- Email: [email protected]
The effect of aggregation on city sustainability rankings
Ecological Indicators 112 (2020) 106076
Contents lists available at ScienceDirect
Ecological Indicators journal homepage: www.elsevier.com/locate/ecolind
The effect of aggregation on city sustainability rankings ⁎
T
Dean Laslett , Tania Urmee Murdoch University, Australia
A R T I C LE I N FO
A B S T R A C T
Keywords: City sustainability indicator Sustainability index City ranking Aggregation method
Although sustainability is a multifactorial concept, many sustainability indexes use weighted additive aggregation of sets of different indicators to derive a single index which can be used to rank different cities. One of the limitations of this approach is that a poor or low rating in one area can be compensated by a strong or high rating in another area. However sustainability cannot be measured linearly. There is at least a triple bottom line: environmental, social and economic. To be truly sustainable, a city must be sustainable in all areas. A deficiency in one area is likely to have a negative effect in larger proportion than suggested by the magnitude of the deficiency. Conversely, a strong result in an indicator is likely to have less effect on overall sustainability than its magnitude suggests. The concept of constraint and maximisation indicators has been proposed to represent this property of sustainability. We investigate the effect on city rankings of using aggregations that aim to represent the constraint and maximisation properties of sustainable development indicators, compared to the commonly used arithmetic (linear) aggregation. Three such aggregation methods (geometric, harmonic and an adjustable compensation method) can cause difficulties with ranking if one or more of the individual indices have a zero normalised value. We show that the use of a small offset can avoid this problem and enable practical use of these aggregation methods to better capture the nature of sustainability. We also formulate a similarity score for different ranking systems that compare a large number of cities.
1. Introduction Sustainable development is a conceptual framework that seeks to capture all aspects that are needed for welfare in the “here and now”, “later” and “elsewhere” dimensions (Smits and Hoekstra, 2011). This framework has recently been clarified through the adoption by the United Nations of the 17 sustainable development Goals and 169 targets (United Nations, 2015). Goal 11 is sustainable cities and communities, which states “Make cities and human settlements inclusive, safe resilient and sustainable” (UNDP, 2015a). The world has experienced unprecedented urban growth in recent years. According to the United Nations, the projected number of people living in cities will increase to 5 billion by the end of 2030 (ECOSOC, 2017). Another concept related to cities, “green growth”, has been developed and generally refers to economic growth that not only preserves but enhances the natural resources we have inherited (Gurría, 2012). A social dimension is often included in this concept of growth, in that environmentally sound economic growth must also improve the well being of people. The resulting approach is more comprehensively known as inclusive green growth (World Bank, 2012). Green growth arose from the realisation that typically the green elements (mainly
⁎
natural capital) are the most oppressed due to economic development and therefore should be the focus for policy development and monitoring (Statistics Netherlands, 2013). Green growth is not a new paradigm, instead, it is an operational strategy to reconcile the urgent need for growth while avoiding irreversible far-reaching environmental consequences. This should also be done in such a way as to alleviate poverty. That is, green growth is a “modus operandi” to implement the sustainable development paradigm which is “growth that is forceful and at the same time socially and environmentally sustainable” (WCED, 1987). The concept of green growth is considered to have global strategic merit by forming a narrative about opportunities through collective action that might change the dynamics of international negotiations (Bowen and Hepburn, 2014). Bartelmus (2013) argues that sustainable development policy focus should concentrate on the parameters of green growth because they are more measurable compared to the more abstract and qualitative concepts of sustainable development itself, and therefore initiatives are more assessible. The scope of measurability is being extended to encompass inclusive green growth (Narloch et al., 2016), 1 and the synergies between green growth/green economy strategies and sustainable development become more evident when evaluating how green
Corresponding author. E-mail address: [email protected] (D. Laslett).
https://doi.org/10.1016/j.ecolind.2020.106076 Received 17 September 2018; Received in revised form 25 November 2019; Accepted 5 January 2020 1470-160X/ © 2020 Elsevier Ltd. All rights reserved.
Ecological Indicators 112 (2020) 106076
D. Laslett and T. Urmee
Once an index is established, comparisons and rankings between different cities can be made. Many different city sustainability index systems have been identified in the literature (Cohen, 2017). Three examples of city sustainability index systems which are notable because of their global scope are the “City Prosperity” index, the “Sustainable Cities” index and the “Cities in Motion” index. The United Nations City Prosperity index is based on productivity, infrastructure development, quality of life, equity and social inclusion, environmental sustainability, and governance and legislation (Moreno and Murgula, 2015). The Sustainable Cities index is based on the three pillars of sustainability: people, profit and planet. This index combines indicators measuring the social, environmental, and economic dimensions of sustainability (Arcadis, 2016). The Cities in Motion index was developed by the university of Navarra IESE business school. This index evaluated indicators grouped into the areas of economy, technology, human capital, social cohesion, international outreach, environment, mobility and transportation, urban planning, public management and governance to measure the performance of cities (Berrone and Ricart, 2016). The use of indicators, composite indexes and ranking is increasingly used to inform city policy (Giffinger et al., 2010). Recently, there has been a trend toward real time representation using visualisation aids, or “dashboards”, that are available to the general population as well as policy makers, planners and managers. Thus, indicators and indexes are also now influencing how a city is imagined (Kitchin et al., 2015). One example is the trend for cities to brand themselves as a “smart city” or “smart sustainable city”, based partly on a favourable city ranking (Anthopoulos, 2017). The concept of a smart city is based on sustainability and quality of life, but adds technological and informational dimensions (Marsal-Llacuna et al., 2015). The ongoing information revolution has enabled more frequent and comprehensive monitoring of sustainability and other smart city indicators, generating massive amounts of data (van Zoonen, 2016). Thus there is an increasing need to generate, in a timely fashion, composite indexes that help to give a more understandable overview of the data, both to city managers and the public dashboards. However, despite the growing importance of indicators, indexes and ranking systems, consensus has not been reached on their objectivity. Giffinger et al. (2010) found that the objectivity of city ranking systems has a dependency on the calculation method (which includes aggregation). For example, the three index systems described above can rank the same cities in different orders. Stockholm is ranked above Zurich by the City Prosperity index, while it is ranked lower than Zurich by the Sustainable Cities index and the Cities in Motion index. Melbourne is ranked above Madrid by the City Prosperity index and the Cities in Motion index, but ranked below Madrid by the Sustainable Cities index. Holden and Moreno Pires (2015) argue that data and indicator systems can never be entirely objective, but they have the potential to force greater transparency and accountability into decision making processes, and ignoring them could lead to worse outcomes for cities. So greater understanding of their scope and limitations should be sought. This study takes one small step toward that goal by examining the effect of aggregation on city sustainability rankings.
Fig. 1. Comparison between green growth and sustainable development.
interventions in the economy interact with society and the environment (UNEP, 2014). A useful comparison of the interaction between green growth in cities and sustainable development is shown in Fig. 1.To evaluate various aspects of urban development including inclusive green growth and sustainable development, it is common to compare the performance of different cities, and rank them against each other. These rankings are seen as becoming increasingly important as cities find ways to distinguish themselves in competition with each other, in order to attract high value adding services and industries (Anttiroiko, 2015). The majority of city ranking systems use indicators. An indicator aims to quantify or measure a particular aspect of the city, either directly or indirectly. Indicators are now seen as fundamental in the provision of information to inform development, implementation and assessment of policies and decision making (Dizdaroglu, 2017). The growing effort to develop policy initiatives that promote sustainable development has driven the need for new indicators based on the principles of inclusive green growth (GGKP, 2013). To this end numerous initiatives have been implemented to develop specific indicators that adequately capture the economy-environment nexus in the context of an equitable social dimension (Rametsteiner et al., 2011). An example that illustrates the complexity involved in selecting a comprehensive set of indicators, and the interaction between indicators and initiatives, is the approach taken by the United Nations Environmental Program (UNEP). UNEP does not provide a single list of indicators, but instead provides guidance on selection of relevant indicators throughout an integrated policy making cycle. Specifically, emphasis is placed on three stages where indicators are relevant (UNEP, 2014):
• Issue identification and agenda settings • Policy formation and policy assessment, and • Monitoring and evaluation The indicators used in the first stage are chosen to identify and prioritise problems to be addressed by policy. Indicators for problem identification help frame the issue, and indicators for policy formulation help design initiatives, impact indicators estimate the cross-sectoral impacts of initiatives chosen, while indicators for policy monitoring and evaluation support the assessment of the initiative implemented. However, the large swath of indicators used in setting and evaluating policy in the UNEP approach does not facilitate straightforward understanding or comparison. Similarly, the framework of indicators used by other organisations such as the World Bank, the Organisation for Economic Co-operation and Development, the United Nations Economic and Social Commission for Asia and the Pacific, and the Green Growth Knowledge Platform are cumbersome when communicating green growth progress or lack thereof with policy makers, stakeholders and the community. To overcome these challenges, significant efforts have been undertaken to develop a summary indicator or approach (often called an “index”) for communicating the current status of green growth. An index is formed by combining (or “aggregating”) several indicators together using a systematic methodology.
2. Background As can be seen from the different examples given in the introduction, there is no universal method for the compilation of a single composite index from a number of different indicators (Mazziotta and Pareto, 2016a). Mori and Yamashita (2015) introduced the concept of constraint and maximisation factors. A pure constraint factor confines sustainability within environmental and socioeconomic limits and sustainability cannot be achieved if any one constraint factor is poor. A pure maximisation factor increases benefits within the limits but is not critical. In reality, most factors will be a mixture of both, and a maximisation factor is likely to take on the properties of a constraint factor 2
Ecological Indicators 112 (2020) 106076
D. Laslett and T. Urmee
rij =
x ij − minj (x ij ) maxj (x ij ) − minj (x ij )
(3)
and for negative indicators:
rij =
maxj (x ij ) − x ij maxj (x ij ) − minj (x ij )
(4)
Sometimes an additional standardisation step is used, whereby the values of the normalised indicators are adjusted so that their overall sum is 1. The standardised value of the indicator i measured at city j, fij, is given by:
fij =
rij n
∑ rij
(5)
j=1
To form a single index, several indicators are combined (aggregated) together with different (but invariant) weights implying different relative importance. One method for deciding what values the weights should take is to use the concept of entropy. In the field of information theory, Shannon (1948) developed an entropy measure of the uncertainty of alternative states. Entropy is maximised when all alternative states have a similar probability, and uncertainty over which state will be chosen is greatest. Recently, Shannon entropy theory has been adapted to calculation of weights for indexing systems, the idea being that a higher variation (lower “entropy”) in the reported values of an indicator means this indicator is more important and should receive a greater weight relative to other indicators (Wang and Lee, 2009). In the context of sustainability indicators, the entropy function Hi for the ith indicator can be defined as:
Fig. 2. The steps required to compile a single index from raw indicator values. Figure derived from Langhans et al. (2014), Shen et al. (2015), Mazziotta and Pareto (2016a) and Tan et al. (2017).
as its value becomes poorer and other sectors of the ecological, economic and social systems of the city are more and more affected. Mori and Yamashita (2015) also linked this paradigm to strong sustainability, where weakness in one factor (i.e. a value that indicates a lack of sustainability) cannot be substituted by strength in another. All must be strong for the city to be truly sustainable. In contrast, with weak sustainability, one attribute can be compensated with another. Therefore strong sustainability requires that all factors become constraint factors if their values are weak. An implication of using factors with constraint is that the most important indicators for determining sustainability could be different for different cities. For example, Phillis et al. (2017) found that municipal waste generation and greenhouse gas emissions were the main constraints for cities in developed countries, whereas crime and poverty were the main constraints for cities in developing countries. However, it is common for sustainable development indicators to be added linearly when composing an index, indicating weak sustainability (Gan et al., 2017). The compilation of a single index from a large set of indicators can be complex and require several steps (Fig. 2). Since indicators are measuring different facets of sustainability they are likely to have a widely varying range of values. Therefore a process of normalisation must be performed before different indicators can be related to each other. Different normalisation methods can be used. For a set of m indicators applied to n cities, Shen et al. (2015) used the following equation to normalise positive indicators:
rij =
Hi =
(6)
m
⎛⎜m − ∑ H ⎟⎞ i i=1 ⎝ ⎠
(7)
where wi is the weighting for indicator i and m is the total number of indicators. The weightings have the property that:
(1)
m
∑ wi = 1 i=1
(8)
Commonly, the overall index is formed by weighted arithmetic aggregation of the standardised indicator values (Mazziotta and Pareto, 2016a):
minj (x ij ) x ij
j=1
(1 − Hi )
wi =
where rij is the normalised value of indicator i at city j, xij is the unnormalised (raw) value of the indicator and maxj(xij) is the maximum value of indicator i over the range of j from 1 to n. For negative indicators, Shen et al. (2015) used:
rij =
n
∑ fij ln fij
If fij is zero, then fijlnfij is set to zero. As a simple conceptual illustration, an indicator measured at two cities has the form of its entropy function Hi shown in Fig. 3. fi refers to the normalised indicator value in the first location. Because there are only two cities considered, the standardised value for the indicator at the second location will be 1-fi. If the two indicator values are the same (fi = 0.5), then the entropy function will be maximised. If the two indicator values are different, then the entropy function is minimised. Therefore the variability in the measured values of an indicator is maximised when the entropy is minimised, and if the indicator is one part of a composite index, then the “objective” importance, or weighting, assigned to this indicator can be quantified using:
x ij maxj (x ij )
1 ln(n)
m
(2)
Ij =
∑ wi fij i=1
where minj(xij) is the minimum value of indicator i over the same range. However this causes difficulty if the minimum is zero, or the raw value of the indicator xij is zero. Tan et al. (2017) took a more linear and relative approach. For positive indicators, the authors used:
(9)
where Ij is the index for city j. Weighted arithmetic aggregation of the normalised indicator values has also been used, for example in Tan et al. (2017): 3
Ecological Indicators 112 (2020) 106076
D. Laslett and T. Urmee
Fig. 3. Entropy function of an indicator with two standardised values. fi denotes the first value. The second value will be 1 – fi.
Ij =
1 m
m
∑ wi rij i=1
Pareto, 2016b). The introduction described several examples of indexes being used to rank the sustainability performance of different cities compared to each other. However there is also a potential shortcoming if geometric aggregation is used for this purpose. A normalised value of zero in any one of the indicator values will generate an overall index value of zero, regardless of the values of the other indicators, which is purely noncompensatory. However, if this occurs in more than one city (even with different indicators that are zero), it will be impossible to rank those cities compared with each other. Both will have an index of zero, even though one city may perform better in other areas. This is perhaps one reason why geometric aggregation is not used more often when ranking city sustainability. This effect can be avoided if a small arithmetic offset ε is introduced into the geometric mean calculation:
(10)
While the entropy technique provides a systematic method for assigning weights, the actual importance of each indicator is not represented. The indicator with the greatest variability is given the highest weight, regardless of its importance. Also if the overall index is formed in a way similar to equations 9 or 10, then there is no transition between maximisation and constraint as the normalised value of the indicator decreases. A number of non-linear aggregation methods have been formulated that may better represent this transition. The simplest of these is the use of a geometric aggregation rather than an arithmetic one: m
Ij =
m
∏ wi rij i=1
(11)
⎛ Ij = ⎜m ⎝
Equations (10) and (11) are equivalent to the arithmetic mean and geometric mean respectively. Since the magnitudes of the wi and rij terms are always less than or equal to 1, the geometric mean is always less than or equal to the arithmetic mean, and is only equal if all of the weighted terms wirij are identical. As one or more of the weighted terms become lower than the others, then the geometric mean becomes less than the arithmetic mean (Mazziotta and Pareto, 2016a), which fits the concept of a transition from maximisation to constraint if an indicator decreases. Like arithmetic aggregation, geometric aggregation requires that all of the weighted terms are zero or positive, and have the same polarity, so for a mix of positive and negative indicators, the normalisation process must transform one polarity into the other. Aggregation methods can be classified according to their degree of compensation, which is related to the concepts of maximisation and constraint factors, and weak and strong sustainability, described above. With a fully compensatory aggregation method, a weak or low value in one or more indicators can be compensated by strong or high values in other indicators. With a fully non-compensatory aggregation method, there is no compensation. A weak or low value will drag down the value of the index. A partially non-compensatory aggregation method lies somewhere in between these two limits. If maintaining the trajectory of inclusive green growth requires adherence to strong sustainability, then the use of non-compensatory aggregation methods are required for indices that are formed with the purpose of measuring an aspect of inclusive green growth. These aggregation methods can also give impetus to using a more balanced and comprehensive approach to management of sustainability goals, as the weakest indicators must be improved in order to raise the value of the overall composite index (Mazziotta and
m
⎞
∏ (ε + wi rij ) ⎟ − ε ⎠
i=1
(12)
Therefore if the normalised value of one (or more) indicators is zero, then the root term does not become zero, but has a minimum value of ε when all the indicators are at their minimum possible normalised value (rij = 0 for all i). The offset is subtracted outside the root term so that in this case the effect of the offset is cancelled out, and the minimum value of Ij is still 0. Another non-compensatory aggregation method is the harmonic mean (Langhans et al., 2014):
Ij =
1 m
∑ i=1
wi rij
(13)
If the value of any one of the normalised indicator values is zero, then the denominator of equation (13) becomes infinite, and the value of the index is set to zero. Hence the harmonic mean has the same ranking limitation as just described for the geometric mean, and similarly, this effect can be avoided if a small offset ε is introduced into the harmonic mean calculation:
Ij =
1 m
∑ i=1
wi ε + rij
−
ε m
∑ wi i=1
(14)
Therefore if the normalised value of one or more indicators is zero, but not all, then the denominator does not become infinite and the value of the index remains above zero. The subtraction of the offset divided by the sum of the weights ensures that if all the indicators are at 4
Ecological Indicators 112 (2020) 106076
D. Laslett and T. Urmee
(16) to obtain the modified forms. The effect of the offset on the behaviour of these methods will be examined by setting up an extreme situation where one half of the indicators have a normalised value of 1, and the other half are zero. For the modified DBR aggregation method, various values of λ between 0 and 1 will be tried, to find breakpoints where the city ranking suddenly changes. When rankings for a large number of cities are compared, tracking the rank for each individual city becomes less insightful. Therefore a score for the overall similarity, Sxy, between two aggregation methods x and y will be used. Sxy is formulated using the sum of the ranking differences for each individual city:
their minimum possible normalised value (rij = 0 for all i), then the effect of the offset is cancelled out, and the minimum value of Ij is still 0. It could be said that the degree of compensation for the arithmetic, geometric and harmonic methods is fixed, and cannot be controlled. In contrast, Diaz-Balteiro and Romero (2004) introduced an index (called the DBR index here) where the overall degree of compensation can be explicitly specified: m
I j = (1 − λ )[mini (wi rij )] + λ ∑ wi rij
(15)
i=1
where λ is the compensation parameter, ranging from 0 to 1. If λ = 1 then the index is the fully compensatory arithmetic mean. For any value of λ > 0, the DBR index is considered to be partially compensatory (Pollesch and Dale, 2015). If λ = 0 then the index is the fully noncompensatory minimum value of the weighted indicators, and at this value once again the DBR index suffers from the same ranking limitation identified with the geometric and harmonic aggregation methods, which again can be avoided if a small arithmetic offset ε is introduced. Also, Pollesch and Dale (2015) used a reformulation of the DBR equation that removes the weighting from the minimisation term. A combination of these two modifications yields:
Ij =
1 ⎛ (1 − λ )mini (rij ) + (λ + ε ) 1+ε⎜ ⎝
m
i=1
⎠
4. Results and discussion (16)
Geometric aggregation with an offset was found to have the greatest divergence from geometric aggregation with no offset if half of the indicators were set at a normalised value of 1, and the other half were reduced to zero. The effect on the index using geometric aggregation was negligible for values of ε ≤ 0.0001 (Fig. 4). The effect on the index using harmonic aggregation with an offset ε = 0.0001 was also found to be negligible (Fig. 5). The effect on the index using DBR aggregation with ε = 0.0001 was negligible, and there was no visible difference between using an offset and not using an offset. Hence it was found that offsets can be included in these aggregation methods without significantly changing their behaviour. An offset of ε = 0.0001 was then used with all three aggregation methods to rank the cities in both data sets. The use of the offset enabled the ranking operation to be maintained when using the non-compensatory methods even when one of the normalised indicator values was zero. For the first data set, the ranking of cities was found to differ significantly when aggregation methods other than arithmetic were used (Table 1). Compared to arithmetic aggregation, the city of London benefited most from the transition from maximisation to constraint, rising in ranking from fifth to second using geometric and harmonic aggregation, and gaining first place using modified DBR aggregation with λ ≤ 0.01. Sao Paulo suffered the most, dropping four places using harmonic aggregation, two places using geometric aggregation and one place using modified DBR aggregation with λ ≤ 0.27. Next came Vancouver, dropping three places using harmonic aggregation, two places using geometric aggregation and modified DBR aggregation with λ ≤ 0.16, and one place with modified DBR aggregation when 0.16 < λ ≤ 0.53. Tokyo lost two places using harmonic aggregation only, maintaining the same rank otherwise. Johannesburg and Beijing both gained one place and New York gained two places using harmonic aggregation only. Sydney gained one place using harmonic aggregation, and lost one place using modified DBR aggregation with λ ≤ 0.35. Stockholm was ranked either first or second, and Beijing was ranked either last or second last with harmonic aggregation. The only city to maintain the same ranking using every aggregation method was middle ranking Mexico city. As λ decreased from a value of 1 (fully compensatory), the modified DBR aggregation method changed from having the same ranking as the arithmetic method (expected because they are identical when λ = 1) to approaching the ranking of the geometric method (partially
Inclusion of the offset term ε ensures that the index retains a very small amount of compensation even when λ = 0. If one or more indicators is zero, but not all, then the value of the index Ij remains above zero. Division by 1 + ε ensures that the maximum possible value of the index Ijmax (when all rij = 1) remains 1 for any value of λ. Division of the arithmetic component by the sum of the weights ensures that the maximum value of this component is 1, regardless of the weighting system used. We call this equation modified DBR aggregation. We will examine the effect of using these different non-compensatory aggregation methods on the ranking of city sustainability. 3. Proposed method In this study two data sets will be analysed. The first is the city indicator data provided by Tan et al. (2017) which will be used to compare the ranking of ten cities based on 20 different indicators. The second is from UNDP (2015b) and will be used to compare the rankings of 35 cities based on 13 indicators. These data sets have been chosen because the raw indicator values are available for both, and hence alternate weighting and aggregation methods can be applied independently of the original studies. The indicator values for the first data set were measured over a timescale of one year (mainly 2012). The timescale of the indicator values for the second data set is not explicitly stated although a timescale of one year is implied (mainly 2014). However, timescale is not a limiting factor in this analysis, and the proposed methodology can be applied to data of any timescale. Weighting values for the indicators will be calculated according to the entropy method, and normalised values of the indicators will used so that indicators of positive and negative polarity can be combined. Four different methods of aggregation: arithmetic, geometric, harmonic and DBR, will be used to calculate a final composite index for each city, and then the cities will be ranked according to these indices. To compare different aggregation methods, the index will be normalised to a range from 0 to 100 by dividing by the maximum possible value of the index, Ijmax:
Index j = 100
Ij I j max
(18)
where Rxj is the rank (or order) of city j under aggregation method x, and Ryj is the rank under method y. In other words, the more cities that have a different rank, and the further the ranks are apart, then the lower the similarity score. Two aggregation methods that generate identical city ranks will have a similarity score of 100.
m
∑ wi rij/ ∑ wi⎞⎟ i=1
m
⎛ ∑ (Rxj − Ryj ) ⎞ ⎟ ⎜ j=1 Sxy = 100 1 − 2 ⎜ (m − 1)2 ⎟ ⎟ ⎜ ⎠ ⎝
(17)
An arithmetic offset will be added to the geometric, harmonic and DBR aggregation calculations according to equations (12), (14) and 5
Ecological Indicators 112 (2020) 106076
D. Laslett and T. Urmee
Fig. 4. Effect on index value with geometric aggregation for different offsets ε, with half the indicators reduced toward a normalised value of zero.
Fig. 5. Effect on index value with harmonic aggregation for different offsets ε, with half the indicators reduced toward a normalised value of zero. Table 1 Sustainability ranking of 10 cities using four different aggregation methods. Aggregation method Rank 1 2 3 4 5 6 7 8 9 10
Arithmetic
Geometric with offset
Harmonic with offset
Modified DBR (λ = 0.53)
Modified DBR (λ = 0.35)
Modified DBR (λ = 0.27)
Modified DBR (λ = 0.16)
Modified DBR (λ = 0.01)
Vancouver Stockholm Sao Paulo Sydney London Mexico city New York Tokyo Johannesburg Beijing
Stockholm London Vancouver Sydney Sao Paulo Mexico city New York Tokyo Johannesburg Beijing
Stockholm London Sydney Vancouver New York Mexico city Sao Paulo Johannesburg Beijing Tokyo
Stockholm* Vancouver* Sao Paulo Sydney London Mexico city New York Tokyo Johannesburg Beijing
Stockholm Vancouver Sao Paulo London* Sydney* Mexico city New York Tokyo Johannesburg Beijing
Stockholm Vancouver London* Sao Paulo* Sydney Mexico city New York Tokyo Johannesburg Beijing
Stockholm London* Vancouver* Sao Paulo Sydney Mexico city New York Tokyo Johannesburg Beijing
London* Stockholm* Vancouver Sao Paulo Sydney Mexico city New York Tokyo Johannesburg Beijing
City indicator data taken from Tan et al. (2017). For the modified DBR method, * indicates a change in ranking compared to the next left column, or compared to Arithmetic aggregation for λ = 0.53.
6
Ecological Indicators 112 (2020) 106076
80.25 90.12 65.43
Arithmetic
Geometric with offset
Harmonic with offset
Arithmetic with offset Geometric with offset Harmonic with offset
100 78.89 78.2
78.89 100 85.12
78.2 85.12 100
95.06 85.19 60.49
90.12 85.19 60.49
85.19 90.12 65.43
80.25 95.06 70.37
constraining). There was just one difference in ranking between DBR and geometric (Sao Paulo and Sydney swapped) when λ = 0.16, and there were just two differences in ranking between DBR and geometric (London and Stockholm swapped, and Sao Paulo and Sydney swapped) with λ = 0.01 down to λ = 0. At λ = 0, the modified DBR method is considered to be fully non-compensatory, while for any value of λ > 0, the DBR method is considered to be partially non-compensatory. These findings show that the choice of aggregation method has the potential to significantly change the ranking of cities, and could make the conclusions more ambiguous if more than one aggregation method were used, with varying constraint characteristics. Since more than one city changed rank by more than one place when geometric or harmonic aggregation was used, the findings of other ranking systems that use arithmetic aggregation, such as Moreno and Murgula (2015) and Arcadis (2016) might be different if these other aggregation methods were used. More generally, these results imply that there will be significant implications for the > 85% of index studies in the published literature surveyed by Gan et al. (2017) that used arithmetic aggregation, and all studies using ranking systems that do not address the constraint characteristics of the indicators they use. When compared to the arithmetic aggregation method, the similarity score for the harmonic method (S = 55.56) was lower than the geometric method (S = 80.2). The similarity score between these two methods was S = 75.31 (Table 2). For λ ≤ 0.27, the geometric method was more similar to the modified DBR method than either the arithmetic or harmonic methods, indicating that this method may have the most non-compensation of all the fixed methods studied here. There was a peak in similarity for both the geometric and harmonic methods as λ reduced from 1 to 0.16, followed by a drop off for λ ≤ 0.01. Generally the harmonic method was the most dissimilar method to all the others. The second data set had many more cities, so the similarity score was used to compare the ranking using the different aggregation methods. It was found that the arithmetic and geometric methods had a similarity score of 78.89, while the arithmetic and harmonic methods had a slightly lower similarity score of 78.2 (Table 3). The similarity score between geometric and harmonic was 85.12, indicating that for this data set, the geometric and harmonic methods were more similar to each other than to the arithmetic data set. As the value of λ decreased, the similarity between the arithmetic method and the modified DBR method decreased, as expected (Fig. 6). The similarity scores between the geometric and harmonic methods and the modified DBR method both rose as λ decreased, until the value of λ was around 0.51 for the geometric method and 0.16 for the harmonic method, then the similarity scores decreased as λ decreased further. This peak in similarity is similar to the pattern found with the first data set, but at different values of λ. Comparison of the results from both data sets indicated that it would be simplistic to say that two aggregation methods are more similar than a third, for example. The similarity has a dependence on the data set being used.
City indicator data taken from Tan et al. (2017).
55.56 75.31 100 100 80.25 55.56 Arithmetic with offset Geometric with offset Harmonic with offset
80.25 100 75.31
Modified DBR (λ = 0.53) Harmonic with offset
Aggregation method
City indicator data taken from UNDP (2015b).
Arithmetic
Geometric with offset
Table 3 Similarity score for sustainability ranking of 35 cities using three different fixed aggregation methods.
Aggregation method
Table 2 Similarity score for sustainability ranking of 10 cities using four different aggregation methods.
Modified DBR (λ = 0.35)
Modified DBR (λ = 0.27)
Modified DBR (λ = 0.16)
Modified DBR (λ = 0.01)
D. Laslett and T. Urmee
5. Conclusion We have shown that the aggregation method has a material effect 7
Ecological Indicators 112 (2020) 106076
D. Laslett and T. Urmee
Fig. 6. Ranking similarity of the arithmetic, geometric and harmonic aggregation methods to the modified DBR aggregation method with compensation parameter λ. Rankings used indicator data for 35 cities from UNDP (2015b).
CRediT authorship contribution statement
on city rankings, and if the principle of strong sustainability is to be followed, then this cannot be ignored. By using a small arithmetic offset, we have shown a way to make the use of geometric mean and harmonic mean aggregation more practical, and these aggregation methods should be preferred over the use of arithmetic aggregation for city sustainability rankings. The modified DBR method provides a mechanism for coarse control between maximisation and constraint, but using pure constraint can prevent ranking of the worst performing cities. Using a small arithmetic offset also overcame this limitation. Further algorithmic development of aggregation methods is needed so that the transition from maximisation to constraint can be controlled for each indicator individually. The results of this study show that the research scope of ranking system studies can be extended by considering different aggregation methods, with more or less degree of constraint. The similarity score could be used to assess the sensitivity of ranking systems to the type of aggregation method used. Consideration of aggregation method should not be seen as merely a mathematical novelty, but as relevant to the measurement of sustainability and becoming essential as the use of city ranking systems gain more prominence and importance. The use of non-compensatory aggregation methods, that reflect stronger sustainability, means that shortcomings or lack of progress illuminated by one or a few indicators are less likely to be hidden within the majority swathe of indicators that are showing an overall positive status or progress. This gives impetus to cities that are aiming to be seen as sustainable, and are ranked against other cities, to address weaknesses that are dragging down their ranking rather than further developing existing strengths in order to compensate for the weaknesses. So even though different cities might focus their sustainability monitoring and management effort in different ways, there would be a tendency toward more balanced progress overall within each city. It is hoped that this study, by improving the usability of non-compensatory aggregation methods in city ranking systems, will further enable this balanced approach to sustainability, such that city rankings become a valid tool for sustainable urban planning, and not just a competition between cities. The techniques developed here might also be extended to index based ranking systems in other areas of study that have predominantly used compensatory aggregation methods.
Dean Laslett: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Writing original draft, Writing - review & editing, Visualization. Tania Urmee: Investigation, Writing - original draft, Writing - review & editing, Visualization, Supervision, Project administration. Acknowledgement Associate professor Urmee would like to acknowledge HanseWissesschaftskolleg (HWK), Germany, for initiating this research. References Anthopoulos, L., 2017. Smart utopia VS smart reality: Learning by experience from 10 smart city cases. Cities 63, 128–148. https://doi.org/10.1016/j.cities.2016.10.005. Anttiroiko, A.-V., 2015. City Branding as a Response to Global Intercity Competition: Global Intercity Competition. Growth Change 46, 233–252. https://doi.org/10.1111/ grow.12085. Arcadis,, 2016. Sustainable Cities Index 2016. Putting People at the Heart of City Sustainability, Arcadis Design and Consultancy for natural and built assets, Amsterdam. Bartelmus, P., 2013. The future we want: green growth or sustainable development? Environ. Dev. 7, 165–170. https://doi.org/10.1016/j.envdev.2013.04.001. Berrone, P., Ricart, J.E., 2016. IESE Cities in Motion Index. University of Navarra, Pamplona. Bowen, A., Hepburn, C., 2014. Green growth: an assessment. Oxf. Rev. Econ. Policy 30, 407–422. https://doi.org/10.1093/oxrep/gru029. Cohen, M., 2017. A Systematic Review of Urban Sustainability Assessment Literature. Sustainability 9, 2048. https://doi.org/10.3390/su9112048. Dizdaroglu, D., 2017. The Role of Indicator-Based Sustainability Assessment in Policy and the Decision-Making Process: A Review and Outlook. Sustainability 9, 1018. https:// doi.org/10.3390/su9061018. Dı́az-Balteiro, L., Romero, C.,, 2004. In search of a natural systems sustainability index. Ecol. Econ. 49, 401–405. https://doi.org/10.1016/j.ecolecon.2004.02.005. ECOSOC, 2017. Progress towards the Sustainable Development Goals. Report of the Secretary-General, United Nations Economic and Social Council, New York. Gan, X., Fernandez, I.C., Guo, J., Wilson, M., Zhao, Y., Zhou, B., Wu, J., 2017. When to use what: Methods for weighting and aggregating sustainability indicators. Ecol. Indic. 81, 491–502. https://doi.org/10.1016/j.ecolind.2017.05.068. GGKP, 2013. Moving towards a Common Approach on Green Growth Indicators. Green Growth Knowledge Platform, Switzerland. Giffinger, R., Haindlmaier, G., Kramar, H., 2010. The role of rankings in growing city competition. Urban Res. Pract. 3, 299–312. https://doi.org/10.1080/17535069. 2010.524420. Gurría, A., 2012. Green Growth: Making it Happen [WWW Document]. Organ. Econ. CoOper. Dev. https://www.oecd.org/greengrowth/greengrowthmakingithappen.htm (accessed 7.3.19).
8
Ecological Indicators 112 (2020) 106076
D. Laslett and T. Urmee
indicator development—Science or political negotiation? Ecol. Indic. 11, 61–70. https://doi.org/10.1016/j.ecolind.2009.06.009. Shannon, C.E., 1948. A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423. https://doi.org/10.1002/j.1538-7305.1948.tb01338.xx. Shen, L., Zhou, J., Skitmore, M., Xia, B., 2015. Application of a hybrid Entropy–McKinsey Matrix method in evaluating sustainable urbanization: A China case study. Cities 42, 186–194. https://doi.org/10.1016/j.cities.2014.06.006. Smits, J.P., Hoekstra, R., 2011. Measuring Sustainable Development and Societal Progress: Overview and Conceptual Approach. Statistics Netherlands (Centraal Bureau voor de Statistiek), Den Haag. Statistics Netherlands, 2013. Sustainable Development and Green Growth: Comparison of the Measurement Frameworks at Statistics Netherlands. Centraal Bureau voor de Statistiek (CBS), Den Haag. Tan, S., Yang, J., Yan, J., Lee, C., Hashim, H., Chen, B., 2017. A holistic low carbon city indicator framework for sustainable development. Appl. Energy 185, 1919–1930. https://doi.org/10.1016/j.apenergy.2016.03.041. UNDP, 2015a. Sustainable Development Goals. United Nations Development Program, New York. UNDP, 2015b. China Sustainable Cities Report. Measuring Ecological Input and Human Development, United Nations Development Program, China. UNEP, 2014. Using Indicators for Green Economy Policymaking. United Nations Environment Program, Nairobi. United Nations, 2015. Resolution adopted by the General Assembly on 25 September 2015. Transforming our world: the 2030 Agenda for Sustainable Development. New York. van Zoonen, L., 2016. Privacy concerns in smart cities. Gov. Inf. Q. 33, 472–480. https:// doi.org/10.1016/j.giq.2016.06.004. Wang, T.-C., Lee, H.-D., 2009. Developing a fuzzy TOPSIS approach based on subjective weights and objective weights. Expert Syst. Appl. 36, 8980–8985. https://doi.org/10. 1016/j.eswa.2008.11.035. WCED, 1987. Report of the World Commission on Environment and Development: Our Common Future. Oxford University Press, Oxford. World Bank, 2012. Inclusive Green Growth. The Pathway to Sustainable Development. International Bank for Reconstruction and Development, Washington DC.
Holden, M., Moreno Pires, S., 2015. The minority report: social hope in next generation indicators work. Commentary on Rob Kitchin et al’.s ‘Knowing and governing cities through urban indicators, city benchmarking, and real-time dashboards’. Reg. Stud. Reg. Sci. 2, 33–38. https://doi.org/10.1080/21681376.2014.987541. Kitchin, R., Lauriault, T.P., McArdle, G., 2015. Knowing and governing cities through urban indicators, city benchmarking and real-time dashboards. Reg. Stud. Reg. Sci. 2, 6–28. https://doi.org/10.1080/21681376.2014.983149. Langhans, S.D., Reichert, P., Schuwirth, N., 2014. The method matters: a guide for indicator aggregation in ecological assessments. Ecol. Indic. 45, 494–507. https://doi. org/10.1016/j.ecolind.2014.05.014. Marsal-Llacuna, M.-L., Colomer-Llinàs, J., Meléndez-Frigola, J., 2015. Lessons in urban monitoring taken from sustainable and livable cities to better address the Smart Cities initiative. Technol. Forecast. Soc. Change 90, 611–622. https://doi.org/10.1016/j. techfore.2014.01.012. Mazziotta, M., Pareto, A., 2016a. Methods for Constructing Non-Compensatory Composite Indices: A Comparative Study. Forum Soc. Econ. 45, 213–229. https://doi. org/10.1080/07360932.2014.996912. Mazziotta, M., Pareto, A., 2016b. On a Generalized Non-compensatory Composite Index for Measuring Socio-economic Phenomena. Soc. Indic. Res. 127, 983–1003. https:// doi.org/10.1007/s11205-015-0998-2. Moreno, E.L., Murgula, R.O., 2015. The City Prosperity Initiative. Global City Report. UNHabitat, Nairobi. Mori, K., Yamashita, T., 2015. Methodological framework of sustainability assessment in City Sustainability Index (CSI): a concept of constraint and maximisation indicators. Habitat Int. 45, 10–14. https://doi.org/10.1016/j.habitatint.2014.06.013. Narloch, U., Kozluk, T., Lloyd, A., 2016. Measuring Inclusive Green Growth at the Country Level. Taking Stock of Measurement Approaches and Indicators. Green Growth Knowledge Platform, Switzerland. Phillis, Y.A., Kouikoglou, V.S., Verdugo, C., 2017. Urban sustainability assessment and ranking of cities. Comput. Environ. Urban Syst. 64, 254–265. https://doi.org/10. 1016/j.compenvurbsys.2017.03.002. Pollesch, N., Dale, V.H., 2015. Applications of aggregation theory to sustainability assessment. Ecol. Econ. 114, 117–127. https://doi.org/10.1016/j.ecolecon.2015.03. 011. Rametsteiner, E., Pülzl, H., Alkan-Olsson, J., Frederiksen, P., 2011. Sustainability
9
Contents lists available at ScienceDirect
Ecological Indicators journal homepage: www.elsevier.com/locate/ecolind
The effect of aggregation on city sustainability rankings ⁎
T
Dean Laslett , Tania Urmee Murdoch University, Australia
A R T I C LE I N FO
A B S T R A C T
Keywords: City sustainability indicator Sustainability index City ranking Aggregation method
Although sustainability is a multifactorial concept, many sustainability indexes use weighted additive aggregation of sets of different indicators to derive a single index which can be used to rank different cities. One of the limitations of this approach is that a poor or low rating in one area can be compensated by a strong or high rating in another area. However sustainability cannot be measured linearly. There is at least a triple bottom line: environmental, social and economic. To be truly sustainable, a city must be sustainable in all areas. A deficiency in one area is likely to have a negative effect in larger proportion than suggested by the magnitude of the deficiency. Conversely, a strong result in an indicator is likely to have less effect on overall sustainability than its magnitude suggests. The concept of constraint and maximisation indicators has been proposed to represent this property of sustainability. We investigate the effect on city rankings of using aggregations that aim to represent the constraint and maximisation properties of sustainable development indicators, compared to the commonly used arithmetic (linear) aggregation. Three such aggregation methods (geometric, harmonic and an adjustable compensation method) can cause difficulties with ranking if one or more of the individual indices have a zero normalised value. We show that the use of a small offset can avoid this problem and enable practical use of these aggregation methods to better capture the nature of sustainability. We also formulate a similarity score for different ranking systems that compare a large number of cities.
1. Introduction Sustainable development is a conceptual framework that seeks to capture all aspects that are needed for welfare in the “here and now”, “later” and “elsewhere” dimensions (Smits and Hoekstra, 2011). This framework has recently been clarified through the adoption by the United Nations of the 17 sustainable development Goals and 169 targets (United Nations, 2015). Goal 11 is sustainable cities and communities, which states “Make cities and human settlements inclusive, safe resilient and sustainable” (UNDP, 2015a). The world has experienced unprecedented urban growth in recent years. According to the United Nations, the projected number of people living in cities will increase to 5 billion by the end of 2030 (ECOSOC, 2017). Another concept related to cities, “green growth”, has been developed and generally refers to economic growth that not only preserves but enhances the natural resources we have inherited (Gurría, 2012). A social dimension is often included in this concept of growth, in that environmentally sound economic growth must also improve the well being of people. The resulting approach is more comprehensively known as inclusive green growth (World Bank, 2012). Green growth arose from the realisation that typically the green elements (mainly
⁎
natural capital) are the most oppressed due to economic development and therefore should be the focus for policy development and monitoring (Statistics Netherlands, 2013). Green growth is not a new paradigm, instead, it is an operational strategy to reconcile the urgent need for growth while avoiding irreversible far-reaching environmental consequences. This should also be done in such a way as to alleviate poverty. That is, green growth is a “modus operandi” to implement the sustainable development paradigm which is “growth that is forceful and at the same time socially and environmentally sustainable” (WCED, 1987). The concept of green growth is considered to have global strategic merit by forming a narrative about opportunities through collective action that might change the dynamics of international negotiations (Bowen and Hepburn, 2014). Bartelmus (2013) argues that sustainable development policy focus should concentrate on the parameters of green growth because they are more measurable compared to the more abstract and qualitative concepts of sustainable development itself, and therefore initiatives are more assessible. The scope of measurability is being extended to encompass inclusive green growth (Narloch et al., 2016), 1 and the synergies between green growth/green economy strategies and sustainable development become more evident when evaluating how green
Corresponding author. E-mail address: [email protected] (D. Laslett).
https://doi.org/10.1016/j.ecolind.2020.106076 Received 17 September 2018; Received in revised form 25 November 2019; Accepted 5 January 2020 1470-160X/ © 2020 Elsevier Ltd. All rights reserved.
Ecological Indicators 112 (2020) 106076
D. Laslett and T. Urmee
Once an index is established, comparisons and rankings between different cities can be made. Many different city sustainability index systems have been identified in the literature (Cohen, 2017). Three examples of city sustainability index systems which are notable because of their global scope are the “City Prosperity” index, the “Sustainable Cities” index and the “Cities in Motion” index. The United Nations City Prosperity index is based on productivity, infrastructure development, quality of life, equity and social inclusion, environmental sustainability, and governance and legislation (Moreno and Murgula, 2015). The Sustainable Cities index is based on the three pillars of sustainability: people, profit and planet. This index combines indicators measuring the social, environmental, and economic dimensions of sustainability (Arcadis, 2016). The Cities in Motion index was developed by the university of Navarra IESE business school. This index evaluated indicators grouped into the areas of economy, technology, human capital, social cohesion, international outreach, environment, mobility and transportation, urban planning, public management and governance to measure the performance of cities (Berrone and Ricart, 2016). The use of indicators, composite indexes and ranking is increasingly used to inform city policy (Giffinger et al., 2010). Recently, there has been a trend toward real time representation using visualisation aids, or “dashboards”, that are available to the general population as well as policy makers, planners and managers. Thus, indicators and indexes are also now influencing how a city is imagined (Kitchin et al., 2015). One example is the trend for cities to brand themselves as a “smart city” or “smart sustainable city”, based partly on a favourable city ranking (Anthopoulos, 2017). The concept of a smart city is based on sustainability and quality of life, but adds technological and informational dimensions (Marsal-Llacuna et al., 2015). The ongoing information revolution has enabled more frequent and comprehensive monitoring of sustainability and other smart city indicators, generating massive amounts of data (van Zoonen, 2016). Thus there is an increasing need to generate, in a timely fashion, composite indexes that help to give a more understandable overview of the data, both to city managers and the public dashboards. However, despite the growing importance of indicators, indexes and ranking systems, consensus has not been reached on their objectivity. Giffinger et al. (2010) found that the objectivity of city ranking systems has a dependency on the calculation method (which includes aggregation). For example, the three index systems described above can rank the same cities in different orders. Stockholm is ranked above Zurich by the City Prosperity index, while it is ranked lower than Zurich by the Sustainable Cities index and the Cities in Motion index. Melbourne is ranked above Madrid by the City Prosperity index and the Cities in Motion index, but ranked below Madrid by the Sustainable Cities index. Holden and Moreno Pires (2015) argue that data and indicator systems can never be entirely objective, but they have the potential to force greater transparency and accountability into decision making processes, and ignoring them could lead to worse outcomes for cities. So greater understanding of their scope and limitations should be sought. This study takes one small step toward that goal by examining the effect of aggregation on city sustainability rankings.
Fig. 1. Comparison between green growth and sustainable development.
interventions in the economy interact with society and the environment (UNEP, 2014). A useful comparison of the interaction between green growth in cities and sustainable development is shown in Fig. 1.To evaluate various aspects of urban development including inclusive green growth and sustainable development, it is common to compare the performance of different cities, and rank them against each other. These rankings are seen as becoming increasingly important as cities find ways to distinguish themselves in competition with each other, in order to attract high value adding services and industries (Anttiroiko, 2015). The majority of city ranking systems use indicators. An indicator aims to quantify or measure a particular aspect of the city, either directly or indirectly. Indicators are now seen as fundamental in the provision of information to inform development, implementation and assessment of policies and decision making (Dizdaroglu, 2017). The growing effort to develop policy initiatives that promote sustainable development has driven the need for new indicators based on the principles of inclusive green growth (GGKP, 2013). To this end numerous initiatives have been implemented to develop specific indicators that adequately capture the economy-environment nexus in the context of an equitable social dimension (Rametsteiner et al., 2011). An example that illustrates the complexity involved in selecting a comprehensive set of indicators, and the interaction between indicators and initiatives, is the approach taken by the United Nations Environmental Program (UNEP). UNEP does not provide a single list of indicators, but instead provides guidance on selection of relevant indicators throughout an integrated policy making cycle. Specifically, emphasis is placed on three stages where indicators are relevant (UNEP, 2014):
• Issue identification and agenda settings • Policy formation and policy assessment, and • Monitoring and evaluation The indicators used in the first stage are chosen to identify and prioritise problems to be addressed by policy. Indicators for problem identification help frame the issue, and indicators for policy formulation help design initiatives, impact indicators estimate the cross-sectoral impacts of initiatives chosen, while indicators for policy monitoring and evaluation support the assessment of the initiative implemented. However, the large swath of indicators used in setting and evaluating policy in the UNEP approach does not facilitate straightforward understanding or comparison. Similarly, the framework of indicators used by other organisations such as the World Bank, the Organisation for Economic Co-operation and Development, the United Nations Economic and Social Commission for Asia and the Pacific, and the Green Growth Knowledge Platform are cumbersome when communicating green growth progress or lack thereof with policy makers, stakeholders and the community. To overcome these challenges, significant efforts have been undertaken to develop a summary indicator or approach (often called an “index”) for communicating the current status of green growth. An index is formed by combining (or “aggregating”) several indicators together using a systematic methodology.
2. Background As can be seen from the different examples given in the introduction, there is no universal method for the compilation of a single composite index from a number of different indicators (Mazziotta and Pareto, 2016a). Mori and Yamashita (2015) introduced the concept of constraint and maximisation factors. A pure constraint factor confines sustainability within environmental and socioeconomic limits and sustainability cannot be achieved if any one constraint factor is poor. A pure maximisation factor increases benefits within the limits but is not critical. In reality, most factors will be a mixture of both, and a maximisation factor is likely to take on the properties of a constraint factor 2
Ecological Indicators 112 (2020) 106076
D. Laslett and T. Urmee
rij =
x ij − minj (x ij ) maxj (x ij ) − minj (x ij )
(3)
and for negative indicators:
rij =
maxj (x ij ) − x ij maxj (x ij ) − minj (x ij )
(4)
Sometimes an additional standardisation step is used, whereby the values of the normalised indicators are adjusted so that their overall sum is 1. The standardised value of the indicator i measured at city j, fij, is given by:
fij =
rij n
∑ rij
(5)
j=1
To form a single index, several indicators are combined (aggregated) together with different (but invariant) weights implying different relative importance. One method for deciding what values the weights should take is to use the concept of entropy. In the field of information theory, Shannon (1948) developed an entropy measure of the uncertainty of alternative states. Entropy is maximised when all alternative states have a similar probability, and uncertainty over which state will be chosen is greatest. Recently, Shannon entropy theory has been adapted to calculation of weights for indexing systems, the idea being that a higher variation (lower “entropy”) in the reported values of an indicator means this indicator is more important and should receive a greater weight relative to other indicators (Wang and Lee, 2009). In the context of sustainability indicators, the entropy function Hi for the ith indicator can be defined as:
Fig. 2. The steps required to compile a single index from raw indicator values. Figure derived from Langhans et al. (2014), Shen et al. (2015), Mazziotta and Pareto (2016a) and Tan et al. (2017).
as its value becomes poorer and other sectors of the ecological, economic and social systems of the city are more and more affected. Mori and Yamashita (2015) also linked this paradigm to strong sustainability, where weakness in one factor (i.e. a value that indicates a lack of sustainability) cannot be substituted by strength in another. All must be strong for the city to be truly sustainable. In contrast, with weak sustainability, one attribute can be compensated with another. Therefore strong sustainability requires that all factors become constraint factors if their values are weak. An implication of using factors with constraint is that the most important indicators for determining sustainability could be different for different cities. For example, Phillis et al. (2017) found that municipal waste generation and greenhouse gas emissions were the main constraints for cities in developed countries, whereas crime and poverty were the main constraints for cities in developing countries. However, it is common for sustainable development indicators to be added linearly when composing an index, indicating weak sustainability (Gan et al., 2017). The compilation of a single index from a large set of indicators can be complex and require several steps (Fig. 2). Since indicators are measuring different facets of sustainability they are likely to have a widely varying range of values. Therefore a process of normalisation must be performed before different indicators can be related to each other. Different normalisation methods can be used. For a set of m indicators applied to n cities, Shen et al. (2015) used the following equation to normalise positive indicators:
rij =
Hi =
(6)
m
⎛⎜m − ∑ H ⎟⎞ i i=1 ⎝ ⎠
(7)
where wi is the weighting for indicator i and m is the total number of indicators. The weightings have the property that:
(1)
m
∑ wi = 1 i=1
(8)
Commonly, the overall index is formed by weighted arithmetic aggregation of the standardised indicator values (Mazziotta and Pareto, 2016a):
minj (x ij ) x ij
j=1
(1 − Hi )
wi =
where rij is the normalised value of indicator i at city j, xij is the unnormalised (raw) value of the indicator and maxj(xij) is the maximum value of indicator i over the range of j from 1 to n. For negative indicators, Shen et al. (2015) used:
rij =
n
∑ fij ln fij
If fij is zero, then fijlnfij is set to zero. As a simple conceptual illustration, an indicator measured at two cities has the form of its entropy function Hi shown in Fig. 3. fi refers to the normalised indicator value in the first location. Because there are only two cities considered, the standardised value for the indicator at the second location will be 1-fi. If the two indicator values are the same (fi = 0.5), then the entropy function will be maximised. If the two indicator values are different, then the entropy function is minimised. Therefore the variability in the measured values of an indicator is maximised when the entropy is minimised, and if the indicator is one part of a composite index, then the “objective” importance, or weighting, assigned to this indicator can be quantified using:
x ij maxj (x ij )
1 ln(n)
m
(2)
Ij =
∑ wi fij i=1
where minj(xij) is the minimum value of indicator i over the same range. However this causes difficulty if the minimum is zero, or the raw value of the indicator xij is zero. Tan et al. (2017) took a more linear and relative approach. For positive indicators, the authors used:
(9)
where Ij is the index for city j. Weighted arithmetic aggregation of the normalised indicator values has also been used, for example in Tan et al. (2017): 3
Ecological Indicators 112 (2020) 106076
D. Laslett and T. Urmee
Fig. 3. Entropy function of an indicator with two standardised values. fi denotes the first value. The second value will be 1 – fi.
Ij =
1 m
m
∑ wi rij i=1
Pareto, 2016b). The introduction described several examples of indexes being used to rank the sustainability performance of different cities compared to each other. However there is also a potential shortcoming if geometric aggregation is used for this purpose. A normalised value of zero in any one of the indicator values will generate an overall index value of zero, regardless of the values of the other indicators, which is purely noncompensatory. However, if this occurs in more than one city (even with different indicators that are zero), it will be impossible to rank those cities compared with each other. Both will have an index of zero, even though one city may perform better in other areas. This is perhaps one reason why geometric aggregation is not used more often when ranking city sustainability. This effect can be avoided if a small arithmetic offset ε is introduced into the geometric mean calculation:
(10)
While the entropy technique provides a systematic method for assigning weights, the actual importance of each indicator is not represented. The indicator with the greatest variability is given the highest weight, regardless of its importance. Also if the overall index is formed in a way similar to equations 9 or 10, then there is no transition between maximisation and constraint as the normalised value of the indicator decreases. A number of non-linear aggregation methods have been formulated that may better represent this transition. The simplest of these is the use of a geometric aggregation rather than an arithmetic one: m
Ij =
m
∏ wi rij i=1
(11)
⎛ Ij = ⎜m ⎝
Equations (10) and (11) are equivalent to the arithmetic mean and geometric mean respectively. Since the magnitudes of the wi and rij terms are always less than or equal to 1, the geometric mean is always less than or equal to the arithmetic mean, and is only equal if all of the weighted terms wirij are identical. As one or more of the weighted terms become lower than the others, then the geometric mean becomes less than the arithmetic mean (Mazziotta and Pareto, 2016a), which fits the concept of a transition from maximisation to constraint if an indicator decreases. Like arithmetic aggregation, geometric aggregation requires that all of the weighted terms are zero or positive, and have the same polarity, so for a mix of positive and negative indicators, the normalisation process must transform one polarity into the other. Aggregation methods can be classified according to their degree of compensation, which is related to the concepts of maximisation and constraint factors, and weak and strong sustainability, described above. With a fully compensatory aggregation method, a weak or low value in one or more indicators can be compensated by strong or high values in other indicators. With a fully non-compensatory aggregation method, there is no compensation. A weak or low value will drag down the value of the index. A partially non-compensatory aggregation method lies somewhere in between these two limits. If maintaining the trajectory of inclusive green growth requires adherence to strong sustainability, then the use of non-compensatory aggregation methods are required for indices that are formed with the purpose of measuring an aspect of inclusive green growth. These aggregation methods can also give impetus to using a more balanced and comprehensive approach to management of sustainability goals, as the weakest indicators must be improved in order to raise the value of the overall composite index (Mazziotta and
m
⎞
∏ (ε + wi rij ) ⎟ − ε ⎠
i=1
(12)
Therefore if the normalised value of one (or more) indicators is zero, then the root term does not become zero, but has a minimum value of ε when all the indicators are at their minimum possible normalised value (rij = 0 for all i). The offset is subtracted outside the root term so that in this case the effect of the offset is cancelled out, and the minimum value of Ij is still 0. Another non-compensatory aggregation method is the harmonic mean (Langhans et al., 2014):
Ij =
1 m
∑ i=1
wi rij
(13)
If the value of any one of the normalised indicator values is zero, then the denominator of equation (13) becomes infinite, and the value of the index is set to zero. Hence the harmonic mean has the same ranking limitation as just described for the geometric mean, and similarly, this effect can be avoided if a small offset ε is introduced into the harmonic mean calculation:
Ij =
1 m
∑ i=1
wi ε + rij
−
ε m
∑ wi i=1
(14)
Therefore if the normalised value of one or more indicators is zero, but not all, then the denominator does not become infinite and the value of the index remains above zero. The subtraction of the offset divided by the sum of the weights ensures that if all the indicators are at 4
Ecological Indicators 112 (2020) 106076
D. Laslett and T. Urmee
(16) to obtain the modified forms. The effect of the offset on the behaviour of these methods will be examined by setting up an extreme situation where one half of the indicators have a normalised value of 1, and the other half are zero. For the modified DBR aggregation method, various values of λ between 0 and 1 will be tried, to find breakpoints where the city ranking suddenly changes. When rankings for a large number of cities are compared, tracking the rank for each individual city becomes less insightful. Therefore a score for the overall similarity, Sxy, between two aggregation methods x and y will be used. Sxy is formulated using the sum of the ranking differences for each individual city:
their minimum possible normalised value (rij = 0 for all i), then the effect of the offset is cancelled out, and the minimum value of Ij is still 0. It could be said that the degree of compensation for the arithmetic, geometric and harmonic methods is fixed, and cannot be controlled. In contrast, Diaz-Balteiro and Romero (2004) introduced an index (called the DBR index here) where the overall degree of compensation can be explicitly specified: m
I j = (1 − λ )[mini (wi rij )] + λ ∑ wi rij
(15)
i=1
where λ is the compensation parameter, ranging from 0 to 1. If λ = 1 then the index is the fully compensatory arithmetic mean. For any value of λ > 0, the DBR index is considered to be partially compensatory (Pollesch and Dale, 2015). If λ = 0 then the index is the fully noncompensatory minimum value of the weighted indicators, and at this value once again the DBR index suffers from the same ranking limitation identified with the geometric and harmonic aggregation methods, which again can be avoided if a small arithmetic offset ε is introduced. Also, Pollesch and Dale (2015) used a reformulation of the DBR equation that removes the weighting from the minimisation term. A combination of these two modifications yields:
Ij =
1 ⎛ (1 − λ )mini (rij ) + (λ + ε ) 1+ε⎜ ⎝
m
i=1
⎠
4. Results and discussion (16)
Geometric aggregation with an offset was found to have the greatest divergence from geometric aggregation with no offset if half of the indicators were set at a normalised value of 1, and the other half were reduced to zero. The effect on the index using geometric aggregation was negligible for values of ε ≤ 0.0001 (Fig. 4). The effect on the index using harmonic aggregation with an offset ε = 0.0001 was also found to be negligible (Fig. 5). The effect on the index using DBR aggregation with ε = 0.0001 was negligible, and there was no visible difference between using an offset and not using an offset. Hence it was found that offsets can be included in these aggregation methods without significantly changing their behaviour. An offset of ε = 0.0001 was then used with all three aggregation methods to rank the cities in both data sets. The use of the offset enabled the ranking operation to be maintained when using the non-compensatory methods even when one of the normalised indicator values was zero. For the first data set, the ranking of cities was found to differ significantly when aggregation methods other than arithmetic were used (Table 1). Compared to arithmetic aggregation, the city of London benefited most from the transition from maximisation to constraint, rising in ranking from fifth to second using geometric and harmonic aggregation, and gaining first place using modified DBR aggregation with λ ≤ 0.01. Sao Paulo suffered the most, dropping four places using harmonic aggregation, two places using geometric aggregation and one place using modified DBR aggregation with λ ≤ 0.27. Next came Vancouver, dropping three places using harmonic aggregation, two places using geometric aggregation and modified DBR aggregation with λ ≤ 0.16, and one place with modified DBR aggregation when 0.16 < λ ≤ 0.53. Tokyo lost two places using harmonic aggregation only, maintaining the same rank otherwise. Johannesburg and Beijing both gained one place and New York gained two places using harmonic aggregation only. Sydney gained one place using harmonic aggregation, and lost one place using modified DBR aggregation with λ ≤ 0.35. Stockholm was ranked either first or second, and Beijing was ranked either last or second last with harmonic aggregation. The only city to maintain the same ranking using every aggregation method was middle ranking Mexico city. As λ decreased from a value of 1 (fully compensatory), the modified DBR aggregation method changed from having the same ranking as the arithmetic method (expected because they are identical when λ = 1) to approaching the ranking of the geometric method (partially
Inclusion of the offset term ε ensures that the index retains a very small amount of compensation even when λ = 0. If one or more indicators is zero, but not all, then the value of the index Ij remains above zero. Division by 1 + ε ensures that the maximum possible value of the index Ijmax (when all rij = 1) remains 1 for any value of λ. Division of the arithmetic component by the sum of the weights ensures that the maximum value of this component is 1, regardless of the weighting system used. We call this equation modified DBR aggregation. We will examine the effect of using these different non-compensatory aggregation methods on the ranking of city sustainability. 3. Proposed method In this study two data sets will be analysed. The first is the city indicator data provided by Tan et al. (2017) which will be used to compare the ranking of ten cities based on 20 different indicators. The second is from UNDP (2015b) and will be used to compare the rankings of 35 cities based on 13 indicators. These data sets have been chosen because the raw indicator values are available for both, and hence alternate weighting and aggregation methods can be applied independently of the original studies. The indicator values for the first data set were measured over a timescale of one year (mainly 2012). The timescale of the indicator values for the second data set is not explicitly stated although a timescale of one year is implied (mainly 2014). However, timescale is not a limiting factor in this analysis, and the proposed methodology can be applied to data of any timescale. Weighting values for the indicators will be calculated according to the entropy method, and normalised values of the indicators will used so that indicators of positive and negative polarity can be combined. Four different methods of aggregation: arithmetic, geometric, harmonic and DBR, will be used to calculate a final composite index for each city, and then the cities will be ranked according to these indices. To compare different aggregation methods, the index will be normalised to a range from 0 to 100 by dividing by the maximum possible value of the index, Ijmax:
Index j = 100
Ij I j max
(18)
where Rxj is the rank (or order) of city j under aggregation method x, and Ryj is the rank under method y. In other words, the more cities that have a different rank, and the further the ranks are apart, then the lower the similarity score. Two aggregation methods that generate identical city ranks will have a similarity score of 100.
m
∑ wi rij/ ∑ wi⎞⎟ i=1
m
⎛ ∑ (Rxj − Ryj ) ⎞ ⎟ ⎜ j=1 Sxy = 100 1 − 2 ⎜ (m − 1)2 ⎟ ⎟ ⎜ ⎠ ⎝
(17)
An arithmetic offset will be added to the geometric, harmonic and DBR aggregation calculations according to equations (12), (14) and 5
Ecological Indicators 112 (2020) 106076
D. Laslett and T. Urmee
Fig. 4. Effect on index value with geometric aggregation for different offsets ε, with half the indicators reduced toward a normalised value of zero.
Fig. 5. Effect on index value with harmonic aggregation for different offsets ε, with half the indicators reduced toward a normalised value of zero. Table 1 Sustainability ranking of 10 cities using four different aggregation methods. Aggregation method Rank 1 2 3 4 5 6 7 8 9 10
Arithmetic
Geometric with offset
Harmonic with offset
Modified DBR (λ = 0.53)
Modified DBR (λ = 0.35)
Modified DBR (λ = 0.27)
Modified DBR (λ = 0.16)
Modified DBR (λ = 0.01)
Vancouver Stockholm Sao Paulo Sydney London Mexico city New York Tokyo Johannesburg Beijing
Stockholm London Vancouver Sydney Sao Paulo Mexico city New York Tokyo Johannesburg Beijing
Stockholm London Sydney Vancouver New York Mexico city Sao Paulo Johannesburg Beijing Tokyo
Stockholm* Vancouver* Sao Paulo Sydney London Mexico city New York Tokyo Johannesburg Beijing
Stockholm Vancouver Sao Paulo London* Sydney* Mexico city New York Tokyo Johannesburg Beijing
Stockholm Vancouver London* Sao Paulo* Sydney Mexico city New York Tokyo Johannesburg Beijing
Stockholm London* Vancouver* Sao Paulo Sydney Mexico city New York Tokyo Johannesburg Beijing
London* Stockholm* Vancouver Sao Paulo Sydney Mexico city New York Tokyo Johannesburg Beijing
City indicator data taken from Tan et al. (2017). For the modified DBR method, * indicates a change in ranking compared to the next left column, or compared to Arithmetic aggregation for λ = 0.53.
6
Ecological Indicators 112 (2020) 106076
80.25 90.12 65.43
Arithmetic
Geometric with offset
Harmonic with offset
Arithmetic with offset Geometric with offset Harmonic with offset
100 78.89 78.2
78.89 100 85.12
78.2 85.12 100
95.06 85.19 60.49
90.12 85.19 60.49
85.19 90.12 65.43
80.25 95.06 70.37
constraining). There was just one difference in ranking between DBR and geometric (Sao Paulo and Sydney swapped) when λ = 0.16, and there were just two differences in ranking between DBR and geometric (London and Stockholm swapped, and Sao Paulo and Sydney swapped) with λ = 0.01 down to λ = 0. At λ = 0, the modified DBR method is considered to be fully non-compensatory, while for any value of λ > 0, the DBR method is considered to be partially non-compensatory. These findings show that the choice of aggregation method has the potential to significantly change the ranking of cities, and could make the conclusions more ambiguous if more than one aggregation method were used, with varying constraint characteristics. Since more than one city changed rank by more than one place when geometric or harmonic aggregation was used, the findings of other ranking systems that use arithmetic aggregation, such as Moreno and Murgula (2015) and Arcadis (2016) might be different if these other aggregation methods were used. More generally, these results imply that there will be significant implications for the > 85% of index studies in the published literature surveyed by Gan et al. (2017) that used arithmetic aggregation, and all studies using ranking systems that do not address the constraint characteristics of the indicators they use. When compared to the arithmetic aggregation method, the similarity score for the harmonic method (S = 55.56) was lower than the geometric method (S = 80.2). The similarity score between these two methods was S = 75.31 (Table 2). For λ ≤ 0.27, the geometric method was more similar to the modified DBR method than either the arithmetic or harmonic methods, indicating that this method may have the most non-compensation of all the fixed methods studied here. There was a peak in similarity for both the geometric and harmonic methods as λ reduced from 1 to 0.16, followed by a drop off for λ ≤ 0.01. Generally the harmonic method was the most dissimilar method to all the others. The second data set had many more cities, so the similarity score was used to compare the ranking using the different aggregation methods. It was found that the arithmetic and geometric methods had a similarity score of 78.89, while the arithmetic and harmonic methods had a slightly lower similarity score of 78.2 (Table 3). The similarity score between geometric and harmonic was 85.12, indicating that for this data set, the geometric and harmonic methods were more similar to each other than to the arithmetic data set. As the value of λ decreased, the similarity between the arithmetic method and the modified DBR method decreased, as expected (Fig. 6). The similarity scores between the geometric and harmonic methods and the modified DBR method both rose as λ decreased, until the value of λ was around 0.51 for the geometric method and 0.16 for the harmonic method, then the similarity scores decreased as λ decreased further. This peak in similarity is similar to the pattern found with the first data set, but at different values of λ. Comparison of the results from both data sets indicated that it would be simplistic to say that two aggregation methods are more similar than a third, for example. The similarity has a dependence on the data set being used.
City indicator data taken from Tan et al. (2017).
55.56 75.31 100 100 80.25 55.56 Arithmetic with offset Geometric with offset Harmonic with offset
80.25 100 75.31
Modified DBR (λ = 0.53) Harmonic with offset
Aggregation method
City indicator data taken from UNDP (2015b).
Arithmetic
Geometric with offset
Table 3 Similarity score for sustainability ranking of 35 cities using three different fixed aggregation methods.
Aggregation method
Table 2 Similarity score for sustainability ranking of 10 cities using four different aggregation methods.
Modified DBR (λ = 0.35)
Modified DBR (λ = 0.27)
Modified DBR (λ = 0.16)
Modified DBR (λ = 0.01)
D. Laslett and T. Urmee
5. Conclusion We have shown that the aggregation method has a material effect 7
Ecological Indicators 112 (2020) 106076
D. Laslett and T. Urmee
Fig. 6. Ranking similarity of the arithmetic, geometric and harmonic aggregation methods to the modified DBR aggregation method with compensation parameter λ. Rankings used indicator data for 35 cities from UNDP (2015b).
CRediT authorship contribution statement
on city rankings, and if the principle of strong sustainability is to be followed, then this cannot be ignored. By using a small arithmetic offset, we have shown a way to make the use of geometric mean and harmonic mean aggregation more practical, and these aggregation methods should be preferred over the use of arithmetic aggregation for city sustainability rankings. The modified DBR method provides a mechanism for coarse control between maximisation and constraint, but using pure constraint can prevent ranking of the worst performing cities. Using a small arithmetic offset also overcame this limitation. Further algorithmic development of aggregation methods is needed so that the transition from maximisation to constraint can be controlled for each indicator individually. The results of this study show that the research scope of ranking system studies can be extended by considering different aggregation methods, with more or less degree of constraint. The similarity score could be used to assess the sensitivity of ranking systems to the type of aggregation method used. Consideration of aggregation method should not be seen as merely a mathematical novelty, but as relevant to the measurement of sustainability and becoming essential as the use of city ranking systems gain more prominence and importance. The use of non-compensatory aggregation methods, that reflect stronger sustainability, means that shortcomings or lack of progress illuminated by one or a few indicators are less likely to be hidden within the majority swathe of indicators that are showing an overall positive status or progress. This gives impetus to cities that are aiming to be seen as sustainable, and are ranked against other cities, to address weaknesses that are dragging down their ranking rather than further developing existing strengths in order to compensate for the weaknesses. So even though different cities might focus their sustainability monitoring and management effort in different ways, there would be a tendency toward more balanced progress overall within each city. It is hoped that this study, by improving the usability of non-compensatory aggregation methods in city ranking systems, will further enable this balanced approach to sustainability, such that city rankings become a valid tool for sustainable urban planning, and not just a competition between cities. The techniques developed here might also be extended to index based ranking systems in other areas of study that have predominantly used compensatory aggregation methods.
Dean Laslett: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Writing original draft, Writing - review & editing, Visualization. Tania Urmee: Investigation, Writing - original draft, Writing - review & editing, Visualization, Supervision, Project administration. Acknowledgement Associate professor Urmee would like to acknowledge HanseWissesschaftskolleg (HWK), Germany, for initiating this research. References Anthopoulos, L., 2017. Smart utopia VS smart reality: Learning by experience from 10 smart city cases. Cities 63, 128–148. https://doi.org/10.1016/j.cities.2016.10.005. Anttiroiko, A.-V., 2015. City Branding as a Response to Global Intercity Competition: Global Intercity Competition. Growth Change 46, 233–252. https://doi.org/10.1111/ grow.12085. Arcadis,, 2016. Sustainable Cities Index 2016. Putting People at the Heart of City Sustainability, Arcadis Design and Consultancy for natural and built assets, Amsterdam. Bartelmus, P., 2013. The future we want: green growth or sustainable development? Environ. Dev. 7, 165–170. https://doi.org/10.1016/j.envdev.2013.04.001. Berrone, P., Ricart, J.E., 2016. IESE Cities in Motion Index. University of Navarra, Pamplona. Bowen, A., Hepburn, C., 2014. Green growth: an assessment. Oxf. Rev. Econ. Policy 30, 407–422. https://doi.org/10.1093/oxrep/gru029. Cohen, M., 2017. A Systematic Review of Urban Sustainability Assessment Literature. Sustainability 9, 2048. https://doi.org/10.3390/su9112048. Dizdaroglu, D., 2017. The Role of Indicator-Based Sustainability Assessment in Policy and the Decision-Making Process: A Review and Outlook. Sustainability 9, 1018. https:// doi.org/10.3390/su9061018. Dı́az-Balteiro, L., Romero, C.,, 2004. In search of a natural systems sustainability index. Ecol. Econ. 49, 401–405. https://doi.org/10.1016/j.ecolecon.2004.02.005. ECOSOC, 2017. Progress towards the Sustainable Development Goals. Report of the Secretary-General, United Nations Economic and Social Council, New York. Gan, X., Fernandez, I.C., Guo, J., Wilson, M., Zhao, Y., Zhou, B., Wu, J., 2017. When to use what: Methods for weighting and aggregating sustainability indicators. Ecol. Indic. 81, 491–502. https://doi.org/10.1016/j.ecolind.2017.05.068. GGKP, 2013. Moving towards a Common Approach on Green Growth Indicators. Green Growth Knowledge Platform, Switzerland. Giffinger, R., Haindlmaier, G., Kramar, H., 2010. The role of rankings in growing city competition. Urban Res. Pract. 3, 299–312. https://doi.org/10.1080/17535069. 2010.524420. Gurría, A., 2012. Green Growth: Making it Happen [WWW Document]. Organ. Econ. CoOper. Dev. https://www.oecd.org/greengrowth/greengrowthmakingithappen.htm (accessed 7.3.19).
8
Ecological Indicators 112 (2020) 106076
D. Laslett and T. Urmee
indicator development—Science or political negotiation? Ecol. Indic. 11, 61–70. https://doi.org/10.1016/j.ecolind.2009.06.009. Shannon, C.E., 1948. A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423. https://doi.org/10.1002/j.1538-7305.1948.tb01338.xx. Shen, L., Zhou, J., Skitmore, M., Xia, B., 2015. Application of a hybrid Entropy–McKinsey Matrix method in evaluating sustainable urbanization: A China case study. Cities 42, 186–194. https://doi.org/10.1016/j.cities.2014.06.006. Smits, J.P., Hoekstra, R., 2011. Measuring Sustainable Development and Societal Progress: Overview and Conceptual Approach. Statistics Netherlands (Centraal Bureau voor de Statistiek), Den Haag. Statistics Netherlands, 2013. Sustainable Development and Green Growth: Comparison of the Measurement Frameworks at Statistics Netherlands. Centraal Bureau voor de Statistiek (CBS), Den Haag. Tan, S., Yang, J., Yan, J., Lee, C., Hashim, H., Chen, B., 2017. A holistic low carbon city indicator framework for sustainable development. Appl. Energy 185, 1919–1930. https://doi.org/10.1016/j.apenergy.2016.03.041. UNDP, 2015a. Sustainable Development Goals. United Nations Development Program, New York. UNDP, 2015b. China Sustainable Cities Report. Measuring Ecological Input and Human Development, United Nations Development Program, China. UNEP, 2014. Using Indicators for Green Economy Policymaking. United Nations Environment Program, Nairobi. United Nations, 2015. Resolution adopted by the General Assembly on 25 September 2015. Transforming our world: the 2030 Agenda for Sustainable Development. New York. van Zoonen, L., 2016. Privacy concerns in smart cities. Gov. Inf. Q. 33, 472–480. https:// doi.org/10.1016/j.giq.2016.06.004. Wang, T.-C., Lee, H.-D., 2009. Developing a fuzzy TOPSIS approach based on subjective weights and objective weights. Expert Syst. Appl. 36, 8980–8985. https://doi.org/10. 1016/j.eswa.2008.11.035. WCED, 1987. Report of the World Commission on Environment and Development: Our Common Future. Oxford University Press, Oxford. World Bank, 2012. Inclusive Green Growth. The Pathway to Sustainable Development. International Bank for Reconstruction and Development, Washington DC.
Holden, M., Moreno Pires, S., 2015. The minority report: social hope in next generation indicators work. Commentary on Rob Kitchin et al’.s ‘Knowing and governing cities through urban indicators, city benchmarking, and real-time dashboards’. Reg. Stud. Reg. Sci. 2, 33–38. https://doi.org/10.1080/21681376.2014.987541. Kitchin, R., Lauriault, T.P., McArdle, G., 2015. Knowing and governing cities through urban indicators, city benchmarking and real-time dashboards. Reg. Stud. Reg. Sci. 2, 6–28. https://doi.org/10.1080/21681376.2014.983149. Langhans, S.D., Reichert, P., Schuwirth, N., 2014. The method matters: a guide for indicator aggregation in ecological assessments. Ecol. Indic. 45, 494–507. https://doi. org/10.1016/j.ecolind.2014.05.014. Marsal-Llacuna, M.-L., Colomer-Llinàs, J., Meléndez-Frigola, J., 2015. Lessons in urban monitoring taken from sustainable and livable cities to better address the Smart Cities initiative. Technol. Forecast. Soc. Change 90, 611–622. https://doi.org/10.1016/j. techfore.2014.01.012. Mazziotta, M., Pareto, A., 2016a. Methods for Constructing Non-Compensatory Composite Indices: A Comparative Study. Forum Soc. Econ. 45, 213–229. https://doi. org/10.1080/07360932.2014.996912. Mazziotta, M., Pareto, A., 2016b. On a Generalized Non-compensatory Composite Index for Measuring Socio-economic Phenomena. Soc. Indic. Res. 127, 983–1003. https:// doi.org/10.1007/s11205-015-0998-2. Moreno, E.L., Murgula, R.O., 2015. The City Prosperity Initiative. Global City Report. UNHabitat, Nairobi. Mori, K., Yamashita, T., 2015. Methodological framework of sustainability assessment in City Sustainability Index (CSI): a concept of constraint and maximisation indicators. Habitat Int. 45, 10–14. https://doi.org/10.1016/j.habitatint.2014.06.013. Narloch, U., Kozluk, T., Lloyd, A., 2016. Measuring Inclusive Green Growth at the Country Level. Taking Stock of Measurement Approaches and Indicators. Green Growth Knowledge Platform, Switzerland. Phillis, Y.A., Kouikoglou, V.S., Verdugo, C., 2017. Urban sustainability assessment and ranking of cities. Comput. Environ. Urban Syst. 64, 254–265. https://doi.org/10. 1016/j.compenvurbsys.2017.03.002. Pollesch, N., Dale, V.H., 2015. Applications of aggregation theory to sustainability assessment. Ecol. Econ. 114, 117–127. https://doi.org/10.1016/j.ecolecon.2015.03. 011. Rametsteiner, E., Pülzl, H., Alkan-Olsson, J., Frederiksen, P., 2011. Sustainability
9