**2. Conceptual framework**

Progress on the knowledge about social disaster risk construction has positioned the analysis and assessment of the social dimensions as key processes for understanding the underlying risk factors in a territory. These dimensions account for the heterogeneity of a territory expressed in local peculiarities, social perceptions of risk, conditions of vulnerability, and resilience capabilities of the population. A better understanding of the risk drivers requires the identification of social‐ecological feedbacks. This is a very challenging issue because of disconnects between social actions and system feedbacks. Feedback mechanisms can be masked through economic distortions, and they may also be deferred in time and space (Berkes et al., 2006; Adger et al., 2009).

assessment and improvement in managing risk has increased notably after the impacts produced by the February 27, 2010 earthquake followed by tsunami. The disaster which affected great parts of the national territory revealed not only the high exposure of the country to the hazard but also the high vulnerability in its various dimensions. The complexity and relevance of the theme deserve special attention to better understand the factors involved in the risk equation

More than a decade ago, Lavell (2003) said that disaster corresponds to the materialization of the pre‐existing risks in a society, which involve multiple dimensions. Risks should be identified and evaluated urgently in order to take action, going beyond structural measures aimed at reducing the hazard, addressing aspects related to the reduction of vulnerability and

In this sense, new determinants that explain the risk conditions in Chile have been mainly associated with changes in the development model of economic globalization followed in recent decades which have brought immense territorial changes. More recently, the climate change scenario, considered an amplifier of extreme events risk, has generated a need for new mitigation and adaptation strategies geared toward an increase in the resilience of the

In this context, the research questions that have been raised in this study relate to the issues described by Wilches Chaux (1993) about how risks arise, grow, and accumulate in a particular context. Later, a comprehensive multi‐sectoral approach was introduced to improve disaster planning and build more resilient communities (Folke et al., 2002; Walker et al., 2002 in Henly‐ Shepard et al., 2015:110). Our research emphasizes the need to examine the interactions of the natural and anthropogenic phenomena which constitute the risk in a study area, and the

Our study methods are based on the analysis of data from previous research of the authors, the characteristics of the natural physical system in which the community is located, the perspective of evaluation processes that can become threatening, and the population vulner‐ ability and resilience. Risk assessment, the main objective of this research, was based on the analysis of the three variables: hazard (H), vulnerability, and exposure (E). It was performed by applying multi‐models and using the analytic hierarchy process (AHP) method (Saaty, 1980). The results allowed the definition of risk areas hierarchy in the three cities considered: Iquique, Puerto Varas, and Puerto Montt. The outcomes of this study will allow, at a later stage,

Progress on the knowledge about social disaster risk construction has positioned the analysis and assessment of the social dimensions as key processes for understanding the underlying risk factors in a territory. These dimensions account for the heterogeneity of a territory expressed in local peculiarities, social perceptions of risk, conditions of vulnerability, and resilience capabilities of the population. A better understanding of the risk drivers requires

the proposal of areas for protection and occupancy restriction in the territory.

and the ability to face future events in better conditions.

population living in specific territories.

**2. Conceptual framework**

exposure of the population and their assets (Siddayao et al., 2014).

166 Applications and Theory of Analytic Hierarchy Process - Decision Making for Strategic Decisions

analysis of the dynamics and trends in the construction of risk.

The risk is understood as the possibility of suffering losses due to the impact of adverse events such as earthquakes, tsunamis, landslides, and floods. It is related to both the likelihood that an event of specific characteristics occurs and its potential to cause damage which is associated with social and individual considerations as perception (Yamin et al., 2013).

The study of disaster risks has evolved significantly in recent years, having to adapt to new factors and processes that condition them such as the permanent increase in the population's vulnerability, especially in urban areas. As indicated by Kabisch et al., (2011), the risk is increased by factors such as new demographic trends and regional economic developments, which implies the need to study various territorial realities to define underlying causes of general and particular risks, seeking for a comprehensive understanding of the problem.

Earlier methodologies focused on the detection and mapping of natural hazard areas, and on handling emergencies, topics that continue to be relevant and in which significant progress has been made by the various disciplines involved. In this regard, Martinez (2009) notes that natural phenomena (of geological, geo‐morphological, and hydro‐climatic origin) represent complex subsystems, and become hazards in the presence of humans. The interactions between hazards and populations are under constant change, generating indeterminable possibilities that are manifested in determined levels of risk.

Currently, the need to incorporate the analysis of social vulnerability and exposure in risk assessment is also recognized, advancing a preventive approach that considers the different dimensions of this problem. This is consistent with Olcina's (2008) view that the risk analysis method has evolved from the detailed study of the natural hazard to the vulnerability assessment that those hazards imply and society's response capacity toward the effects of the phenomena of extraordinary range. Gellert (2012) highlights the role of social sciences that has helped address the problem in a more systemic and holistic manner, where a potentially dangerous natural phenomenon can become a hazard in the presence of vulnerable human groups. Actually, vulnerability is understood as a condition, encompassing characteristics of exposure, susceptibility, and coping capacity, shaped by dynamic historical processes, political economy, and power relations, rather than as a direct outcome of a perturbation or stress (Blaikie et al., 1994; Eakin and Luers, 2006 in Miller et al., 2010).

This factor is directly associated with the conditions of social, economic, and environmental fragility (Cardona, 2001), and with the development conditions (Cuny, 1983). These conditions are also defined as prevalent or inherent vulnerability, that is, the conditions under which a society is found when facing an extreme event, and on them depend in an important manner, the level of impact and their differential expression in a territory (Castro‐Correa, 2014). According to Cutter et al., (2008), the potential risk is attenuated or increased by a geographic filter (site characteristics), as well as the social network that faces the event. This social network could have community experience in previous events, which can be seen as its capacity to respond, cope, recover, and adapt to adverse events, abilities which are, at the same time, influenced by economic, demographic, and housing characteristics.

Chardon (2002) describes three main problems referring to the risk in Latin American cities. The first relates to the difficulty of avoiding natural hazards (e.g., the case of earthquakes). Then, there is the scope and expansion mode of the urban phenomenon that normally increases risk and, lastly, the absence of the control of the urbanization process (e.g., land use, zoning, and building regulations).

However, individuals and social groups present vulnerabilities and capacities that increase or decrease resilience. The vulnerability includes the susceptibility of people and their livelihoods to suffer harm when facing a hazard, while resilience refers to the capacity of the same subjects to absorb changes and return to their original state (Mayunga, 2007), their ability to anticipate changes, and learn from the experience (Dovers & Handmer, 1992; Folke, 2006; Matyas & Pelling, 2012).

Recent discussions on the relationship between vulnerability and resilience have concluded that these concepts can no longer be analyzed in opposite ways; their analysis must strengthen areas of convergence and synergy between the two, depending on the complexity constituted by the study of socio‐territorial systems (Miller et al., 2010). Resilience is not the opposite of vulnerability; the concepts are functionally interrelated. While vulnerability measures the susceptibility of a family group or community to a disturbance, resilience explores the abilities of families and communities to resist and recover from an impact. At the same time, both concepts have attributes that simultaneously manifest and affect the territory (Paton, 2000; Manyena, 2006).

The assessment of risk factors associated with a disaster allows us to identify interventions to improve territorial planning and contribute to increased security and welfare (Wachinger, G and Renn, O, 2010).

#### **2.1. Assessing complex problems: features and advances in multi‐criteria modeling methods**

According to Yamin et al., (2013), risk assessment should include surveillance and monitoring of hazardous phenomena, along with studies of maps and models of hazard and exposure, to assess the vulnerability of the exposed components. The authors suggest that the difficulties to find adequate risk measurement models in objective terms has serious consequences, as it limits the decision‐making process from the perspective of physical planning and the reduction and transfer of risk.

The incorporation of social values in risk assessment requires methods to measure the differences among entities such as money, environmental quality, health, and happiness. There is a broad agreement on the relevance of social aspects in the construction of risk; however, it is at the level of measurement where the challenge remains, because it is difficult to assess the various dimensions of vulnerability and its multi‐faceted and dynamic nature (Birkmann and Fernando, 2008). However, the widespread incorporation and use of social scales and theory of measurement has not been incorporated. To address this problem, Professor Thomas L. Saaty, Ph.D. in mathematics from Yale University, created a mathematical model called AHP in the late 1970s, an effective way to define measures for such elements and use them in the decision‐making processes.

respond, cope, recover, and adapt to adverse events, abilities which are, at the same time,

Chardon (2002) describes three main problems referring to the risk in Latin American cities. The first relates to the difficulty of avoiding natural hazards (e.g., the case of earthquakes). Then, there is the scope and expansion mode of the urban phenomenon that normally increases risk and, lastly, the absence of the control of the urbanization process (e.g., land use, zoning,

However, individuals and social groups present vulnerabilities and capacities that increase or decrease resilience. The vulnerability includes the susceptibility of people and their livelihoods to suffer harm when facing a hazard, while resilience refers to the capacity of the same subjects to absorb changes and return to their original state (Mayunga, 2007), their ability to anticipate changes, and learn from the experience (Dovers & Handmer, 1992; Folke, 2006; Matyas &

Recent discussions on the relationship between vulnerability and resilience have concluded that these concepts can no longer be analyzed in opposite ways; their analysis must strengthen areas of convergence and synergy between the two, depending on the complexity constituted by the study of socio‐territorial systems (Miller et al., 2010). Resilience is not the opposite of vulnerability; the concepts are functionally interrelated. While vulnerability measures the susceptibility of a family group or community to a disturbance, resilience explores the abilities of families and communities to resist and recover from an impact. At the same time, both concepts have attributes that simultaneously manifest and affect the territory (Paton, 2000;

The assessment of risk factors associated with a disaster allows us to identify interventions to improve territorial planning and contribute to increased security and welfare (Wachinger, G

**2.1. Assessing complex problems: features and advances in multi‐criteria modeling methods** According to Yamin et al., (2013), risk assessment should include surveillance and monitoring of hazardous phenomena, along with studies of maps and models of hazard and exposure, to assess the vulnerability of the exposed components. The authors suggest that the difficulties to find adequate risk measurement models in objective terms has serious consequences, as it limits the decision‐making process from the perspective of physical planning and the reduction

The incorporation of social values in risk assessment requires methods to measure the differences among entities such as money, environmental quality, health, and happiness. There is a broad agreement on the relevance of social aspects in the construction of risk; however, it is at the level of measurement where the challenge remains, because it is difficult to assess the various dimensions of vulnerability and its multi‐faceted and dynamic nature (Birkmann and Fernando, 2008). However, the widespread incorporation and use of social scales and theory of measurement has not been incorporated. To address this problem, Professor Thomas L.

influenced by economic, demographic, and housing characteristics.

168 Applications and Theory of Analytic Hierarchy Process - Decision Making for Strategic Decisions

and building regulations).

Pelling, 2012).

Manyena, 2006).

and Renn, O, 2010).

and transfer of risk.

The AHP allows identification of the best alternative according to the needs and resources allocated. It acts as a scientific tool to address issues that are difficult to quantify, but never‐ theless require a unit of measurement. AHP allows working with several scenarios at the same time with the ability to prioritize economic, environmental, cultural, and political goals. Moreover, it can be used with simultaneous participation of different groups with several objectives, criteria, and alternatives. Its use helps the working group to reach consensus between the interests of different stakeholders or power groups (Saaty & Peniwati, 2008).

The above ideas have been gradually validating themselves (Whitaker, 2007) and incorporat‐ ing other application areas including the location of power facilities (Marinoni & Hoppe, 2006), planning of investment portfolios (Vaidya & Kumar, 2006), research technologies under uncertainty, territorial planning (Garuti & Castro, 2011; FAO, 1993), assessment of *smart cities* (Lombardi, 2012), local development strategies (Silva, 2003), land use and zoning (Siddayao et al. 2014), diagnostic assistance (Maruthur et al, 2014.), shiftwork prioritization (Garuti & Sandoval, 2006), measurements in weighted environments (Garuti, 2012), and decision‐making in complex scenarios (Garuti & Escudey, 2005), among others.

The AHP methodology fits well to address problems where the variables involved are of different nature (economic, political, social, cultural, or environmental) and generally difficult to measure. The AHP methodology corresponds to a metric where there is none, or if there is, is not representative or shared unanimously by the decision makers. In fact, this methodology, is with the highest application in the world, has witnessed the fastest growth among the known multi‐criteria methodologies (Wallenius et al., 2008).

The theoretical underpinnings of AHP are: (1) the theory of measurement, (2) the graph theory, (3) the sum of Cesaro, (4) the Perron‐Frobenius theorem, (5) the theory of disturbances and equilibrium states. AHP also originates from psychological elements and is of biological character: (6) the processes of stimulus‐response, and (7) the human capacity for interpretation and transmission of this information on the intensity and amount of electrical discharges of neurons.

The first five points are associated with the theory required to build a model of dominance intensity measurement, also known as *order topology*, where processes of type are to be determined. For example, if AdB (A dominates B), CdB, and CdA, what is the preference relation between them? Here, it is worth recalling the Arrow's Impossibility Theorem, which says: "In an arrangement of dominances as the one indicated there can be no possibility of complete order."<sup>1</sup> However, it has been demonstrated that this proposition is incomplete (Saaty, 2001); (Saaty, 2006); (Saaty & Peniwati, 2008); (Garuti, 2012), as it supposed—as implicit hypothesis—that such dominances not be taken as cardinal values. That is to say, it is not

<sup>1</sup> Complete order, refers to respecting the five natural properties of ordering set by Arrow).

possible to construct dominance cardinal intensities among the elements, which corresponds to an incorrect hypothesis, including the social aggregation of preferences.

The pursuit of these dominance intensities is associated with the first five points described. From this theoretical basis comes one of the most remarkable results of this method, and that corresponds to identify the vector itself as a reciprocal positive matrix (vector representing the final equilibrium state of a non‐consistent or disturbed preference matrix), directly related to the intensities of preference or dominance. This allows associating a cardinal preferences vector to the preferences or dominance judgments initially issued by all decision makers present. On the other hand, the last two points (6 and 7) mentioned above are related to the law of stimuli perception, discovered by the psychologists Weber and Fechner in the nine‐ teenth century. The basic principle of cognitive psychology, which explains stimuli perception, states: "If a stimulus grows in geometric progression, the perception will evolve in arithmetic progression." The principle delivers results in reason or ratio between stimuli as the basis of a fundamental scale (a logarithmic progression).

Thus, these two points (6 and 7) correspond to the construction of a fundamental scale (absolute ratio scale), representing the capabilities and limitations of human beings, and at the same time, respecting the Weber‐Fechner law as a proportional cardinal type, that is, it allows the four arithmetic operations within it. All these scale properties are within Saaty's fundamental scale which ranges from 1 to 9, where the value 1 represents the comparison of two equally important elements (A = B), also called neutral value. The value 9 represents the state when one element is extremely important in comparison with the other (A = 9B). More details about this topic can be found in Saaty's book "Decision Making for Leaders".

The AHP theory and its metrics are very useful for complex problems such as risk assessment, where both quantitative and qualitative diverse variables interact synergistically, that must be synthesized to obtain, as in this case, a certain level of risk. These models also allow the analysis of sensitivity of results that can simulate future scenarios and the trends of risk and its components to evaluate decision alternatives.

In this sense, the **objective** of this paper is to conduct a risk assessment of three Chilean cities that have experienced strong growth in recent decades and which present different economic bases and geographical locations. This approach allows identification of the underlying risk factors that illustrate the process of disaster risk construction in intermediate Chilean cities.

#### **2.2. Working hypothesis**

The hypothesis guiding this research emphasizes the importance of the social dimension in shaping risk. Risk increase is mainly related to urban sprawl and the significant weakness in land use planning, which have resulted in an increase in population exposure to natural hazards. At the same time, some risks can be accentuated by the manifestation of climate change and climate variability.

#### **2.3. Study area**

possible to construct dominance cardinal intensities among the elements, which corresponds

The pursuit of these dominance intensities is associated with the first five points described. From this theoretical basis comes one of the most remarkable results of this method, and that corresponds to identify the vector itself as a reciprocal positive matrix (vector representing the final equilibrium state of a non‐consistent or disturbed preference matrix), directly related to the intensities of preference or dominance. This allows associating a cardinal preferences vector to the preferences or dominance judgments initially issued by all decision makers present. On the other hand, the last two points (6 and 7) mentioned above are related to the law of stimuli perception, discovered by the psychologists Weber and Fechner in the nine‐ teenth century. The basic principle of cognitive psychology, which explains stimuli perception, states: "If a stimulus grows in geometric progression, the perception will evolve in arithmetic progression." The principle delivers results in reason or ratio between stimuli as the basis of

Thus, these two points (6 and 7) correspond to the construction of a fundamental scale (absolute ratio scale), representing the capabilities and limitations of human beings, and at the same time, respecting the Weber‐Fechner law as a proportional cardinal type, that is, it allows the four arithmetic operations within it. All these scale properties are within Saaty's fundamental scale which ranges from 1 to 9, where the value 1 represents the comparison of two equally important elements (A = B), also called neutral value. The value 9 represents the state when one element is extremely important in comparison with the other (A = 9B). More details about

The AHP theory and its metrics are very useful for complex problems such as risk assessment, where both quantitative and qualitative diverse variables interact synergistically, that must be synthesized to obtain, as in this case, a certain level of risk. These models also allow the analysis of sensitivity of results that can simulate future scenarios and the trends of risk and its

In this sense, the **objective** of this paper is to conduct a risk assessment of three Chilean cities that have experienced strong growth in recent decades and which present different economic bases and geographical locations. This approach allows identification of the underlying risk factors that illustrate the process of disaster risk construction in intermediate Chilean cities.

The hypothesis guiding this research emphasizes the importance of the social dimension in shaping risk. Risk increase is mainly related to urban sprawl and the significant weakness in land use planning, which have resulted in an increase in population exposure to natural hazards. At the same time, some risks can be accentuated by the manifestation of climate

this topic can be found in Saaty's book "Decision Making for Leaders".

to an incorrect hypothesis, including the social aggregation of preferences.

170 Applications and Theory of Analytic Hierarchy Process - Decision Making for Strategic Decisions

a fundamental scale (a logarithmic progression).

components to evaluate decision alternatives.

**2.2. Working hypothesis**

change and climate variability.

The three cities selected as study areas (**Figure 1**) have experienced significant spatial change and relevant urban modifications, processes which are explained by the development of their production bases: (1) Iquique (20°13.00′S–70°10′00′W), capital of the Tarapacá Region, free trade city port zone, with great expansion of tourism in the coastal zone, vulnerable to earthquake and tsunami hazards; (2) Puerto Montt (41°28′00′S–72°56′00′W), capital of Los Lagos Region, port and fishing city; and (3) Puerto Varas (41°19′00"–72°50′00′W) of great tourist expansion and satellite town of Puerto Montt. Both Puerto Montt and Puerto Varas are subject to seismic and volcanic hazards.

The three cities selected are prone to hazards of low frequency but high magnitude, in addition to meteorological hazards characterized by high frequency and low magnitude, especially in the south.

**Figure 1.** Area of study: Location of Iquique, Puerto Montt, and Puerto Varas cities.
