%
2%
4%
6%
0.298 0.299 0.300 0.301 0.302 0.303 0.304 0.305
Growth Rate
Gini
In this area, a status with
more equality is more
preferred collectively

22. Step 2: Showing CPO
• Outside the
area of
ordinary
growth, the
pattern turns
different.
22
Figure 4-2. How Statuses are Ranked (2)
Data Source: JHPS2011-2012; World Bank; Solt (2009; 2016)
Note: Shown are Japan's Gini coefficients (post-transfer Gini) and growth rates
(annual growth in real GNI per capita) for respective years. In the square
brackets with "R" letter are the rank values of the status among ten periods
compared.
2005 [R3]
2006 [R6]
2007 [R5]
2008 [R7]
2009 [R10]
2010 [R4]
2011 [R9]
2012 [R8]
2013 [R2]
2014 [R1]
‐6%
‐4%
‐2%
0%
2%
4%
6%
0.298 0.299 0.300 0.301 0.302 0.303 0.304 0.305
Growth Rate
Gini
The status of 2010 beats
that of 2007 etc. because of
its exceptionally higher
growth rate, although 2010
is more unequal

23. Step 2: Showing CPO
• Outside the
area of
ordinary
growth, the
pattern turns
different.
23
Figure 4-3. How Statuses are Ranked (3)
Data Source: JHPS2011-2012; World Bank; Solt (2009; 2016)
Note: Shown are Japan's Gini coefficients (post-transfer Gini) and growth rates
(annual growth in real GNI per capita) for respective years. In the square
brackets with "R" letter are the rank values of the status among ten periods
compared.
2005 [R3]
2006 [R6]
2007 [R5]
2008 [R7]
2009 [R10]
2010 [R4]
2011 [R9]
2012 [R8]
2013 [R2]
2014 [R1]
‐6%
‐4%
‐2%
0%
2%
4%
6%
0.298 0.299 0.300 0.301 0.302 0.303 0.304 0.305
Growth Rate
Gini
The statuses of 2008 and
2009 are beaten by more
unequal statuses because
of exceptionally low growth
rates

24. Conclusion
and
Discussion
24

25. Conclusion and Discussion
• We have presented the method to find how statuses of a
society are evaluated, and also have showed the results.
• As substantial findings, we can give the following points.
– Based on Japanese citizens’ evaluation criteria, generally
speaking, more equal statuses are preferred collectively.
– When there is a very high or low economic growth which is
seen exceptional for contemporary Japan, such growth
rate may change the ranking different from that
corresponding to equality.
25

26. Conclusion and Discussion
• Discussion
– Although we have emphasized the aggregation is
conducted “objectively,” the choice of the aggregation
method is made by researchers’ subjective criteria.
• Such a choice may need more elaborate discussion.
– In estimating IEF, we utilized a model with fairly strong
assumptions.
• More desirably, we may be able to find the individual
evaluations with weaker assumptions through
experimental designs (Kuziemko et al. 2015; Lara and
Shores 2017).
26

27. 27
References
Kuziemko, Ilyana, Michael I. Norton, Emmanuel Saez, and
Stefanie Stantcheva. 2015. “How Elastic Are Preferences for
Redistribution? Evidence from Randomized Survey
Experiments.” American Economic Review 105 (4): 1478–1508.
Lara, Bernardo, and Kenneth Shores. 2017. “Identifying
Preferences for Equal Educational Opportunity, Income, and
Income Equality.” Available at SSRN:
https://ssrn.com/abstract=2996575.
Data Sources
Solt, Frederick. 2016. “The Standardized World Income
Inequality Database.” Social Science
Quarterly 97. SWIID Version 6.0, July 2017.
World Bank. 2017. World Development Indicators. (Last
Updated September 18, 2017; Datasets are retrieved from
https://data.worldbank.org/country/japan).

28. Thank you for your warm attention!
Comments are welcome!!
E‐mail: kojiy@kojiy.org
28
Acknowledgement
This study has been supported by JSPS KAKENHI Grant Numbers JP16H00287,
JP11J06528, and JP18830018. The data for this analysis, Japan Household
Panel Survey (JHPS/KHPS), was provided by the Keio University Panel Data
Research Center. This work was supported by the MEXT‐Supported Program
for the Strategic Research Foundation at Private Universities of Japan, 2014‐
2018 (S1491003).

29. Appendix: Detailed
Description of Step 1
29

30. Approach and Model
• We develop a theoretical model which assumes individual
redistributive preference may be affected by the perceived
fact about relationship between redistribution and economic
growth
• Concretely, we assume each person has IEF (Individual
Evaluation Function on Status of Society) and one prefers the
policy which maximize the evaluated value under perceived
restriction
30

31. Approach and Model
• Model:
– IEF is evaluated with the equality, EQ, and the economic growth,
GR, and also with parameters of normative criteria
– There is a perceived restriction in each person’ s mind as follow
– The parameter Theta (θ) reflect the perceived fact
– Maximizing IEF subject to the restriction, the optimal values of
EQ and GR are obtained
31
  GREQIEF iiii  )1()( 2

)( 00 EQEQGRGR i  
iiiiiEQ   2/)1(*
00
**
)( GREQEQGR iii  

32. Approach and Model
• Even if people have the same IEF, the optimal points may vary
according to the perceived restriction
– “Gov’t should redistribute more because it enhances
growth!”
– “Gov’t should redistribute less because such a policy
harms growth!”
32

33. 33
GR
EQ
Panel (e)
Figure A1. Concepts: Contour of IEF Values, Restriction Line, and Optimal Point
GR
EQ
Panel (b)
GR
EQ
Panel (a)
Restriction Line (θ < 0)
Status Quo
(EQ0,GR0)
Contour of IEF Values
Evaluated High
Evaluated Medium
Evaluated Low
Optimal Point (θ < 0)
GR
EQ
Panel (c)
GR
EQ
Panel (d)
Optimal Point (θ = 0)
Restriction Line (θ = 0)
Optimal Point (θ > 0)
Restriction Line (θ > 0)

34. Method and Data
• We are to estimate how individual characteristics affect the
parameters in the theoretical model
• Estimation method
– Let us assume the responses of EQ and GR, which optimize IEF,
for each individual
– From the above formulas, Theta (θ) is directly estimated
if EQi ≠ EQ0
– We associate Tau (τ) and Theta (θ) with individual characteristic
variable vector, zi, and unobserved disturbances
– Using aforementioned formula, EQ can be written as follow
where
34
)/()( 00 EQEQGRGR iii 
ii ,  τi βz ii ,  θi βz
iiiEQ ,  τi βz
 2/)1(  )21/(1  

35. Method and Data
• Two Estimation Equations
– We conduct simple OLS for the equations of Theta and EQ
35
ii ,  θi βz
iiiEQ ,  τi βz

36. Method and Data
• Estimation method
– Diagram
36
Figure A2. Diagram for Estimated Equations
Explained Variable EQ
Policy Preference
"How much redistribution
should Gov't conduct?"
Parameter Theta (θ)
Perceived Facts
"Does redistribution improve
economic growth?"
Parameter Tau (τ)
Normative Criteria for Equality
"What is the desirable equality,
other factors being the same?"
Explanatory Variables
Individual Characteristics
e.g. Higher Education

37. Method and Data
• Estimation method
– Tau is not directly obtained; we can interpret the effect of
Tau from the result where the dependent variable is EQ
37
Figure A3. Diagram for Estimated Equations, Tau Hidden
Explained Variable EQ
Policy Preference
"How much redistribution
should Gov't conduct?"
Parameter Theta (θ)
Perceived Facts
"Does redistribution improve
economic growth?"
Parameter Tau (τ)
Normative Criteria for Equality
"What is the desirable equality,
other factors being the same?"
Explanatory Variables
Individual Characteristics
e.g. Higher Education

38. Method and Data
• Data
– JHPS: Japan’s nationwide panel survey
• not SWB data
– Use responses in 2011 and 2012
• Item: asked concrete amounts of money for desired
redistribution in “a fictional society” and the perceived
external effect on economic growth
– The information on these is utilized to construct each
respondent’s optimal EQ and GR values
38

39. Method and Data
• Questionnaire Item
39
Fictional society:
The society includes households A, B, and C. Each household has
4 persons. The government collects taxes and social insurance,
and uses them to ensure one’s living. If the government does not
collect taxes or social insurance, household A’s income would be
3.5 million yen, B’s 7 million yen, C’s 12.5 million yen per annum.
(1) How much in taxes and social insurance premiums do you
think should be collected, and paid as benefits to the
households? Answer each question in 10,000 yen units. Do not
separate taxes and social insurance premiums, and answer the
total amount. If you think no collection or payment is necessary,
write 0.

40. Method and Data
• Questionnaire Item (Cont.)
40
(2) If someone from one of the households in this society became
unemployed, and the income became 0, how much should the
government pay the household per year to ensure their living? Write
your answer in 10,000 yen units.
(3) Some may think that if the government collects taxes, or pay
benefits to every household, it affects economical growth. If the
government in this fictional society decided to introduce the policy
that you suggested in (1) and (2), compared with the government not
taking any action, what would happen to economical growth?
[Alternatives: 1. It would worsen dramatically. / 2. It would worsen
slightly. / 3. It would not change. / 4. It would improve slightly. / 5. It
would improve dramatically. / 6. Not sure. ]

41. Method and Data
• Variables of main interest: (answered = optimal) EQ and GR
– EQ is based on Gini coefficient after redistribution
• To include information of assured minimum income and to
avoid bias, a continuous income distribution is used; Gini is
calculated from the distribution, by a Monte Carlo method
• EQ is obtained by monotonically decreasing transformation
of the resultant Gini coefficient
– GR is a value which corresponds to the expression in a natural
language, like “worsen dramatically”
• We conducted another small survey to assign each value, i.e.
a concrete amount, for each natural‐language expression of
“growth in growth”
• Other variables: gender, age, marital status, higher education, white
collar job, household income
41

42. 42
Table A1. Estimation Results
Coef. (S.E.) Coef. (S.E.) Coef. (S.E.)
0.013 *
(0.005)
Male
Age/100 0.002 (0.048) 0.522 *
(0.244) -0.005 (0.048)
Married -0.006 (0.017) 0.105 (0.075) -0.007 (0.017)
Higher Education 0.031 *
(0.013) 0.144 **
(0.054) 0.029 *
(0.013)
Female
Age/100 0.080 (0.054) 0.009 (0.335) 0.080 (0.054)
Married -0.008 (0.018) 0.269 **
(0.093) -0.012 (0.018)
Higher Education 0.052 **
(0.019) 0.162 *
(0.074) 0.050 **
(0.019)
Source : JHPS2011-2012
N of Obs. 3084 3084 3084
Note: +:p<0.10, *:p<0.05, **:p<0.01
The value of θ is multiplied by 1000 so that the coefficients are decently displayed.
θ
(Perceived Improvement of
Growth by Unit Equalization)
--- ---
For both genders, White Collar and Household Income (Log) are included but turn out to
be insignificant. Constant, Male Dummy, and Year Dummy (2012) are also included.
R
2
0.011 0.011 0.016
Explanatory Variables
Model 1 Model 2 Model 3
Dep. Var. Dep. Var. Dep. Var.
EQ θ EQ