The ordered weighted government transparency average: Colombia case

Abstract

The main aim of this paper is to propose a new aggregation operator to improve the evaluation of the transparency index. This new operator is called the prioritized induced ordered weighted average weighted average (PIOWAWA) operator. The main characteristics of the PIOWAWA operator are that it allows considering the degree of importance, reordering and weight factors given to the information in the same formulation by the decision maker. A mathematical application is performed using a Colombia transparency case. The findings highlight that according to the operator used, there are significant changes in the ranking. The main implications are given by using these aggregation operators for the generation of scenarios by considering the changes in the allocation of weights, the level of importance and the ordering of information simultaneously.

Keywords

Transparency OWA operator Colombia decision making aggregation operators

1 Introduction

In decision-making problems, it is noteworthy to analyze attitude based on analogous information analysis and the uncertainty of human behavior [1]. An issue that deserves to be studied within decision problems is the way in which the government generates and presents information to their citizens. This interchange of information between the government and its citizens is called transparency; this term is part of a multidisciplinary concept in which the insertion of political sciences, law, public administration, sociology and, in general, several social sciences is made [2].

Transparency generates in public institutions an understanding of activities and their responsibility and guarantees, through access to information, government supervision and commitment. Furthermore, it is noteworthy that the cultural and attitudinal aspects of citizens are relevant to carrying out an effective transparency process. Indeed, considering the contexts since it is possible to observe the predisposition that citizens have about the actions of the government and creating a perception about them are of the utmost importance.

In Latin America, transparency actions have been included in public policy [49]. This policy agenda involves aspects such as access to information, conflict regulation and interest management and the creation of control agencies. In Colombia, since 2002, the measurement of the transparency index of public entities, known by the acronym ITEP, consists of a civil society initiative that contributes to the prevention of corruption. ITEP allows the establishment of corruption risk levels using existing information on institutional practices and conditions. These levels are defined as the probability of occurrence of corruption activities by government actors in public entities. These processes are associated with the decision making of public authorities and based on the application of norms that tend to improve the quality of life of people [3, 4].

Since the evaluation of the index is based on the use of information from the governments of the day, it is likely to be modified according to the most convenient criteria to show better results. These actions are subject to the degree of importance, management and weight factor given to the information by the decision maker. In this sense, the use of new tools that allow capturing these aspects can help to produce a scenario about the perceptions of transparency levels.

In the literature, there are already proposed methods that allow these types of information to be captured, such as aggregation operators. Aggregation operators allow the gathering of different types of information to reach a conclusion without omitting information during the process [5]. Thus, aggregation operators allow information fusion by combining several values into a single value [5]. Within this research field, several aggregation methods have been proposed. One of them is the ordered weighted average (OWA) operator proposed by [6]. Thus, according to [6], an OWA operator is characterized by a coefficient that is not directly associated with a particular attribute but rather directly associated with an order position.

Using this operator, several propositions have been developed using linguistic information [7, 8], intuitionistic [9], probabilistic [10], distance [11, 12], Choquet integral [13], Bonferroni mean [14], uncertain [15], induced [16], geometric mean [17], power [18], heavy [19], and dependent [20] operators, from which new extensions have been proposed. These operators enable the aggregation of information guided by quantifiers [5] to solve decision-making problems, where the attitudes and criteria of persons have a great influence on the final result.

Based on the above, the main aim of this paper is to propose a new aggregation operator to improve the evaluation of the transparency index. This new proposition is called the prioritized induced ordered weighted average weighted average (PIOWAWA) operator. The main characteristic of this new operator is that it allows considering the degree of importance, reordering and use of two different weighting vectors, one using the weights assigned by the government and another using the information provided by experts related to which elements are most important. The benefit of using this new operator is that it can bring together the idea of transparency of the government and experts in the same formulation to generate a better view and understanding of the situation of a country/state and what changes need to be made.

A mathematical application of this new method is performed for a Colombia transparency case. The findings highlight that according to the operator used, there are significant changes in the ranking. This is because the level of importance that an expert can give to different variables may be greater even if the initial weight of the variables is lower. The main implications are given by using these aggregation operators for the generation of scenarios by considering the changes in the allocation of weights, the level of importance and the ordering of information simultaneously.

This paper is structured as follows: Section 2 presents the main concepts of transparency. Section 3 describes the main concepts of the OWA operator and its extensions. Section 4 presents a new extension of the OWA operator, which is called the prioritized induced ordered weighted average weighted average (PIOWAWA) operator. Section 5 illustrates a mathematical application of a Colombian transparency case through aggregation operators. Section 6 presents the main conclusions.

2 Government transparency

Governments generate information for communication with the population. This allows the functioning of democratic societies [50]. Thus, the interchange of information between the government and its citizens is called transparency. This information is either made public or kept at discretion. This information can comply with government functions; be used as propaganda; and be published as documents, spreadsheets or databases. In this way, the information provides enough variables to the public for attention, interest and skills [21].

Therefore, the value of transparency is framed in the integrity and effectiveness of the government. However, information asymmetry becomes an obstacle that diminishes the abilities of directors to allow monitoring [22]. Thus, the importance and repercussions of government transparency as a mechanism that helps to provide information related to policies, capacities and, in general, data on a democratic society are presented below.

2.1 Importance and repercussions

Transparency was born as a principle of democratic government in the nineteenth century through the school of British liberal philosophy. Jeremy Bentham (1748–1832) is likely the forerunner of the use of this term. However, the term was investigated in ancient Athens and Sparta (500 BC-C. 400 BC) and China (400 BC-C. 337 BC), where it was defined as the use of clear and continuous procedures. The context of theoretical public and open discussion as well as the functioning of political power is found in the works of John Locke (1632–1704), Jean Jacques Rousseau (1712–1778) and Immanuel Kant (1724–1804). Transparency policies involve different levels of government, generating challenges in public administration both in customer satisfaction and in market competition and decentralized decision making [23].

Nevertheless, transparency is part of a multidisciplinary concept in which the insertion of political sciences, law, public administration, sociology and, in general, several social sciences is made [2]. The concept describes the principles and practices within an organization to obtain specific information on the activities carried out. Therefore, the information may involve accounting figures, aggregate meta-information on government plans, and regimentation or regulation of information systems. In this way, transparency is understood as the efficient practices of public policy makers to share necessary information in proper decision making [23].

Thus, the concept has ventured into the measurement of indicators in this regard to control corruption. Among others, the Inter-American Convention Against Corruption [24] of the Organization of American States (OAS); the UN Convention against Corruption [25]; and, in a particular case, Transparency International, established in 1993, have taken as a methodology the measurement of several pillars that include civil society, the private sector, the judiciary, and the executive branch, among others [26].

In this way, transparency has generated in public institutions an understanding of the activities carried out by their peers and their responsibility, guaranteeing, through access to information, government supervision and commitment, somehow slowing down inappropriate behavior. Thus, the growth of government transparency is the consolidation of the democratic process. This implies that with the development of institutions, the actors of society are more powerful in front of the government, which triggers the breaking of the monopoly on information. This leads to the press becoming adept at acquiring confidential information [27]. Likewise, [28] and [29] supported the possibility that activists and ordinary citizens, through access to information, can hold public officials accountable for their behaviors. On the other hand, [30] found three elements for the analysis of transparency: the reconstruction of institutional relations between governmental organizations and the public, the interexchange of information and the changes generated in government activities that become transparent.

However, it should be noted that for [31], the studies that have been conducted on transparency so far change according to the cultural and attitudinal elements of citizens. Therefore, it is pertinent to take national contexts into consideration, in that according to the predisposition of citizens about the government, they significantly affect the perception of government actions. Thus, government transparency must be approached from different spheres as a mechanism of political control and therefore social control, so it is presented below concerning a Latin American case.

2.2 Transparency in Latin America

In Latin America, for approximately the past twenty years, a public policy agenda has been materializing that has included access to information, conflict regulation and interest management, as well as the creation of control agencies. Despite this, application has been carried out in a selective and limited way, which has shown that the execution of the reforms has not generated a tangible and decisive effect on the levels of corruption and transparency, leading to questions regarding the democratic systems of the countries [32]. In [33], the situation in this region is analyzed through transparency policies, accountability and integrity policies.

Therefore, among transparency policies, there has been inequality in aspects such as implementation and institutionalization, as well as in access to public information. In this way, measurements have categorized countries such as México, El Salvador, Uruguay and Chile in a positive way with superior but not optimal results due to their systems of strong regulation and overcoming controversial events. On the other hand, Cuba, Haiti, Bolivia and Venezuela do not have access to information regulations. Regarding the protection of the complainant, most countries do not have this provision, and where it has been implemented, it has been fragile and underfunded. In countries such as Brazil, Colombia, Honduras and México, journalists have suffered increased violence and increased police interference [33].

In relation to this issue, the International Transparency Organization has recommended four measures for Latin America. The first makes it necessary to strengthen institutions that are related to corruption events. The second is the elimination of political immunity in cases of corruption. The third refers to the strengthening of the investigative capacity and an increase in disciplinary measures for the police. The fourth is the creation of accessible and anonymous channels that protect the complainant. Thus, the index of transparency of public entities is presented below for the understanding of transparency measures in the particular case of Colombia.

2.3 Colombia and the index of transparency of public entities

In the case of Colombia, since 2002, the measurement of the transparency index of public entities, known by the acronym ITEP, consists of a civil society initiative that contributes to the prevention of corruption. This allows the establishment of corruption risk levels based on the existence of institutional conditions and practices, which have been defined as the probability of occurrence of corruption activities of government actors in public entities related to administrative management processes (characterized by the generation of the flow of resources and intervention of actors and interests necessary in public investment). These processes are associated with the decision making of public authorities and based on the application of norms that tend to improve the quality of life of people [3, 4].

To do this, the methodological process starts from four major phases consisting entirely of ten steps. In phase 1, the preparation of the index is established in which the conceptual and methodological definitions are established and a request is made for dialogue with the entity to be evaluated. Then, in phase 2, the collection of information is formalized from three sources of information: direct verification (web browsing, telephone simulation and requests for information), primary information (information collection forms in line with the variables, proactive disclosure, human talent, accountability to citizenship, planning and ethical behavior, budgetary and financial management, public procurement, anti-corruption measures, citizen participation, citizen care, internal control management, goods and services management and fiscal control management) and secondary information (General Archive of the Nation, General Audit of the Republic, and Comptroller General of the Republic, among others). Subsequently, in phase 3, the validation of the information on the forms and evaluation of the information is carried out. Finally, in phase 4, the calculation and publication of the results are developed. In this phase, the rating is obtained according to the level of risk. Consequently, a report is generated through a preliminary technical file that allows replication on the part of the entity to establish the purification of the information and finally the delivery of the final technical sheets with socialization in an event open to the community in general [3, 35].

3 Methodology

3.1 Preliminaries

An important aggregation operator is the ordered weighted average (OWA) developed by [6]. The main advantage of this operator is that through a reordering step between the attributes and the weights, different scenarios can be performed between the optimistic and pessimistic criteria. The definition is as follows.

Definition 1. An OWA operator of dimension n is a mapping F : Rⁿ → R with a weight vector w = [w₁, w₂, …, w_n] ^T, where w_j ∈ [0, 1], 1 ≤ i ≤ n and $\sum_{j = 1}^{n} w_{j} = 1$ , such that: $OWA (a_{1}, a_{2}, \dots, a_{n}) = \sum_{j = 1}^{n} w_{j} b_{j},$ (1) where b_j is the jth element that is the largest of the collection a₁, a₂, …, a_n.

An extension that will be used in this paper is the ordered weighted average weighted average (OWAWA) operator [35]. The idea of this operator is the inclusion of two different sets of weights, each with a different degree of importance. This characteristic is important in applications such as the case of transparency, where a specific weighting vector is already assigned (the official one provided by the government) but it is possible to assign a new one based on specific characteristics of the region or country. The same idea can be applied to economics, finance, management, and other fields [36, 37]. The definition of the OWAWA operator is as follows.

Definition 2. An OWAWA operator of dimension n is a mapping OWAWA : Rⁿ → R that has an associated weighing vector W of dimension n such that w_j ∈ [0, 1] and $\sum_{j = 1}^{n} w_{j} = 1$ and is calculated according to the following formula: $OWAWA (a_{1}, \dots, a_{n}) = \sum_{j = 1}^{n} \hat{d_{j}} b_{j},$ (2) where b_j is the jth largest of a_i; each argument a_i has an associated weight (WA) d_i with $\sum_{i = 1}^{n} d_{i} = 1$ where $d_{i} \in [0, 1], \hat{d_{j}} = β w_{j} + (1 - β) d_{j}$ where β ∈ [0, 1] and d_j is ordered according to b_j, that is, according to the jth-largest a_i.

Another extension of the OWA operator that has been used in different group decision-making problems [38 –40] is the prioritized OWA (POWA) operator [41, 42]. The idea of the POWA operator is that in group decision making, not all decision makers have the same degree of importance, and because of that, the information provided by each one cannot be considered equally. The definition of the POWA operator is as follows.

Definition 3. Assume that a collection of criteria is divided into q distinct groups, H₁, H₂, …, H_q, for which H_i ={ C_i1, C_i2, …, C_in } denotes the criteria of the i^th category (i = 1, ... ,q) and n_i is the number of criteria in the class. Furthermore, we have a prioritization between the groups so that H₁ > H₂ > … . > H_q. That is, the criteria in category H_i have a higher priority than those in H_k for all i < k and i, k∈ { 1, …, q }. We denote the total set of criteria as $C = U_{i = 1}^{q} H_{i}$ and the total number of criteria as $n = \sum_{i = 1}^{q} n_{i}$ . Additionally, suppose X ={ x₁, …, x_m } indicates the set of alternatives. For a given alternative x, let C_ij (x) measure the satisfaction of the j^th criteria in the i^th group by alternativex ∈ X for each i = 1, …, q, j = 1, …, i_i. The formula is as follows: $C_{(x)} = \sum_{i = 1}^{q} \sum_{h = 1}^{n_{i}} w_{ij} C_{ij} (x)$ (3) where w_ij is the corresponding weight of the j^th criteria in the i^th category, where i = 1, …, q and j = 1, …, i_i. If w_i = 1/n for all i, the POWA becomes the prioritized average (PA).

Finally, the third extension that will be considered in this paper is the induced OWA (IOWA) operator [16]. This operator introduces induced values in the reordering step of the OWA operator. These induced values represent the ideas of the decision makers/experts in which the attributes are assigned to the weights and not by the maximum or minimum criteria. By doing this, more information about the expectations, attitudes and knowledge can be incorporated into the operator. The definition of the IOWA operator is as follows:

Definition 4. An IOWA operator of dimension n is a mapping IOWA : Rⁿ × Rⁿ → R that has an associated weighting vector W of dimension n, where the sum of the weights is 1 and w_j ∈ [0, 1], where an induced set of ordering variables is included (u_i), so the formula is

$\begin{matrix} IOWA (〈 u_{1}, a_{1} 〉, 〈 u_{2}, a_{2} 〉, \dots, 〈 u_{n}, a_{n} 〉) \\ = \sum_{j = 1}^{n} w_{j} b_{j}, \end{matrix}$ (4) where b_j is the a_i value of the OWA pair <u_i, a_i> having the jth-largest u_i, u_i is the order-inducing variable, and a_i is the argument variable.

These four definitions have been applied in many specific problems [43 –47]. Therefore, they will be the basis for a new extension that takes into account the main ideas of each one and is presented in Section 4.

4 The prioritized induced ordered weighted average weighted average operator

An interesting extension of the OWA operator can be performed if the main characteristics of definitions 2-4 are combined in a single operator. This new operator is called the prioritized induced ordered weighted average weighted average (PIOWAWA) operator. The idea of this operator is that in group decision making, not all experts have the same degree of importance in the results (POWA operator), the reordering step is not performed according to the maximum or minimum criteria but instead through induced values (IOWA operator), and two different weighting vectors are used (OWAWA operator). The definition is as follows.

Definition 6. A PIOWAWA operator of dimension n is a mapping PIOWAWA : RⁿxRⁿ → R that has an associated weight vector w of dimension n, where w_j ∈ [0, 1] and $\sum_{j = 1}^{n} w_{j} = 1$ , so that:

$\begin{matrix} PIOWAWA (〈 u_{1}, b_{1} 〉, 〈 u_{2}, b_{2} 〉, \dots, 〈 u_{n}, b_{n} 〉) \\ = \sum_{i = 1}^{q} \sum_{h = 1}^{n_{i}} b_{j} {\hat{e}}_{ij} C_{ij} (x), \end{matrix}$ (5) where b_j is the jth element that has the largest value of u_i; u_i is the induced order of variables; ${\hat{e}}_{ij}$ is the corresponding weight of the jth criteria in the ith category, where i = 1, …, q, j = 1, …, i_i; each argument b_i has an associated weight (WA) d_i with $\sum_{i = 1}^{n} d_{i} = 1$ where $d_{i} \in [0, 1], \hat{d_{j}} = β w_{j} + (1 - β) d_{j}$ , where β ∈ [0, 1] and d_j is ordered according to b_j; and C_ij (x) measures the satisfaction of the jth criteria in the ith group by alternativex ∈ X, for each i = 1, …, q, j = 1, …, i_i.

The properties of the PIOWAWA operator are as follows.

a) Commutativity: Assume f is the PIOWAWA operator; f (〈u_i, b_i〉, …, 〈u_n, b_n〉) = f (〈u_i, c_i〉, …, 〈u_n, c_n〉).

b) Monotonicity: Assume f is the PIOWAWA operator; if |u_i, b_i| ≥ |u_i, c_i| for all i_i, then f (〈u_i, linebreak b_i〉, …, 〈u_n, b_n〉) ≥ f (〈u_i, c_i〉, …, 〈u_n, c_n〉).

c) Bounded: Assume f is the PIOWAWA operator; then, min{ b_i } ≤ f (〈u_i, b_i〉, …, 〈u_n, b_n〉) ≤ max { b_i }.

d) Idempotency: Assume f is the PIOWAWA operator; if |u_i, b_i| = b for all i, then f (〈u_i, b_i〉, linebreak … , 〈u_n, b_n〉) = b.

It is important to note that the PIOWAWA operator can be reduced to another simpler operator according to the complexity of the problem to be analyzed, and some examples are as follows:

a) if u_i = 1/n, then the operator becomes the prioritized ordered weighted average weighted average (POWAWA) operator.

b) if in $\hat{d_{j}} = β w_{j} + (1 - β) d_{j}$ , β = 1, then the operator becomes the prioritized induced ordered weighted average (PIOWA) operator.

c) if in $\hat{d_{j}} = β w_{j} + (1 - β) d_{j}$ , β = 0, then the operator becomes the prioritized induced weighted average (PIWA) operator.

5 Transparency in Colombia through aggregation operators

Because of the importance of government transparency, the use of the PIOWAWA operator and other OWA operators to identify different scenarios based on the reordering of the weights that incorporate the traditional formulation used in Colombia is proposed. With the use of these operators, it will be possible to identify how much different changes can increase or decrease the transparency score and to propose changes in public policies. The steps that are needed to use the operators in government transparency are as follows.

Step 1. The information to be evaluated is needed. In this paper, the Colombian governorship transparency ranking for 2015-2016 was used (see Annex 1).

Step 2. The actual weights that are used to calculate the final score (see Table 1).

Table 1
Weights used to calculate the transparency score in Colombia

Factor Subfactor Actual weight

Visibility Public information dissemination 5.00%

Disclosure of administrative management 10.00%

Disclosure of budgetary and financial management 10.00%

Disclosure of procedures and citizen service 5.00%

Institutionality Anti-corruption policies, measures and strategies 5.70%

Ethical behavior 5.70%

Planning management 5.70%

Human talent selection 11.50%

Human talent management 11.50%

Control and Sanction System of attention to citizens 4.30%

Accountability to citizens 8.50%

Participation and social control 4.30%

Institutional control 4.30%

Internal management and disciplinary control 8.50%

Transparency Score 100%

Factor	Subfactor	Actual weight
Visibility	Public information dissemination	5.00%
	Disclosure of administrative management	10.00%
	Disclosure of budgetary and financial management	10.00%
	Disclosure of procedures and citizen service	5.00%
Institutionality	Anti-corruption policies, measures and strategies	5.70%
	Ethical behavior	5.70%
	Planning management	5.70%
	Human talent selection	11.50%
	Human talent management	11.50%
Control and Sanction	System of attention to citizens	4.30%
	Accountability to citizens	8.50%
	Participation and social control	4.30%
	Institutional control	4.30%
	Internal management and disciplinary control	8.50%
	Transparency Score	100%

Step 3. The next step is to determine another weighting vector that will be used. To do this, three different experts on transparency in Colombia were asked to provide their opinions about the weights related to each subfactor (see Table 2). In this case, the experts are people from the actual government who have more than 10 years in positions related to governmental transparency and that have helped in the generation of new policies and rules in governmental transparency.

Table 2

Weights provided by the experts

Expert	Weights
e ₁	w₁ = (0.15, 0.15, 0.05, 0.05, 0.05, 0 . , 0.1, 0.1, 0.1, 0.05, 0.05, 0.05, 0.05, 0.01)
e ₂	w₂ = (0.1, 0.05, 0.1, 0.05, 0.1, 0.05, 0.05, 0.1, 0.05, 0.1, 0.05, 0.1, 0.05, 0.05)
e ₃	w₃ = (0.08, 0.08, 0.05, 0.05, 0.05, 0.05, 0.08, 0.06, 0.1, 0.1, 0.1, 0.1, 0.05, 0.05)

Another important factor that needs to be determined is the importance of each weighting vector. In this case, the weighting vector from Step 2 will have a value of 40% and the weights provided by the experts will have a value of 60%.

Step 4. In this step, the information about the induced values has to be determined by each expert (see Table 3).

Table 3

Induced values provided by the experts

Expert	Induced values
e ₁	U₁ = (1, 14, 13, 5, 7, 6, 2, 10, 12, 3, 8, 9, 4, 11)
e ₂	U₂ = (9, 8, 7, 14, 13, 6, 5, 4, 3, 12, 11, 10, 2, 1)
e ₃	U₃ = (7, 6, 5, 4, 3, 2, 1, 12, 11, 10, 9, 8, 13, 14)

Step 5. In this step, the weights that will be assigned to each expert are determined. In this case, the weights were assigned based on the total years of experience of the expert divided by the total years of experience of all experts. The results give the following percentages: e₁ = 0.45, e₂ = 0.35, e₃ = 0.20.

Step 6. With all the information, we proceed to the use of different aggregation operators. In this specific case, the operators that will be used are the OWAWA and IOWAWA operators. The results are presented in Table 4.

Table 4

Results using the OWAWA and IOWAWA operators for each expert

State	Expert 1		Expert 2		Expert 3		Prioritized
	OWAWA	IOWAWA	OWAWA	IOWAWA	OWAWA	IOWAWA	POWAWA	IPOWAWA
Antoquia	88.81	85.92	88.23	84.29	88.12	84.98	88.47	85.16
Meta	82.76	80.76	82.45	77.48	82.19	78.6	82.54	79.18
Santander	82.36	80	81.88	78.15	81.61	77.42	82.04	78.83
Tolima	81.91	79.26	81.25	75.99	81.09	77.95	81.52	77.85
Cundinamarca	81.21	78.41	80.76	78.31	80.74	77	80.96	78.09
Risaralda	81.82	78.89	81.38	76.34	81.15	78.54	81.53	77.93
Casanare	78.32	75.43	77.54	69.56	77.22	71.74	77.82	72.63
Valle del Cauca	76.63	74.95	75.42	70.79	75.29	71.68	75.94	72.84
Caldas	75.16	71.76	74.5	67.14	74.29	70.66	74.76	69.92
Quindio	74.62	70.19	73.12	65.71	72.98	66.98	73.77	67.98
Arauca	73.42	68.04	72.3	65.6	72.16	67.58	72.78	67.1
Huila	70.41	68.54	69.21	64.04	69.16	65.01	69.74	66.26
Norte de Santander	69.17	66.78	67.92	59.05	67.68	64.11	68.43	63.54
Atlantico	69.2	65.19	68.15	58.79	68.04	63.22	68.6	62.56
Cauca	71.66	67.28	70.78	63.97	70.59	65.04	71.14	65.68
Vichada	68.81	63.48	67.68	59.19	67.52	61.22	68.16	61.53
Putumayo	69.83	66.77	68.27	59.82	68.06	62.28	68.93	63.44
Guaviare	67.73	64.68	66.59	59.53	66.53	62.36	67.09	62.41
Boyaca	71.62	61.97	70.01	64.42	69.74	62.29	70.68	62.89
San Andres	59.57	57.58	58.88	48.18	58.7	52.9	59.15	53.35
Nariño	60.17	57.14	58.92	54.43	58.8	55.26	59.46	55.82
Cesar	60.36	55.26	58.94	49.12	58.49	53.31	59.49	52.72
Bolivar	58.79	51.1	57.08	48.73	56.92	50.35	57.82	50.12
Caqueta	61.18	52.73	59.29	50.17	59.03	53.02	60.09	51.89
Cordoba	56.94	53.71	55.51	46.44	55.41	50.62	56.13	50.55
Sucre	59.32	54.9	57.5	47.81	57.33	52.27	58.29	51.89
Vaupes	54.04	50.73	53.27	47.43	52.99	49.74	53.56	49.38
Magdalena	57.65	49.63	56.3	47.71	56.18	50.49	56.88	49.13
Amazonas	55.7	52.6	54.71	43.72	54.53	49.81	55.12	48.93
Guainia	50.06	44.56	49.23	42.74	49.13	45.68	49.58	44.15
La Guajira	49.02	45.77	46.66	38.96	46.58	41.9	47.7	42.61
Choco	38.35	32.33	36.77	25.85	36.29	32.45	37.39	30.08

Step 7. With the results of Table 4, the unification of the results based on the individual information of each expert will be done based on the weights provided in Step 5. The results are presented in Table 5.

Table 5

Variance of the results using different aggregation operators

State	Variance	State	Variance
Antoquia	3.11	Putumayo	12.56
Meta	3.79	Guaviare	7.85
Santander	3.46	Boyaca	17.28
Tolima	4.47	San Andres	14.99
Cundinamarca	2.79	Nariño	5.45
Risaralda	4.58	Cesar	14.9
Casanare	9.56	Bolivar	15.08
Valle del Cauca	4.32	Caqueta	18.29
Caldas	7.72	Cordoba	12.17
Quindio	10.9	Sucre	15.81
Arauca	9.92	Vaupes	5.53
Huila	5.31	Magdalena	16.39
Norte de Santander	10.19	Amazonas	16.46
Atlantico	12.31	Guainia	9.11
Cauca	11.03	La Guajira	11.27
Vichada	12.82	Choco	17.54

Step 8. In this step, the analysis of the results will be performed. First, it is important to note that the changes in the Top 10 states based on the different aggregation operators are presented in Table 6.

Table 6

Top 10 rankings of transparency in Colombia

Ranking	Expert 1		Expert 2		Expert 3		POWAWA	IPOWAWA
	OWAWA	IOWAWA	OWAWA	IOWAWA	OWAWA	IOWAWA
1	Antoquia	Antoquia	Antoquia	Antoquia	Antoquia	Antoquia	Antoquia	Antoquia
2	Meta	Meta	Meta	Cundinamarca	Meta	Meta	Meta	Meta
3	Santander	Santander	Santander	Santander	Santander	Risaralda	Santander	Santander
4	Tolima	Tolima	Risaralda	Meta	Risaralda	Tolima	Risaralda	Cundinamarca
5	Risaralda	Risaralda	Tolima	Risaralda	Tolima	Santander	Tolima	Risaralda
6	Cundinamarca	Cundinamarca	Cundinamarca	Tolima	Cundinamarca	Cundinamarca	Cundinamarca	Tolima
7	Casanare	Casanare	Casanare	Valle del Cauca	Casanare	Casanare	Casanare	Valle del Cauca
8	Valle del Cauca	Valle del Cauca	Valle del Cauca	Casanare	Valle del Cauca	Valle del Cauca	Valle del Cauca	Casanare
9	Caldas	Caldas	Caldas	Caldas	Caldas	Caldas	Caldas	Caldas
10	Quindio	Quindio	Quindio	Quindio	Quindio	Arauca	Quindio	Quindio

With the information provided in Table 6, it is possible to see that Antoquia is always the most transparent state in Colombia, but we also found some interesting changes. For example, in Cundinamarca, 6 of the operators are ranked 6th, one is ranked 4th and one is ranked 2nd. The main reason for these changes is that in the IOWAWA operator, expert 2 gives more importance to the disclosure of procedures and citizen services, anti-corruption policies, measures and strategies and systems of attention to citizens, which are subfactors whose initial weights are less than 6%. In this sense, it is possible to visualize how much a score can change if a subfactor has less or more importance than that in the scores provided by the government.

This variation is important to consider because sometimes states can develop strategies to increase their scores, such as considering only the subfactors with higher weights, and this will make them climb higher at the expense of subfactors that sometimes are less important according to the weights.

This is why it is important to use different aggregation operators to observe the reality that is happening in a country because sometimes based only on a single formulation, not all scenarios can be seen, and valuable information can be omitted. For example, if we calculate the variance of the results based on the initial score and the different aggregation operators, it can be observed that the average of the variation is 10.22 (see Annex 1). For example, Atlántico ranges from 58.79 to 68.15, Boyaca ranges from 61.97 to 71.62, and Quindio ranges from 65.71 to 74.62.

With this analysis, it can be affirmed that the same information can produce multiple scenarios based on the aggregation that is added or changes in the order that the arguments and weights are assigned. This is why it is important for the government, enterprises and, in general, decision makers to use aggregation operators and visualize different scenarios, which will help them to have a better understanding of problems to be solved and make better and more accurate decisions. The main idea of presenting different rankings and results is that the policy-making process is conducted with the information that is available; however, if the results are not as high or as low as the initial results indicate, the actions that the government will take can vary or change and improve the benefits for the governed. This is where the use of different aggregation operators becomes indispensable to visualize these situations.

6 Conclusions

The objective of this paper is to present a new extension of the OWA operator that can be applied to government transparency ranking. This new operator is called the prioritized induced ordered weighted average weighted average (PIOWAWA) operator.

This new operator combines the IOWA, POWA and OWAWA characteristics in the same formulation. This operator aids in solving problems in group decision making. When not all experts determine the same degree of importance in the results, the reordering step is not performed according to the maximum or minimum criteria but instead through induced values, and two different weighting vectors are used.

The application of this operator is carried out in the creation of scenarios on the levels of transparency in Colombia. Thus, identifying how much different changes can increase or decrease the transparency score is presented to propose changes in public policies. The findings highlight that according to the operator used, there are significant changes in the ranking. For example, Antoquia is always the most transparent state in Colombia, and Cundinamarca in 6 of the operators is ranked 6th, in one is ranked 4th and in one is ranked 2nd. Thus, it is shown how much a score can change if a subfactor has less or more importance than that in the scores provided by the government. This variation deserves attention since a strategy can be carried out to increase the index when considering subfactors with higher weights.

The main implications are given by using these aggregation operators for the generation of scenarios by considering the changes in the allocation of weights, the level of importance and the ordering of information simultaneously. In addition, this approach allows capturing the attitudes of experts when considering their opinions in a more dynamic and complex operator. Likewise, it is shown that aggregation operators, such as the one proposed, are useful for visualizing different scenarios for a better understanding of problems to be more resilient and precise in decision making.

In future investigations, this operator can be extended to other techniques such as the Bonferroni mean, Choquet integral, Muirhead mean, Maclaurin symmetric mean and logarithmic operators [51, 52]. Likewise, it can be applied to other cases of decision-making problems, such as personnel selection and investment.

Footnotes

Appendix

Colombian governorship rankings for 2015-2016

Factor	Subfactor	Antioquia	Meta	Santander	Tolima	Cundinamarca	Risaralda	Casanare	Valle del Cauca
Visibility	Public information dissemination	85.40	71.10	64.20	47.90	81.70	63.50	66.30	59.00
	Disclosure of administrative management	87.30	93.90	86.10	89.90	90.90	78.30	94.30	86.00
	Disclosure of budgetary and financial management	98.30	75.00	91.10	100.00	83.30	88.90	85.20	100.00
	Disclosure of procedures and citizen services	91.40	71.60	99.30	81.40	82.70	90.40	83.90	75.40
Institutionality	Anti-corruption policies, measures and strategies	72.90	57.90	69.60	87.60	90.30	87.90	85.00	92.50
	Ethical behavior	93.80	91.70	91.70	58.30	78.50	45.80	95.80	63.20
	Planning management	100.00	77.80	44.40	55.60	88.90	88.90	66.70	44.40
	Human talent selection	93.10	67.50	75.30	77.30	59.80	70.90	71.70	64.40
	Human talent management	74.10	88.90	76.90	67.30	80.80	71.30	65.30	72.80
Control and Sanction	System of attention to citizens	78.60	67.90	76.90	45.00	52.80	61.10	34.40	49.40
	Accountability to citizens	75.80	92.20	91.00	96.00	82.60	57.10	69.90	64.40
	Participation and social control	83.10	88.50	77.40	95.00	87.60	91.40	41.30	85.90
	Institutional control	82.60	72.00	40.30	86.40	66.10	79.20	40.00	49.50
	Internal management and disciplinary control	80.30	87.40	93.80	75.00	59.50	100.00	99.20	76.80
	Transparency Score	85.60	80.10	79.20	77.80	77.50	76.80	74.70	72.50
Factor	Subfactor	Caldas	Quindío	Arauca	Huila	Norte de Santander	Atlántico	Cauca	Vichada
Visibility	Public information dissemination	41.70	57.90	70.40	55.10	36.80	37.10	71.10	48.80
	Disclosure of administrative management	76.60	69.10	72.40	80.00	88.10	56.60	77.70	62.70
	Disclosure of budgetary and financial management	83.30	100.00	91.00	100.00	91.90	87.50	88.90	72.20
	Disclosure of procedures and citizen services	92.50	66.80	96.50	70.30	54.50	82.30	82.20	75.70
Institutionality	Anti-corruption policies, measures and strategies	37.60	69.00	63.10	69.80	54.10	40.00	39.60	47.20
	Ethical behavior	55.50	77.10	81.30	41.70	51.40	89.60	66.00	68.00
	Planning management	88.90	100.00	77.80	77.80	44.40	66.70	77.80	100.00
	Human talent selection	63.10	50.30	60.20	44.20	77.70	66.20	36.00	74.10
	Human talent management	64.50	50.50	41.00	67.50	52.40	73.40	29.10	49.10
Control and Sanction	System of attention to citizens	55.90	23.30	26.90	36.90	29.00	45.00	37.30	30.30
	Accountability to citizens	71.20	72.90	49.10	67.90	64.30	29.20	66.10	41.10
	Participation and social control	71.00	77.20	61.80	77.40	74.10	60.60	82.00	75.10
	Institutional control	82.70	47.90	80.30	52.60	87.20	74.70	52.00	35.60
	Internal management and disciplinary control	87.40	81.30	65.90	59.00	60.90	68.80	96.00	84.00
	Transparency Score	70.30	68.30	66.10	65.90	64.90	63.70	63.50	62.90
Factor	Subfactor	Putumayo	Guaviare	Boyaca	San Andres	Nariño	Cesar	Bolivar	Caqueta
Visibility	Public information dissemination	80.30	62.90	28.50	23.20	61.40	42.30	36.80	35.60
	Disclosure of administrative management	89.30	88.30	43.00	77.60	84.30	39.10	51.60	37.30
	Disclosure of budgetary and financial management	99.10	85.80	63.90	75.00	66.70	78.50	55.40	55.60
	Disclosure of procedures and citizen services	91.70	68.20	78.30	74.10	68.30	79.60	75.10	61.80
Institutionality	Anti-corruption policies, measures and strategies	52.00	45.00	90.90	26.20	59.00	34.60	43.40	25.30
	Ethical behavior	45.80	33.30	100.00	59.70	46.50	18.80	18.80	20.80
	Planning management	55.60	77.80	33.30	77.80	22.20	44.40	88.90	88.90
	Human talent selection	64.10	76.80	69.40	55.30	46.90	65.20	80.60	69.00
	Human talent management	60.40	41.10	75.30	53.40	36.10	60.30	35.90	36.70
Control and Sanction	System of attention to citizens	27.80	45.10	53.50	24.00	25.30	18.60	30.00	42.40
	Accountability to citizens	12.50	42.70	53.70	18.80	45.00	17.10	57.10	36.50
	Participation and social control	74.80	67.80	98.30	60.00	79.30	82.00	25.80	78.70
	Institutional control	40.80	66.20	41.30	35.00	47.60	41.10	26.90	49.90
	Internal management and disciplinary control	60.40	57.60	48.30	72.20	60.40	90.90	74.00	91.50
	Transparency Score	62.80	62.60	62.40	54.80	53.90	53.10	53.00	52.20
Factor	Subfactor	Cordoba	Sucre	Vaupes	Magdalena	Amazonas	Guainia	La Guajira	Choco
Visibility	Public information dissemination	29.20	25.00	30.10	28.80	39.60	29.20	23.90	17.40
	Disclosure of administrative management	55.90	60.00	67.00	44.10	73.70	35.30	66.60	42.10
	Disclosure of budgetary and financial management	77.30	77.80	77.80	58.90	64.40	55.60	84.90	41.70
	Disclosure of procedures and citizen services	66.00	79.60	65.10	55.50	69.60	69.10	71.30	55.90
Institutionality	Anti-corruption policies, measures and strategies	25.80	55.10	45.10	33.40	20.20	42.30	35.80	11.10
	Ethical behavior	45.10	35.40	18.80	56.90	18.80	39.60	18.80	–
	Planning management	77.80	66.70	33.30	77.80	55.60	55.60	55.60	–
	Human talent selection	34.80	31.40	63.80	64.90	49.20	51.20	22.80	52.70
	Human talent management	51.50	39.60	21.90	39.10	44.40	22.50	35.10	5.00
Control and Sanction	System of attention to citizens	34.00	23.60	29.90	34.00	10.00	28.30	28.30	7.50
	Accountability to citizens	25.30	10.40	57.90	26.90	–	12.50	14.60	4.20
	Participation and social control	50.20	56.70	49.00	70.00	79.10	51.50	30.40	23.40
	Institutional control	47.90	40.50	61.20	82.90	59.00	61.10	35.50	57.30
	Internal management and disciplinary control	75.80	97.90	44.80	33.30	77.10	65.40	41.70	79.20
	Transparency Score	50.80	50.60	49.40	49.20	48.30	43.00	41.70	30.20

Acknowledgments

Author Leon-Castro acknowledges support from the Chilean government through FONDECYT initiation grant No. 11190056.

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