# E-government Benchmarking in European Union: A Multicriteria Extreme Ranking Approach

Eleftherios Siskos, Michail Malafekas, Dimitris Askounis, John Psarras

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Eleftherios Siskos, Michail Malafekas, Dimitris Askounis, John Psarras. E-government Benchmarking in European Union: A Multicriteria Extreme Ranking Approach. 12th Conference on e-Business, e-Services, and e-Society (I3E), Apr 2013, Athens, Greece. pp.338-348, 10.1007/978-3-642-37437-1_28 hal-01470544

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# E-government Benchmarking in European Union: A Multicriteria Extreme Ranking Approach

Eleftherios Siskos<fnref n="1" />, Michail Malafekas<fnref n="2" />, Dimitris Askounis<fnref n="1" />, John Psarras<fnref n="1" />

**Abstract.** E-government benchmarking is being conducted by various organizations but its assessment is based on a limited number of indicators and does not highlight the multidimensional nature of the electronically provided services. This paper outlines a multicriteria evaluation system based on four points of view: (1) infrastructures, (2) investments, (3) e-processes, and (4) users' attitude in order to evaluate European Union countries. In this paper, twenty one European Union countries are evaluated and ranked over their e-government progress. Their ranking is obtained through an additive value model which is assessed by an ordinal regression method and the use of the decision support system MIIDAS. In order to obtain robust evaluations, given the incomplete determination of inter-criteria model parameters, the extreme ranking analysis method, based on powerful mathematical programming techniques, has been applied to estimate each country's best and worst possible ranking position.

**Keywords:** E-government, Multicriteria analysis, Robustness, Benchmarking, Ordinal regression, Extreme ranking analysis.

## 1 Introduction

E-government benchmarks are used to assess the progress made by an individual country over a period of time and compare its growth against other countries. A focused assessment of e-government and other initiatives such as e-commerce, e-education, e-health, and e-science is essential if a country is to make substantial progress (Ojo et al., 2007). Benchmarks can have a significant practical impact, both political and potentially economic and can influence the development of e-government services (Bannister, 2007). The results of benchmarking and ranking studies, particularly global projects conducted by international organizations, attract considerable interest from a variety of observers, including governments (ITU, 2009).

Indices and indicators used in benchmarks are generally quantitative in nature, and collectively form a framework for assessment and ranking. Rorissa et al. (2011) classified the frameworks to those based on measurable characteristics of the entities; those that use one or

<footnote n="1">¹ Decision Support Systems Laboratory, School of Electrical & Computer Engineering, National Technical University of Athens, Greece
{lsiskos, askous, john}@epu.ntua.gr</footnote>

<footnote n="2">² Decision Support Systems Laboratory, School of Electrical & Computer Engineering, National Technical University of Athens, Greece
mmalafekas@gmail.com</footnote>
more subjective measures; and the rest few that employ a combination of both. They also state that frameworks based on grounded and broadly applicable measures tend to attract fewer criticisms. On the other hand, the frameworks based on subjective measures are liable to controversies and complaints, especially from those countries or institutions who consider their characterization as inaccurate. Therefore, rankings should be supported by well understood and clarified frameworks and indices as well as transparent computational procedures to maximize their acceptability by the governments and the scientific community. Two among others well-known e-government benchmarks still being conducted are those of the United Nations and the European Commission (see United Nations, 2012 and European Commission, 2010 for more details).

Recently, Siskos et al. (2012) proposed a multicriteria evaluation system based on four points of view: (1) infrastructures, (2) investments, (3) e-processes, and (4) users' attitude from which eight criteria are modeled (see below) to evaluate twenty one European Union countries for which the related data are available. Their ranking is obtained through an additive value model which is assessed by an ordinal regression method. The whole approach consists of helping decision makers (DM), experts or potential evaluators in determining their own country evaluations, based on their own value systems and their own ways of preferring, in order to propose alternative evaluation solutions in contrast to standard published benchmarks.

The aim of this paper is to extend this decision support methodology to take into account the incomplete determination of inter-criteria model parameters and to obtain a robust evaluation of the countries. These targets were achieved with the aid of the extreme ranking analysis (Kadzinski et al., 2012) that estimates each country's best and worst possible rank. This method is based on powerful mathematical programming techniques.

The paper is organized as follows: In section 2 the consistent family of criteria is briefly outlined. Section 3 presents the assessment of the multicriteria evaluation model for a single specific decision maker-evaluator while section 4 presents the extreme ranking analysis method and the obtained results. Finally section 5 concludes the paper.

## 2 Multicriteria Benchmarking Modeling

In order to achieve an overall assessment of global e-government, a consistent family of criteria was built according to the classical modeling methodology of Roy (1985), in the following way:

### Infrastructure criteria

*g*₁: Access to the web. This criterion expresses the percentage of households and businesses that have access to the web by any means.

*g*₂: Broadband internet connection. It shows the percentage of each country's households and businesses with a fixed broadband internet connection.

### Investments criterion
g₃: Percentage of gross domestic product (GDP) spent on information & communications technology (ICT) and research & development (R&D). ICT and R&D expenditure data were retrieved from Eurostat and the International Monetary Fund (IMF), respectively.

## E-processes criteria

g₄: Online sophistication: It shows each country's maturity on online service delivery. The data composing this criterion stem from the European Commission's 9th Benchmark Measurement published in 2010 (Digitizing Public Services in Europe: Putting ambition into action).

g₅: E-participation. It expresses the interaction achieved between governments and citizens in a manner of information sharing, e-consultation and e-decision making. The source of the e-participation criterion is the United Nation's survey on e-government published in 2012.

## Users' attitude criteria

g₆: Citizens' online interaction with authorities. This criterion indicates the percentage of citizens that are already using the web to interact with the authorities.

g₇: Businesses' online interaction with authorities. It indicates the percentage of businesses that are using the web to interact with the authorities.

g₈: Users' experience. This criterion expresses citizens' experience over the 20 e-services and the national portal. The data composing this criterion stem from the European Commission's 9th Benchmark Measurement.

<table><caption>**Table 1.** Criteria evaluation scales and sources.</caption><thead><tr><td>Criterion</td><td>Index</td><td>Worst level</td><td>Best level</td><td>Source</td></tr></thead><tbody><tr><td>g₁</td><td>% population</td><td>0</td><td>100</td><td>Eurostat</td></tr><tr><td>g₂</td><td>% population</td><td>0</td><td>100</td><td>Eurostat</td></tr><tr><td>g₃</td><td>% GDP</td><td>0</td><td>5</td><td>Eurostat and IMF</td></tr><tr><td>g₄</td><td>%</td><td>0</td><td>100</td><td>European Commission</td></tr><tr><td>g₅</td><td>index [0-1]</td><td>0</td><td>1</td><td>United Nations</td></tr><tr><td>g₆</td><td>% citizens</td><td>0</td><td>100</td><td>Eurostat</td></tr><tr><td>g₇</td><td>% businesses</td><td>0</td><td>100</td><td>Eurostat</td></tr><tr><td>g₈</td><td>% index</td><td>0</td><td>100</td><td>European Commission</td></tr></tbody></table>
<table><caption>**Table 2.** Multicriteria evaluation of twenty one European countries.</caption><thead><tr><th></th><th>g<sub>1</sub></th><th>g<sub>2</sub></th><th>g<sub>3</sub></th><th>g<sub>4</sub></th><th>g<sub>5</sub></th><th>g<sub>6</sub></th><th>g<sub>7</sub></th><th>g<sub>8</sub></th></tr></thead><tbody><tr><td>Belgium</td><td>86.5</td><td>81.5</td><td>3.3</td><td>92</td><td>0.59</td><td>28</td><td>15</td><td>68</td></tr><tr><td>Czech Rep.</td><td>94</td><td>90</td><td>3.3</td><td>85</td><td>0.13</td><td>35</td><td>47</td><td>22</td></tr><tr><td>Denmark</td><td>83.5</td><td>85.5</td><td>3.8</td><td>95</td><td>0.64</td><td>11</td><td>31</td><td>30</td></tr><tr><td>Germany</td><td>71.5</td><td>80.5</td><td>3.8</td><td>99</td><td>0.61</td><td>16</td><td>26</td><td>55</td></tr><tr><td>Estonia</td><td>86</td><td>78</td><td>4.0</td><td>97</td><td>0.69</td><td>35</td><td>18</td><td>21</td></tr><tr><td>Ireland</td><td>77</td><td>97</td><td>3.5</td><td>100</td><td>0.44</td><td>40</td><td>33</td><td>49</td></tr><tr><td>Greece</td><td>86.5</td><td>80.5</td><td>2.4</td><td>70</td><td>0.26</td><td>57</td><td>62</td><td>33</td></tr><tr><td>Spain</td><td>76.5</td><td>85</td><td>3.1</td><td>98</td><td>0.83</td><td>75</td><td>74</td><td>86</td></tr><tr><td>France</td><td>84</td><td>92</td><td>3.7</td><td>94</td><td>0.60</td><td>65</td><td>83</td><td>83</td></tr><tr><td>Italy</td><td>93.5</td><td>94.5</td><td>2.7</td><td>99</td><td>0.21</td><td>84</td><td>67</td><td>85</td></tr><tr><td>Hungary</td><td>90</td><td>80</td><td>3.4</td><td>80</td><td>0.31</td><td>57</td><td>79</td><td>80</td></tr><tr><td>Netherlands</td><td>75</td><td>87.5</td><td>3.5</td><td>97</td><td>0.60</td><td>80</td><td>83</td><td>80</td></tr><tr><td>Austria</td><td>83</td><td>78</td><td>3.3</td><td>100</td><td>0.50</td><td>85</td><td>87</td><td>90</td></tr><tr><td>Poland</td><td>77.5</td><td>60.5</td><td>2.7</td><td>87</td><td>0.24</td><td>88</td><td>81</td><td>81</td></tr><tr><td>Portugal</td><td>79</td><td>81</td><td>3.8</td><td>100</td><td>0.27</td><td>79</td><td>59.5</td><td>75.5</td></tr><tr><td>Slovenia</td><td>68</td><td>72.5</td><td>3.4</td><td>99</td><td>0.51</td><td>91</td><td>87</td><td>68.5</td></tr><tr><td>Slovakia</td><td>87</td><td>77</td><td>3.1</td><td>81</td><td>0.07</td><td>91</td><td>93</td><td>94.5</td></tr><tr><td>Finland</td><td>67</td><td>70</td><td>4.3</td><td>96</td><td>0.41</td><td>51</td><td>80</td><td>93.5</td></tr><tr><td>Sweden</td><td>79.5</td><td>65.5</td><td>4.1</td><td>99</td><td>0.49</td><td>70</td><td>88</td><td>92.5</td></tr><tr><td>Norway</td><td>88.5</td><td>90</td><td>2.5</td><td>92</td><td>0.50</td><td>83.5</td><td>89</td><td>87</td></tr><tr><td>Un. Kingdom</td><td>83.5</td><td>87.5</td><td>4.3</td><td>97</td><td>0.77</td><td>83.5</td><td>76.5</td><td>91</td></tr></tbody></table>

All details about the criteria construction techniques are thoroughly described in Siskos et al. (2012). Tables 1 and 2 present the criteria evaluation scales and the criteria scores achieved by the twenty one European countries, respectively.

### 3 Assessing an Overall Evaluation Model

The main target of the proposed methodological frame is the assessment of a multicriteria additive value system, for a single decision maker, that is described by the following formulae:

$$u(g) = \sum_{i=1}^{n} p_i u_i(g_i) \qquad (1)$$
$$u_i(g_{i*}) = 0, \quad u_i(g_i^*) = 1, \quad \text{for} \quad i = 1, 2, \dots, n$$

$$u_i(g_{i*}) = 0, \quad u_i(g_i^*) = 1, \quad \text{for} \quad i = 1, 2, \dots, n \qquad (2)$$
$$\sum_{i=1}^{n} p_i = 1$$

$$u_i(g_i), i = 1, 2, \dots, n \text{ are non decreasing marginal value functions of the performances } g_i, i = 1, 2, \dots, n; \text{ and } p_i \text{ is the relative weight of the i-th function } u_i(g_i). \text{ Thus, for a given}$$

$$u_i(g_i), i = 1, 2, \dots, n \text{ are non decreasing marginal value functions of the performances } g_i, i = 1, 2, \dots, n; \text{ and } p_i \text{ is the relative weight of the i-th function } u_i(g_i). \text{ Thus, for a given}$$

where $g = (g_1, g_2, \dots, g_n)$ is the performance vector of a country on the $n$ criteria; $g_{i*}$ and $g_i^*$ are the least and most preferable levels of the criterion $g_i$, respectively;
country a, g(a) and u[g(a)] represent the multicriteria vector of performances and the global value of the country a respectively.

Both the marginal and the global value functions have the monotonicity property of the true criterion. For instance, in the case of the global value function, given two countries a and b the following properties hold:

$$ (5) \qquad u[g(a)] > u[g(b)] \Leftrightarrow a \ P \ b \ (\text{Preference}) $$

$$ (6) \qquad u[g(a)] = u[g(b)] \Leftrightarrow a \ I \ b \ (\text{Indifference}) $$

The necessary hypothesis to validate an additive value function for a given decision maker (DM) is the preferential independence of all the criteria (see Keenney and Raiffa, 1976, Keeney, 1992 for instance). A pair of criteria (gᵢ, gⱼ) is preferentially independent from the rest of the criteria when the trade-offs between the gᵢ and gⱼ criteria are not dependent on the values of the rest of the criteria. All criteria are supposed to be preferentially independent when the same condition holds for all pairs of criteria. When the uᵢ functions in formula (1) are already assessed, the linear model (1)-(4) exists if and only if the inter-criteria parameters (weighs) pᵢ are constant substitution rates (value trade-offs) between uᵢ.

This value system can be obtained utilizing various methods (see Keeney and Raiffa, 1976, Keeney, 1992, Figueira et al., 2005). Because of the objective difficulties to convince decision makers in externalizing tradeoffs between heterogeneous criteria and verify the preferential conditions cited above, decision analysts usually prefer to infer the DM's additive value function from global preference structures, by applying disaggregation or ordinal regression methods (see Jacquet-Lagrèze and Siskos, 1982, 2001, Greco et al., 2008, 2010).

In this study the disaggregation UTA II method is implemented by assessing the additive model (1)-(4) in two phases: In the first phase the expert is asked to assign some value points uᵢ(gᵢ) of the corresponding evaluation scale for every criterion separately. Then, each marginal value function is optimally fitted (see Fig. 1) and accepted by the DM. In a second phase, the criteria weights pᵢ are estimated using inference procedures (see next section).

$$ u_1(g_1) = 0.6786g_1^2 + 0.3257g_1 \quad \mathbf{g}_1 $$

<figure><img src="image_2.png" /></figure>

$$ u_2(g_2) = 0.4375g_2^2 + 0.5596g_2 - 0.0036 \quad \mathbf{g}_2 $$

<figure><img src="image_3.png" /></figure>
<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 1. Marginal value functions of the eight criteria</figcaption></figure>

# 4 Estimation of Weights and Extreme Ranking Analysis

Through this phase the UTA II disaggregation procedure is used to infer the inter-criteria parameters $p_i$, $i = 1, 2, ..., n$. Specifically, the DM-evaluator is asked to give a ranking (weak order) on a set of reference countries $A_r = (a_1, a_2, ..., a_k)$, that are fictitious country profiles
differing on two or at most three criteria values. The reference countries are ranked by the DM in such a way that $a_1$ is the head and $a_k$ the tail of the ranking.

Therefore, for every pair of consecutive countries ($a_m, a_{m+1}$) holds, either $a_mPa_{m+1}$ (preference of $a_m$) or $a_mIa_{m+1}$ (indifference). UTA II solves the linear program (7)-(11) below that has $k$ constraints because of the transitivity of the ($P, I$) preference system.

$$ [min]F, F = \sum_{i=1}^{k}(\sigma^{+}(\alpha_{i}) + \sigma^{-}(\alpha_{i})) \qquad (7) $$

Subject to:

$$ \text{for } m = 1, 2, \dots, k-1 \qquad \sum_{i=1}^{n} p_i u_i[g_i(a_m)] - \sigma^{+}(a_m) + \sigma^{-}(a_m) - [\sum_{i=1}^{n} p_i u_i[g_i(a_{m+1})]] - \sigma^{+}(a_{m+1}) + \sigma^{-}(a_{m+1}) \geq \delta, \text{ if } a_m P a_{m+1} \qquad (8) $$

$$ \text{or} \qquad = 0 \quad \text{if } a_m I a_{m+1} \qquad (9) $$

$$ \sum_{i=1}^{n} p_i = 1 \qquad (10) $$

$$ p_i \geq 0, \text{ for } i = 1, 2, \dots, n; \sigma^{+}(a_j) \geq 0, \sigma^{-}(a_j) \geq 0, \text{ for } j = 2, \dots, k \qquad (11) $$

where $\delta$ is a small positive number, equal to 0.001 for instance; $g_i(a_m)$ is the evaluation of the $a_m$ country on the $i$-th criterion and $u_i[g_i(a_m)]$ its corresponding marginal value; $\sigma^+(a_j)$, $\sigma^-(a_j)$ are the over-estimation and the under-estimation errors concerning the $j$-th country's position, respectively.

This technique was applied for a set of thirteen country profiles and a zero error sum was obtained ($F = 0$). The optimally most characteristic weighting factors are reported in formula (12) while the corresponding ranking of the European countries is presented in Table 3. More details about UTA II illustration is given in Siskos et al. (2012).

$$ u(\mathbf{g}) = 0.1276u_1(g_1) + 0.1607u_2(g_2) + 0.1097u_3(g_3) + 0.2579u_4(g_4) + 0.0743u_5(g_5) + 0.1209u_6(g_6) + 0.0536u_7 + 0.0952u_8(g_8) \qquad (12) $$

$\mathbf{g} = (g_1, g_2, \dots, g_8)$, is the performance vector of a country on the eight criteria.
<table><caption>**Table 3.** E-government ranking of the twenty one European countries.</caption><thead><tr><td>Rank position</td><td>European Country</td><td>Global Value</td></tr></thead><tbody><tr><td>1</td><td>Sweden</td><td>0.825</td></tr><tr><td>2</td><td>Denmark</td><td>0.821</td></tr><tr><td>3-4</td><td>Finland</td><td>0.796</td></tr><tr><td>3-4</td><td>Netherlands</td><td>0.796</td></tr><tr><td>5</td><td>Norway</td><td>0.765</td></tr><tr><td>6-7</td><td>Germany</td><td>0.745</td></tr><tr><td>6-7</td><td>United Kingdom</td><td>0.744</td></tr><tr><td>8</td><td>France</td><td>0.738</td></tr><tr><td>9</td><td>Estonia</td><td>0.729</td></tr><tr><td>10-11</td><td>Austria</td><td>0.701</td></tr><tr><td>10-11</td><td>Slovenia</td><td>0.701</td></tr><tr><td>12</td><td>Spain</td><td>0.693</td></tr><tr><td>13</td><td>Belgium</td><td>0.686</td></tr><tr><td>14</td><td>Ireland</td><td>0.679</td></tr><tr><td>15</td><td>Portugal</td><td>0.633</td></tr><tr><td>16</td><td>Czech Republic</td><td>0.582</td></tr><tr><td>17</td><td>Slovakia</td><td>0.578</td></tr><tr><td>18</td><td>Hungary</td><td>0.568</td></tr><tr><td>19</td><td>Poland</td><td>0.548</td></tr><tr><td>20</td><td>Italy</td><td>0.533</td></tr><tr><td>21</td><td>Greece</td><td>0.467</td></tr></tbody></table>

However, the above estimation procedure bears robustness issues. In fact, there exists an infinite number of weighting vectors that are optimally consistent with the whole set of constraints (8)-(11). In order to study the impact of this indetermination on the ranking of the countries the extreme ranking analysis of Kadzinski et al. (2012) has been applied with the aid of the GAMS platform.

The extreme ranking analysis algorithm examines each country individually and estimates the best and worst possible rank it can achieve. The methodology leading to the estimation of the best possible rank of each country is outlined below.

In order to determine the best possible rank of a country A, taking into consideration all the possible combinations of the criteria weighting factors, the number $N_A^*$ of the countries that surpass country A in the ranking under any circumstances is calculated. The countries that surpass country A in the ranking for a limited number of combinations of the criteria weights are not included in the $N_A^*$ set. Therefore, the best possible ranking position that can be achieved by the country A is $N_A^*+1$.
Thus, the problem is reduced to the calculation of the $N_A^*$ set for each individual country. This set is calculated through the modeling and the solution of the mixed integer programming problem presented below:

$$[min]F = \sum_{b \in A \setminus \{a\}} u_b$$

(13)

Subject to:

$$\text{Constraints} \qquad (8) \qquad - \qquad (11)$$

(14)

$$U(\alpha) \geq U(b) - Mu_b, \forall b \in A \setminus \{\alpha\}$$

(15)

where M is an auxiliary variable equal to a big positive value, and $u_b$ is a binary variable associated with comparison of the country A to another country B. There exist N - 1 such variables, each corresponding to $b \in A \setminus \{\alpha\}$. N is the total number of the countries under evaluation, i.e. 21.

The determination of the worst possible ranking of a country A, requires a similar procedure. In this case, however, it is estimated the number of countries $N_{A^*}$ that achieve a worse ranking position for all possible combinations of the weighting factors. Therefore, the worst possible rank a country A can achieve is $N - N_{A^*}$.

$N_{A^*}$ set is calculated through the solution of the integer programming problem outlined below:

$$[min]F = \sum_{b \in A \setminus \{a\}} u_b$$

(16)

Subject to:

$$\text{Constraints} \qquad (8) \qquad - \qquad (11)$$

(17)

$$U(b) \geq U(\alpha) - Mu_b, \forall b \in A \setminus \{\alpha\}$$

(18)

The extreme ranking positions of the 21 European countries assessed, are graphically presented in Fig. 2.
<figure><img src="image_10.png" /><figcaption>Fig. 2. Extreme ranking positions of twenty one European countries.</figcaption></figure>

# 5 Conclusion

The paper addressed the robust assessment of global e-government based on multiple criteria and special extreme ranking procedures. The proposed approach focused on the evaluation of European countries according to the standards of a benchmark.

The e-government evaluation process is an independent procedure enabling each individual to specify his (her) own preferences on criteria value functions and weights, and results in a personalized ranking of the countries. In other words, each evaluator has control over his (her) set of criteria and the assessment of his (her) own evaluation model. The proposed multicriteria techniques offer the possibility to combine different preferences and considerations of multiple decision makers and merge them easily through interactive iterative processes.

The next research steps include the development of robustness control procedures based on cardinal and visualization measures as well as the development of a decision support system aiding anyone to form his own e-government benchmarking.

**Acknowledgements.** The authors wish to acknowledge financial support from the Ministry of Education, Religious Affairs, Culture and Sports of Greece and the European Social Fund, under Grant THALIS, MIS 377350: Methodological approaches for studying robustness in multiple criteria decision making projects.
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15. Siskos, E., Askounis, D., Psarras, J.: *Multicriteria decision support for global e-government evaluation*, Working paper, Decision Support Systems Laboratory, School of Electrical & Computer Engineering, National Technical University of Athens, Greece (2012).

16. United Nations: *E-government survey 2012, E-government for the people* (2012).

Retrieved November 10, 2012, http://www2.unpan.org/egovkb/global_reports/12report.htm