Quantitative characterization of chaordic tourist destination

Tourism Management 47 (2015) 115e126

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Tourism Management journal homepage: www.elsevier.com/locate/tourman

Quantitative characterization of chaordic tourist destination Elena Olmedo a, *, Ruth Mateos b a b

Dep. Economia Aplicada I, Universidad de Sevilla, Avda. Ramon y Cajal 1, 41018 Sevilla, Spain
n Romea 23, 28003 Madrid, Spain Dep. Empresa, Universidad San Pablo-CEU, Julia

h i g h l i g h t s
We
We
We
We
We

propose the consideration of tourism as a complex adaptive system. introduce the concept of chaordic system as a step forward to work in mixed environments that mix order and complexity. introduce five quantitative measures that characterize a system as chaordic. apply these measures to characterize chaordic Majorca as a tourist destination. discuss the implications of this characterization in practice.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 30 January 2014 Accepted 13 September 2014 Available online

This paper highlights the new horizons opening with the applications of concepts from the application of the complexity science to tourism data, which are traditionally treated from an intradisciplinar point of view. From this new point of view, tourism is considered as a complex adaptive system. Complexity theory is rooted in the hard sciences, and social sciences have adopted it in recent times. Going a step further, we introduce the concept of chaordic system in tourism. This new thinking has appeared in the social sciences as a response to the current need to cope with contradictions and inconsistencies, adapting evolution without losing essence. We propose considering tourism as a chaordic system and analyzing the resulting managerial consequences. We propose the use of a set of measures to quantify a system as chaordic. Finally, we empirically analyze tourist arrivals to Majorca (Spain) to verify the existence of a chaordic system. © 2014 Elsevier Ltd. All rights reserved.

Keywords: Complexity Chaos Chaordic system Tourism Arrivals

1. Introduction Tourism is one of the most important economic activities for many countries and regions around the word, particularly in those countries and regions characterized by a strong economic dependence on tourism such as Spain and Majorca. Indeed, according to Instituto Nacional de Estadística, tourism represented in 2012 11% of the GDP and 12% of employment in Spain. Knowing the true dynamics of tourism demand is of crucial importance to managers of diverse business to adopt adequate entrepreneurial policies and strategies and for policymakers to plan required tourism infrastructures, formulate appropriate strategies and anticipate economic and unemployment problems (Alvarez-Díaz and MateuSbert, 2011). Nevertheless, tourism research has generally taken a reductionist approach, with tourism not effectively understood as a

* Corresponding author. Tel.: þ34 954557595. E-mail addresses: [email protected] (E. Olmedo), [email protected] (R. Mateos). http://dx.doi.org/10.1016/j.tourman.2014.09.011 0261-5177/© 2014 Elsevier Ltd. All rights reserved.

complex phenomenon (McDonald, 2009). In fact, the study of tourism has been developed during the 20th century from the perspective of different disciplines (Echtner and Jamal, 1997). These include the institutional approach, which considers the intermediaries and institutions that perform tourism activities; the product approach, which considers the production, marketing and consumption of tourism products; the historical approach, which analyzes tourism activities and institutions evolution over time; the managerial approach, which is focused in managerial activities in tourism enterprises; the economic approach, where economists analyze tourism as an economic activity, using the tools provided by economic theory; the anthropological approach, which considers tourism as an element of human culture; sociological approach, which considers tourism as a social activity; and the geographical approach, which focuses on the spatial features of tourism. McKercher (1999) argues the study of tourism and tourism research, despite being considered a “new” discipline (Jennings, 2001), has been locked in an intellectual time that is up to 30

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Table 1 Characteristic figures of simplification paradigm versus complexity paradigm. Simplification paradigm

Complexity paradigm

Independence between observer and observed Closed systems: systems are considered isolated structures

Dependence between observer and observed Open systems and connectivity: systems are considered structures related to their environments Energy dissipation during relations with environment Disequilibrium: systems move between order and disorder Nonlinearity: the whole is more than the sum of their parts Irreversibility: time is endogenous and internal to the system Disorder

Energy conservation, as a consequence of being closed systems Equilibrium: systems are considered structures in equilibrium Linearity: the whole is approximately the sum of constituting parts Reversibility: time is exogenous and external to the system Order

years old, and it is time for a new framework for guide and add to the discussion of tourism. The great majority of the classical models used for tourist research are based on the idea of a simplified, linearized version of the tourism system. Therefore they have a fair amount of limitations, boundaries, and restrictions (Baggio, 2008). In recent years a new approach has emerged. This approach uses complexity science and the associated chaos theory to offer an alternative paradigm for viewing and understanding tourism phenomena. Complexity science is a multidisciplinary emerging science, compounded by different interrelated blocks and, as Schneider and Somers (2006) point out, there are three interrelated building blocks of complexity science: nonlinear dynamics, chaos theory, and adaptation/evolution. Complexity science is concerned with complex dynamic systems with interdependent and interrelated parts, which evolve unpredictably over time, generating new properties and spontaneously selforganizing into new structures. The environment of the tourist organizations and therefore tourist organization itself has evolved throughout time. Economic globalization, fast changing customer behavior, development of transportation, and information technologies all strongly influence tourism (Baggio, 2008). As a consequence, we could speak about an evolution of strategic management, too. Organizations have evolved from a rigid state to a flexible one. The new organizations are an open system and have a new dynamics, characterized by adaptation and emergence. Tourism is an open, dynamic and complex system, consisting of many components that interact in a complex and unpredictable way (Butler 1991; Gunn 1994; Leiper 1990). Tourism researchers have to evolve to cope with this new environment, applying the new concepts developed by complexity science. Surprisingly, only few papers have applied these new concepts to tourism research. We can outline the seminal papers from Faulkner and Valerio (1995) and Parry and Drost (1995). These papers mark the beginning of a series of studies that use the concepts of complexity theory to characterize tourism systems from a qualitative point of view. We can cite the works by Faulkner and Russell (1997), Russell and Faulkner (1999), McKercher (1999), Faulkner (2000 and 2002), Scott and Laws (2005), Russell (2006), Zahra and Ryan (2007), Farrell and Twining-Ward (2004), Baggio, Scott, and Cooper (2010a), and Tinsley and Lynch (2001). Some studies discuss the effects of crises or disasters, such us Faulkner and Russell (2000), Faulkner and Vikulov (2001) and Speakman and Sharpley (2012). Others apply complexity concepts to management (Russell (2006) and Russell and Faulkner (1999 and 2004), Ritchie (2004), Richards (2011)) or sustainability tourism (Schianetz and Kavanagh (2008), McDonald (2009)). Despite the importance of quantifying tourist complexity in modeling and forecasting, we have found only two papers that are quantitatively focused: Baggio (2008) and Baggio and Sainagui (2011). Going a step further, this paper intends to consider tourism as a chaordic system. Chaordic systems harness a unifying approach to

deal with systems where chaos and complexity on the one hand and on the other by simultaneously coexist (Hock, 1996). Complex systems are actually considered chaordic systems because they are based on the same principles. The advantage of this new way of approaching reality is that it provides a unifying vision, through which you can design systems chaordic way to know address the inconsistencies present in the order-chaos dichotomy. This article proposes an alternative way to explain tourism systems through chaordic systems thinking, and to provide some quantitative evidence in support of the complex nature of tourist phenomena. The chaordic view of an organization studies the balance and flow between the firm's structures and frameworks (order) and the emergent creative self-organizing among employees (chaos) (Nixon & Rieple, 2010). The paper is divided in three sections. In the first section, we outline the alternative understanding of tourism systems proposed by complexity science. Under this new focus, tourism systems are seen as chaordic systems, and management is a process to design organizations as adaptive systems, reinforcing emergence and selfmanagement to adapt to complex environment. In the second section, we analyze empirically the tourism arrivals to Majorca to quantify their chaordic properties. We outline conclusions and discuss some implications of adopting complex adaptive systems framework for management in the third section.

2. Complexity and chaos 2.1. Complexity and chaos in tourism Complexity science tries to study, describe, and explain the behavior of complex adaptive systems. This is not a unique theory, but rather a multidisciplinary science, a set of ideas, concerned with nonlinear dynamic systems which are unpredictable and, at the same time, generate new properties and spontaneously selforganize into new structures (Schneider & Somers, 2006). These systems are capable of showing unpredictable behavior but limited in a quasi-stable pattern named strange attractor. The current world is characterized by the complexity of the problems it must face and solve. We have to make a distinction between complex and merely complicated. Complicated systems have a large number of components with well-defined relationships and roles, which are linear and fixed over time. Complex systems have usually a large number of components with nonlinear relationships and roles that evolve over time. There is no agreement in the definition of complexity (Rosser, 1999) but there are some characteristic figures (Edmonds, 1995) such as diversity, change, large number of elements, and interrelations between them, impossibility of perfect knowledge related to imperfect information and the co-existence of order and disorder simultaneously so we can compare the key concepts involved in the complexity paradigm versus the traditional ones in simplification paradigm (see Olmedo, 2010) in Table 1.

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To summarize the issue, we mention the main points in which the paradigm of complexity differs from the traditional. First, in the paradigm of complexity there is an interconnection between the observer and the observed reality, so that both are not independent. The systems are not isolated, but related to each other and their environment, so that the reality is considered from a global perspective. As a result of the relationships between the system and its environment, the systems are not conservative, but conservative. Balance is not considered as desirable or achievable, since the systems are inherently unstable and dynamic. Related to the above, the relationships between different elements and/or systems are often nonlinear frequently so that the overall system is more than the sum of its parts. Consequently, time is endogenous system and no temporal reversibility. Different actions have consequences that endure over time and relationships evolve dynamically. Therefore, the idea of disorder and adaptability is essential against the idea or order and conservatism. A special class of complex systems called a complex adaptive system (CAS) is the one in which the parts interact in a dynamic nature and are influenced by each other and by the external environment in order to improve their behavior and the behavior of the whole system (Stacey, 1995). Are we now capable of defining a complex system? A single definition does not exist, as happens with complexity, but we can state the following properties to characterize a complex system (Pavard & Dugdale, 2000; Snowden & Boone, 2007): 2.1.1. Self-organization, emergence and resilience. The whole is greater than the sum of its parts A complex system is characterized by emergence. The emergent behavior arises not because of the properties of the individual components of the system, but rather from the complex patterns of interaction that occur between those components (Cilliers, 1998). The interactions between the elements of the system and with the environment create new properties named emergent properties. Emergent properties, create new structures and changes in the roles of the elements and their behavioral patterns. This is called self-organization. Self-organization leads to emergent behaviors and stability within a system and is generated from a bottom-up approach leading to a greater sophistication at a higher level in a systems hierarchy (Johnson, 2001; Lewin, 1992). Self-organization is related to the ability of the system to learn and is related to the diversity of options to face the same goal. In this regard, Russell and Faulkner (1999) attempted to explain a major shift in tourism development on the Gold Coast in Queensland, Australia, in terms of self-organization and emergent behaviors as a result of entrepreneurial activities at the maturity stage of the destination lifecycle model. After 70 years as a tourist destination, the Gold Coast experienced a major shift in tourism development over a 30-year period, beginning in the 1960s, as a result of entrepreneurs taking advantage of external global changes such as booming global economy, rapid advances in communication and in air and land travel, and a sense of global security (Russell & Faulkner, 1999). This diversity that emanates from self-organization determined the adaptability of the system and explains the ability of the system to absorb disturbances making changes but retaining essentially the same characteristics and functions. This ability is usually known as resilience. There is evidence of a substantial resilience of tourism ~ oz and Montero-Martín (2007) speak about systems. Garín-Mun
zquez-Salom ‘consumer loyalty.’ Going a step further, Hof and Bla (2012) highlight the importance of adaptability in the case of Majorca to get a major tourism destination over time. EugenioMartin, Sinclair, and Yeoman (2005) show that some part of tourism demand in Scotland has been hardly affected by international crises. Aly and Strazicich (2002) examine the annual tourist night

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visits to Egypt concluding that in spite of shocks of terrorism, war, and regional instability, visits by tourists remains a trend-reverting series. Narayan (2005) shows that visitor arrivals in Fiji from Australia, New Zealand, and the United States are trend-reverting at the 10% level or better, implying that shocks (due to internal political instabilities) to visitor arrivals have only a transitory effect. For example, to attract quality tourism, one option is the improvement of quality and service in hotels and restaurants, in transport infrastructures, improved cleanliness and facilities in cities, or encouragement of luxury shopping. As soon as a tourist destination begins to form, the local community becomes involved in the issue, and so arise tourism-related businesses, hospitality schools, entertainment business, new shops and improved infrastructure. Lim and Cooper (2009) show the positive effect of community involvement in sustainability of Majorca's tourism. All these entities try to maximize their own success, and this favors the global success of the tourist destination. This is self-organization and emergence, key of a complex system. 2.1.2. Open systems Complex systems are open systems, where energy and infor
mation flow through the system and beyond its frontiers. Rosello and Riera (2012) have shown the influence of internet use on tourism in Balearic Islands. Obviously tourism systems are closely related to government agencies, both in the autonomous communities and local, since they depend on the regulations and infrastructure. They also provide economic benefits in tourism areas because of generating jobs, expanding the market, and attracting investment and infrastructuresealmost three quarters of Balearic economy is sustained by tourism, according Polo and Valle (2008). We can speak about the promotion of cultural and historic traditions, too. And they can help to improve rural areas avoiding rural depopulation and promoting local products. Environmental protection is essential today in any tourism area. In fact, as Anderson (2009) points out, the environmental and natural resources of Balearic Islands have suffered the pressure of tourist activities, so the promotion of ecotourism is a key issue whereas, at the same time, environmental quality is fundamental for the new tourist and
, 2010). also for citizens' quality of life (Jacob, Florido, & Aguilo Complex systems are generally evolving continuously but in states far away from equilibrium: the tourism systems are always evolving in time, looking for increase competitiveness, environment protection, increasing visitor numbers, extend tourist season, develop new tourism forms, and modernize the existent ones. 2.1.3. Limited descomponibility A complex system has a dynamic structure. The permanent interaction among the elements of the system, and with the environment, induces the system to restructure itself and generate selforganization properties. The parts of the system are unable to reproduce the whole system and cannot take it over. This is characteristic of tourism systems, where different agents and realities interact that in turn are evolving over time. Tourism in an area depends on infrastructure, climate, quality of accommodations and restaurants, commerce, policy measures, entertainment options, of the cultural, historical and architectural preservation, staff training, friendliness of the people and the cleaning and maintenance of the city. All these dynamic subsystems are interacting and co-evolve over time. 2.1.4. Nonlinear adaptive relationships Relationships between elements of the system are usually nonlinear, so the relation cause-effect is not clear. For example, Ulubasoglu and Hazari (2004) have shown the presence of Zipf-like relationships in tourism systems. In their work, the authors analyze

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Table 2 Chaos versus complexity. Chaos

Complexity

How simple systems could generate complex behaviors Simple non-linear systems produce extremely complicated behaviors (sensibility to initial conditions) How to recognize, describe and forecast systems with sensibility to initial conditions

How simple behaviors emerge from complex systems Simple interactions produce higher-lever patterns How to discover recognizable patterns when the complicated system is looked at a whole

international tourist arrivals and find the familiar nonlinear rank
size distribution. And Alvarez-Díaz and Mateu-Sbert (2011) used nonlinear to forecast Majorca visitors. Campo and Yagüe (2009) have analyzed the nonlinear relations between price and quality on tourists' satisfaction, Falk (2014) between temperatures and tourism demand and Alavalapati and Adamowicz (2000) between environmental conservation and tourism demand. Additionally, positive or negative feedbacks are usual so the nonlinear relations may evolve with system evolution: we speak about nonlinear adaptive relations. Farrell and TwiningWard (2004) and Schianetz and Kavanagh (2008) point out the importance of the concept of complex adaptive system to achieve sustainable tourism. 2.1.5. Sensibility to initial conditions and long memory Due to the sensibility to initial conditions recent alterations are very important in the system evolution. An exogenous shock can cause large changes in a tourist destination (Speakman and Sharpley (2012) analyze the influenza crisis in Mexico's tourism destinations and Boukas and Ziakas (2014) discuss the relationship between economic crisis and Cyprus' tourism). And due to the presence of nonlinear adaptive relationships, past alterations continue having effects in current state of the system. So the knowledge of the past evolution in complex system is very important. Any tourist system depends on its own past. For example, a mass beach tourism area has infrastructures according with it and will take time to implement changes in demand target. 2.2. Tourism under chaordic system thinking Chaos theory works with nonlinear systems characterized by sensibility to initial conditions, unforecastable and ordered Table 3 Traditional versus chaordic assumptions. Tradicional assumptions

Chaordic assumptions

Materialism or positivism: what we could not measure, do not exist Reductionism: the whole is the sum of its parts Determinism: causeeeffect relationships are linearly co-related, so forecasting and control is possible

Consciousness: there is so much information underlying the apparent material world Connectivity: the universe is one, and all is interconnected Indeterminacy: due to nonlinearity and sensitive dependence on initial conditions, cause-effect relationships are not forecastable, but present is past-dependent Instability/Dissipation: open systems are dynamic and continuously inter-related with environment. Emergence: there are properties that arise in the whole that are not present in its parts, due to inter-related capacities. The whole is more than the sum of its parts

Stability/Conservation: the desired state of the system is stability. Mechanism: people organize simple elements into increasingly more complex phenomena

simultaneously. Chaos essentially appreciates that turbulence is a feature of systems, unlike reductionist perceptions that systems are stable and move towards equilibrium (Russell & Faulkner, 1999). Chaos and complexity are usually considered as synonymous, but there are substantial differences between them (see Table 2, adapted from Fitzgerald & Eijnatten, 2002a). The three points listed in Table 2 insist on the same idea: despite the apparent disorder of the system, there are emergent properties which make that certain ordered patterns are recognized when the system is considered as a whole. The focus of chaos theory is on the manner in which simple systems give rise to complicated unpredictable behaviors, while complexity theory focuses on how systems consisting of many elements can lead to well-organized and (almost) predictable behaviors (Baggio, 2008). The relations between chaos and complexity are so strong that a new concept has been coined: chaordic system (Fitzgerald & Eijnatten, 2002b; Hock, 1999). A chaordic system (see Olmedo, 2011) is a complex and dynamic set of connexions between elements that conforms a unified whole, whose behavior is simultaneously unpredictable (chaotic) and patternly (orderly). The chaordic lens is an approach to designing a complex organizational system; indeed, Chaordic Systems Thinking is an outgrowth of the literature on complexity in organizations (Stacey, 1995). Chaordic Systems Thinking is a framework that provides a new perspective, according to five core properties (Fitzgerald, 2002): consciousness, connectivity, indeterminacy, dissipation, and emergence. These principles are contrary to those provided by traditional approaches (see Table 3).
Consciousness: the traditional approach only cares about the facts, the matter so that measurement, forecasting and control are essential. The chaordic approach states that any human activity affects the bigger system which it belongs and the smaller systems it contains. And ideas are the key factor in systems relations and the influence they have on each other. Wealth is not always measured by GDP because there are concepts like happiness and well-being that are not measurable.
Connectivity: the traditional approach compartmentalizes systems into bounded subsystems, and treats each separately. Earth is seen as a set of resources that we exploited to increase human wealth. Competition is the underlying rule. The chaordic approach states that all is interconnected. There is no separation between observed and observer. There are no boundaries between systems and subsystems. Each system is at the same time part and whole. Systems should co-exist each other and with the environment to maintain themselves.
Indeterminacy: due to the above stated, causeeeffect relationships, core in the traditional approach, are broken. Each event is simultaneously cause and effect. Thus, adaptability is essential.
Dissipation/Instability: the traditional approach seeks stability. The chaordic approach tries to cope with unstability. Systems are continually evolving, in destructioneconstruction cycles, so they should be designed in a way that enables them to transform themselves.
Emergence: collaboration and adaptability made possible selforganization, so that new structures are born to address new situations and problems. These emergent structures produce a new pattern of movements where order could be encouraged out of chaos. These are the “strange attractors”. So a chaordic organization should boost organizational mind (consciousness), minimize boundaries (connectivity), maximize fluidity of structure (indeterminacy), promote a compelling and evolving collective vision that feeds all actions (emergence) and

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design self-triggering mechanism to change before its time (instability). If we compare the characteristics listed in Table 3 for a chaordic system and the characteristics of the tourism sector, we see the similarities. As Morrison (2006) points out, there are also socio-economic and environmental outcomes of tourism over rural and peripheral communities, and many such communities have benefited from both deliberate and organic development of tourism. Tourist destinations are characterized by their evolution over time, looking for new opportunities. In the past concepts like ‘conducted tours’ and ‘theme parks’ (Russell & Faulkner, 2004) were introduced and now contemporary sustainable rural tourism are studied as a development opportunity (Ateljevic, 2009; Fillis, 2009; Kokkranikal & Baum, 2002; Rosa & Joubert, 2009; Tinsley & Lynch, 2001) in Africa, India or New Zealand. Compared to traditional tourism, in which no importance was given to the development of the local community and these were excluded from decision-making, today we talk about sustainable tourism. This “conscious tourism” is characterized by being sensitive to the reality of the destination area, encourage the local community to participate in the decision making process, make a responsible use of natural resources, and an equity distribution of the benefits achieved to prevent the system collapse (Harris, 2009 provides the example of Bario on the island of Borneo). In addition, it is undeniable the wide availability of information in tourism through the use of internet, information that is difficult to measure in practice so it can't be included explicitly in a model. Moreover, a tourism business can never be considered isolated, as there are numerous different types of relationships between businesses, and between them and the environment. Some authors speak about community networks as essential for tourist development (see Farsari & Prastacos, 2003; Kokkranikal & Morrison, 2011). There is not a unique relationship between passengers and their destination, but multiple interrelationships among travelers, destinations and their environment (we can think about transport sector, attractions, activities, landscape, conservation, cleanliness and safety of destinations …). Besides, there is an inherent nonlinearity in the relationships within the tourism sector which prevents us from relating directly causes and consequences, as the traveler behavior depends in a complex way of a great variety of factors. We can speak about a ‘new tourist’, with a more specialized demand, seeking specialization, differentiation, giving importance to environmental issues and culture of the countries they visit, but also adventure, spontaneity, indepen
, Alegre, & Sard, 2005). dence and unpredictability (Aguilo Nor can it be denied that in principle insignificant factors may influence the future behavior of tourists. This behavior can also be affected by endogenous and exogenous shocks to the system (we can think about the effect of Sept. 11 on tourism behavior). For example, Boukas and Ziakas (2014) review the major shocks received by the Cypriot tourism as the opening of roadblocks, the accession to the European Union, the LehmaneBrothers, the Arab Spring and the economic crisis of Cyprus …. They analyze qualitatively their impact over Cypriot tourism. The present is past-dependent because many travelers tend to repeat their destination areas (consumer loyalty) and there is a “lock-in-effect’ because many tourism enterprises are frequently located in places where they have an advantageous position in the past, but not in the present (near a bus station or a train station perhaps, as Faulkner and Valerio (1995) points out). Finally, all the factors related in tourism sector usually operate with some kind of order, creating some emergent features. The policy-makers have to facilitate their formation searching for appropriate strange attractors. Boukas and Ziakas (2014) mention the pursuit of quality tourism -the Russian market, the exploitation

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of Larnaca/Paphos airport e for example, with Ryanair flights. But to achieve this self-organization, the system must be dynamic and evolve over time as conditions change: when the system undergoes a shock, some elements will be adversely affected, and others will benefit by changing their ways so that the system as a whole sur
et al. (2005) mention various measures vives. For example, Aguilo taken in the Balearic Islands tourism involving all implied agents to adapt to the current needs mentioned: quality improvement, diversification of visitor nationalities, increase in cultural and leisure activities to please the ‘new tourist,’ and legal and policy measures to favor quality e ‘tourism excellence program’, and protect natural resources and environment. So really, we can think about tourist systems as chaordic systems: dynamic structures, complex and nonlinear, characterized by a great number of elements interacting with each other and with the environment in a complex way, which evolve through time creating new emergent properties and with sensibility to initial conditions, so their evolution is hardly predictable, but showing orderly patterns. The first implication is the impossibility of long-term planning. Sensibility to initial conditions implies the amplification over time of small perturbations, so that forecasting is impossible. Because of that, crucial long-term planning becomes impossible. This implies a change in strategic thinking: rather than try to forecast, it is better to take into account different scenarios. Short-term prediction is possible, and we can also predict patterns of behavior, instead of precise future behavior. Second, chaordic systems are far from equilibrium: they are always changing, and can spontaneous and endogenously form new complex structures. So managers shouldn't try to reach equilibrium, and should take into account the possibility of new organizational forms, such as long-term contracts or joint ventures. Third, chaordic systems should be affected by unexpectedly dramatic changes. Traditionally, large changes in outcomes only occur because of large changes in initial conditions. But in complex systems (sensibility to initial conditions), small changes can generate very different outcomes. Due to all seen, static and fixed rules are not useful, but general broad guidelines are needed because of the necessity of taking into account different scenarios. And because of the possibility of dramatic changes, these guidelines have to be adaptive. Traditional managerial models seek stability, equilibrium and control to reduce complexity, with decisions devised at the top or organization, based on logical and analytical instruments with experts' assessment and formal teams directly controlled by senior management. On the other hand, chaordic managerial models work with complexity instead of trying to reduce it. Success implies taking advantage of disequilibrium, change and innovation. Decisions are devised at all levels or organizations, based on intuitive instruments in informal teams within boundaries of discretion. It is important to have the creation of environments to favor emergence and to use methods that can help to generate ideas, increasing levels of interaction and communication. As Dobson (Dobson, Starkey, & Richards, 2004) points out, we couldn't equate strategy with planning; planning works in a stable, predictable environment. There is another less rigid vision of strategy, considered as the process of management, so strategic management seeks to facilitate emergence and self-organization, that is, the capability of organizations to adapt to an unpredictable environment, not suitable for planning. So the key point of strategic management will be how to make this possible. 3. The detection of a chaordic tourist destination A tourism destination is a complex systems formed by different economic, social, political, and environmental agents and

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Table 4 Chaordic quantitative measures.

ORDER

CHAOS ORDER þ CHAOS

Property

Measure

Chaord mark

Long memory Self-organization Resilience Nonlinearity Sensibility to initial conditions Self-organization þ nonlinearity

Hurst Coefficient H Zipf-relations Stationarity (unit root tests) Nonlinear Tests Lyapunov Exponent l Embedded system

0.5 < H < 1 Existence Existence Existence l>0 Existence

phenomena that interacts each other and evolve along time. So a tourism destination could be considered as a chaordic system. Nixon and Rieple (2010) have applied the Chaordic System Thinking to examine The Ritz-Carlton dynamics from a qualitative point of view, but there are not references to support the consideration of a tourism organization or destination as a chaordic system from a quantitative point of view. The purpose of the section, following Baggio (2008), is to provide quantitative evidence that support this consideration. Baggio use different quantitative measures to characterize chaotic systems, are we propose the use of some quantitative measures to characterize chaordic systems. We are going to consider five different distinctive characteristic of a chaordic system that could be quantified. We divide these measures into different groups. The first group tries to quantify the ordered pattern of the system: long memory, self-organization, and resilience. The second group tries, in addition, to quantify the chaotic pattern of the system: nonlinearity and sensibility to initial conditions. Additionally, we can relate the embedding of the system with the existence of a nonlinear structure. These chaordic characteristics, their quantitative measures and their behavior in chaordic systems are summed up in Table 4 and will be discussed in following paragraphs. So if the system is chaordic, it should show long memory, selforganization, resilience, nonlinearity and sensibility to initial conditions. The data we used are the daily air arrivals at Majorca airport, obtained from AENA, which oversees Spain's airports. The selected sample size is 4018 data covers from 01/01/2000 to 12/31/2010. Let us consider this series is representative for the study of Majorca as a tourist destination, since more than 90% of tourist arrivals to the island by air do so, according to official data of the Government of the Balearic Islands. As usual in tourism data, seasonality is assumed, so the variable under study will be the log difference of the original data (Fig. 1). But the power spectrum of the transformed time series still shows evidence of seasonality, so we adjust a seasonal-ARIMA to the transformed data, obtaining ARMA(1,1)  ARMA(1,1)7. The power spectrum of the filtered data reduces the evidence of seasonality (see Fig. 2). We are going to call the original time series ARRIVALS, LARRIVALS its log difference and FARRIVALS the errors after linearly filtering the data. We suppose that these filtered data reflects the true internal dynamics of the system. The Hurst exponent (H) is a measure of the long-term memory of a time series. It is related with the autocorrelation function of the time series, in particular with the rate at which it decays with increasing delay. Its value ranges from 0 to 1. If 0 < H < 0.5, the time series is anti-persistent, that is, a high value will be probably follow by a low value, and a low value will be probably follow by a high value, switching low and high values for a long time. If 0.5 < H < 1 the time series is persistent or it has long memory, that is, a high value will be probably follow by a high value, and a low value will be probably follow by a low value, and this behavior remains over a long time. So a chaordic system must have H > 0.5. In the time series of daily arrivals, H ¼ 0.8526, showing a strong long memory,

according with seasonal data. In the filtered data, H ¼ 0.4352 with a 99% bootstrap percentile confidence interval (0.4083,0.5987).1 So we can state that the long memory is related to the non-stationarity of original data. Self-organization is related to the existence of similar patterns that are repeated in different time scales. These auto-similar structures are studied by Fractal Geometry and their presence is characteristic of a complex system. From a quantitative point of view, the existence of a power law relationship is a common signature of a self-organized system. Ulubasoglu and Hazari (2004) and Baggio (2008) have empirically shown the presence of a nonlinear variation of Zipf-like relationship in tourism systems. Applying the same technique, we confirm the same result for our time series, applied to frequency and rank of tourist arrivals, as it shown in Fig. 3. To capture the nonlinear structure present in Fig. 3 and following Ulubasoglu and Hazari (2004) we estimate an augmented regression with the following results:

logðfreqÞi ¼ 0:59 þ 1:53 $logðrankÞi  0:626 $ logðrankÞi ð0:098Þ

ð0:108Þ


2

ð0:029Þ

(l) with R2 ¼ 0.9. The autonomous reorganization capabilities of a system to adapt itself to external shocks are called resilience. So resilience is related to the capacity of a complex system to self-organize. Resilience is related to the stationarity of the time series generated by the system (Baggio, 2008), because a stationary system is capable of continuing its evolution, absorbing possible shocks. There is a battery of statistical tests developed to determine if a time series exhibits stationarity: the augmented Dickey-Fuller (ADF) test (Dickey & Fuller, 1979), the Phillips-Perron (PP) test (Phillips & Perron, 1988), the Zivot and Andrews (ZA) test (Zivot & Andrews, 1992) and the KPSS test (Kwiatkowski, Phillips, Schmidt, & Shin, 1992). The null hypothesis of all these tests is the existence of an unit root except in the case of KPSS test, in which the null hypothesis is the stationarity of the time series. After correcting the seasonality of the series, and therefore staying with the internal dynamics of the system, all these test confirm the stationarity of the dynamics of the system and, therefore, its resilience (see Table 5, where we show the test statistic and the critical value at p ¼ 0.01). On the other hand, self-organization and nonlinear relationships are too related with the existence of a state space system, reconstructed using the time series. Under some conditions (Takens, 1983), the dynamics of this new system e which is known as the embedded system, is the same as the dynamics of the original e unknown, system which has generated the time series we observe. The states of the embedded system are known as m-histories, and are defined using lagged values of the time series. Let {xt} be the filtered stationary time series of daily arrivals, and fam t g

1

Using 1000 bootstrap samples.

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121

Fig. 1. Daily air arrivals ARRIVALS (up) and their logarithmic difference LARRIVALS (bottom).

are the m-dimensional embedded values, where am ¼ ðx ; x ; …; x Þ. The delay used t is the first time that t tt tðm1Þ$t t minimizes the mutual information, and the embedding dimension m is the one that minimizes the percentage of false neighbors ethat is, points that are close because the dimension is too low and not because of the underlying dynamics (Olmedo, 2011). The results should be similar before and after the linear filtering, since this does not affect the reconstruction (see Fig. 4). We find that the first minimum of the mutual information corresponds to t ¼ 1, and the percentage of false neighbors is minimum with m ¼ 7. Improving this initial idea, Cao (Cao, 1997) has developed two coefficients that not only facilitate determining the proper embedding dimension, but also allow distinguishing if the system is deterministic or stochastic. These two coefficients are denoted as E1 and E2. For embedding dimensions higher than the proper one,

it shows E1 ¼ 1. On the other hand, if the system is stochastic, E2 ¼ 1 whatever is embedding dimension (see Fig. 5). We confirm the value of the proper embedding dimension. After that we use some tests to detect nonlinear dynamics in time series data. We propose the use of BDS (Brock, Scheinkman, Dechert, & LeBaron, 1996) and Kaplan test (Kaplan, 1994) because of their generality. These tests come from the chaos theory. The BDS test is a test of independence, but it can be used to produce indirect evidence of nonlinearity if all linear dependence has already been removed. The authors compute a statistic that, under i.i.d., depends on embedding dimension m and epsilon ε that asymptotically follows the standard normal distribution. Using the software by L. Kanzler, available in http://econpapers.repec.org/software/ bocbocode/t871803.htm, and working with the filtered time series, and we obtain null p-values for embedding dimensions from 2

122

E. Olmedo, R. Mateos / Tourism Management 47 (2015) 115e126 Table 5 Unit root test outcomes. The null hypothesis of ADF, PP and ZA is nonstationarity so, as the test statistic is higher, in absolute value, than critical value, we confirm the stationariy of the system. The null hypothesis of KPSS is stationarity so, as the test statistic is smaller, in absolute value, than critical value, we confirm the stationarity of the system.

Fig. 2. Power spectrum of daily arrivals ARRIVALS (up) at the linear filter of its logarithmic difference FARRIVALS (bottom).

to 10 and epsilon distance between 0.5 a 2 times the standard deviation of time series so we confirm the nonlinearity of the system. The Kaplan test (Kaplan, 1994, 1997) was initially formulated for the detection of determinism in the underlying dynamics of a time

Fig. 3. Zipf-like relationship between the frequency and the rank of the daily arrivals.

Test

Test statistic

Critical value (p ¼ 0.01)

Augmented Dickey-Fuller (ADF) Phillips-Perron (PP) Zivot-Andrews (ZA) Kwiatkowski-PhillipsSchmidt-Shin (KPSS)

42.9532

3.4318

64.37142 20.22646 0.029016

3.4318 5.5700 0.7390

series, though thereafter it has been used to contrast the hypothesis of stochastic or deterministic nonlinearities in the generating process of a time series (see Barnett et al., 1995, 1996 and 1997). It depends on the embedding dimension m and works comparing the distances between points in an m-dimensional reconstructed space with the distances between their images. Kaplan's test statistic K is the average of the values of the distances of the images when the distances between the original points are small enough and, under the hypothesis of determinism, K / 0. But its probability distribution is not known, so we work with surrogate techniques. This procedure involves the generation of a linear stochastic process surrogated for the original time series. With this surrogate series, one can estimate the expected values for the K statistic under the hypothesis of linearity (KS). The existence of nonlinearity is confirmed if the test statistic from the surrogates KS is higher than the value of the statistic computed from the original data K (Ktest).The null hypothesis of nonlinearity is rejected if the value of the test statistic from the surrogates KS is lower than the value of the statistic computed from the original data K. Kaplan proposes two different estimations of KS. The first one is the minimum KS estimated using the surrogate series (KSmin). The second one is the average of surrogates minus two or three standard deviations (KS). Nonlinearity is detected when Ktest is lower than KS and KSmin. Using a software based on Kaplan's (available in www.macalester.edu/~kaplan/software) we show the results in Table 6, where for embedding dimensions from 1 to 10 and 1000 surrogate data; in all cases Ktest is higher than KSmin and KS. Once nonlinearity is confirmed, we verify the existence of chaotic dynamics, that is, the presence of sensibility to initial conditions. Lyapunov (1892) proposed a method to measure the rate of divergence between two orbits of a dynamic system when one of them is perturbed. The quantities computed are the Lyapunov exponents and are a measure of the system's instability. If the largest exponent (Lyapunov Characteristic Exponent or LCE) is positive, the distance between orbits grows exponentially in time, so the system shows sensitive dependence on initial conditions. In 1985 Wolf et al. (Wolf et al., 1985) propose the first numerical method to compute LCE and in 1993, Rosentein (Rosentein, Collins, & De Luca, 1993) developed a method valid with small data sets and robust against changes in embedding dimension, delay time, amount of data, and noise level. They apply the definition of Lyapunov exponent, measuring the average separation of neighbors. The calculation of the Lyapunov exponent, using Rosenteins's method, provides LCE ¼ 0.1743 indicating sensitive dependence of initial conditions, that is, chaotic dynamics. The 99% percentile bootstrap confidence interval 1000 bootstrap samples is (0.1715, 0.7333). To sum up the results, we have obtained evidence to support that the characteristics of arrivals at Majorca's airport suggesting that Majorca is a chaordic tourist destination.

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123

Fig. 4. Mutual information (up) and percentage of false nearest neighbors (bottom) for the logarithmic difference of daily arrivals LARRIVALS (A) and its linear filter FARRIVALS (B).

4. Conclusions and implications In recent times complex principles have been applied to tourist destination, and they have been characterized as complex systems. This paper proposes to go a step further, introducing the concept of chaordic system -synthesis of complex and chaotic, in tourism. In it, by employing a series of well-known techniques for the analysis of complex and chaotic systems we have confirmed that the dynamic evolution of Majorca tourist demand approximated by arrivals at the destination airport corresponds to a chaordic system where the five features mentioned above are identified: long memory, selforganization, resilience, nonlinearity, and sensibility to initial conditions. The chaordic lens enables managers to see the organization as an emergent, complex, dynamical, nonlinear entity in which order and chaos coexist (van Eijnatten & van Gallen, 2002; Fitzgerald, 2002; Wafler, 2004). In the chaordic management there are two dimensions at work: One is the process dimension that takes place at the day-to-day operations level though frameworks in place, and the other is the creative dimension driven by the staff at the informal systems level through innovation (Nixon & Rieple, 2010). Consequently, for a tourist organization to be adaptive, it must manage both the formal systems in order as well as other informal contacts among people within an organization to lead to the creation of emergent behavior (Stacey, 1996). Regarding the ordered pattern data of Majorca tourist demand have shown certain traits (long memory, self-organization, and

resilience) that are characteristics of the dimension related with order. The resilience of the system, the degree to which it is capable of absorbing shocks without dramatically modifying its structure or behaviors is a key aspect in a complex system's evolution (Walker, Holling, Carpenter, & Kinzig, 2004). Self-organization is generated from a bottom-up approach and leads to emergent behaviors and stability within a system (Johnson, 2001). At this dimension, managers should improve the capabilities for self-organization and building capacity for learning and adaptation based on the common culture of the organization e the shared beliefs, of where and how the company should operate and progress (Smith & Humphries, 2004). As Zahra and Ryan (2007) argue, although each element in the system may seem to act in an independent manner, collectively the entire system functions in an orderly manner as it is governed by a number of underlying principles that contain the necessary components for regeneration and reorganization, leading to spontaneous order. With respect to the chaotic dimension of the system, there is also evidence of non-linearity and sensibility to initial conditions in data of arrivals at Majorca airport. This means that the tourism system is not linear in nature, but it is an open system which is influenced by complex interactions and inter-relationships. Indeed, the forecasting of tourist flows goes beyond simple relationships of visitor numbers and time to encompass structural changes (Zahra & Ryan, 2007). In this realm, tourism management should be viewed as a process, constantly changing where small incremental impacts or errors in initial assumptions at a local level, could result

E. Olmedo, R. Mateos / Tourism Management 47 (2015) 115e126 1

0.9

0.9

0.8

0.8

0.7

0.7

0.6

0.6

0.5

0.5

0.4

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0.95

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0.85

2

3

4

5 6 7 embedding dimension

8

9

10

(A)

3

4

5 6 7 embedding dimension

8

9

10

2

3

4

5 6 7 embedding dimension

8

9

10

1

0.8

0.5 1

2

0.8 1

(B)

Fig. 5. Cao's coefficients E1 (up) and E2 (down) for the logarithmic difference of daily arrivals LARRIVALS (A) and its linear filter FARRIVALS (B).

in major impacts to the system (Arndt & Bigelow, 2000). Therefore, managing a complex system requires an adaptive attitude, more than a rigid deterministic one (Baggio, 2008). Managers should recognize that the interaction of varying groups of heterogeneous agents or people, ad-hoc meetings, task teams, and other informal mechanisms are the way through which a complex system might evolve (van Eijnatten & Putnik, 2004). We have also found evidence of ‘order from chaos’ based on the existence of a strange attractor that keeps and maintains the system within a set boundary. As Baggio (2008) affirms, although complex system are unpredictable, at least, with the appropriate tools of analyses large-scale behaviors at system level might be foreseeable if it is possible to describe the overall dynamics of the

Table 6 Kaplan test's results. m

KSmean

KSstd

KS

KSmin

Ktest

1 2 3 4 5 6 7 8 9 10

0.0817 0.0815 0.0821 0.0812 0.0818 0.0816 0.0805 0.0796 0.0796 0.0800

0.0004 0.0015 0.0019 0.0034 0.0039 0.0055 0.0069 0.0080 0.0109 0.0125

0.08050 0.07700 0.07640 0.07100 0.07010 0.06510 0.05980 0.05560 0.04690 0.04250

0.0804 0.0775 0.0778 0.0720 0.0735 0.0728 0.0634 0.0566 0.0557 0.0567

0.0731 0.0552 0.0412 0.0308 0.0235 0.0187 0.0164 0.0156 0.0136 0.0104

KSmean: average of computed K in surrogate data. KSstd: standard deviation of computed K in surrogate data. KS: estimation of K in surrogate data.KS¼KSmean3$KSstd KSmin: minimum of computed K in surrogate data. Ktest: computed K in original data.

system including the presence of any attractors and their basins (the regions of phase space in which they act). Once these have been identified, it can be possible to determine whether changes in some specific parameter can produce sudden shifts, or at least infer a probability distribution for their occurrence (Hansell, Craine, & Byers, 1997). This way, in accordance with chaordic systems thinking, the tourist organization is not a fixed structure, but a flow of dynamical processes orderly enough to ensure stability, yet full of flexibility and surprise (van Eijnatten and van Gallen, 2002). Putnik (2009) contends that chaordic systems thinking mechanisms are proved feasible and acceptable within the organization that seeks sustainability enhancing the ability of managers to develop, lead, and bring about change which is an emerging requirement in today's turbulent environments. Thus, through adopting a chaordic systems thinking lens the government of tourism systems would be benefited from the use of adaptive styles that allow a quick react to all the changes that may occur in the destination or in the external environment (Baggio, Scott, & Cooper, 2010b). Rather than trying to obtain and then maintain an idealized equilibrium state, adaptive management progressively accumulates knowledge through “social learning,” preparing managers and stakeholders to experiment, probe, adapt to, and benefit from small and large-scale change (Berkes & Folke, 1998). The conclusion finally drawn is that the chaordic system thinking possesses value by providing a new framework anchored in the meta-praxis of chaos for a better design of the theoretical models that endeavor to explain organizational patterns of tourism systems. This new way of thinking does not replace previous modes of thought, but complements those ways of analysis. Indeed, the main contribution of the chaordic lens is that truly complex social

E. Olmedo, R. Mateos / Tourism Management 47 (2015) 115e126

phenomena like tourist systems are equally capable of displaying simultaneously the order pattern of a formal system and the structures of change of chaotic systemsdall of which reinforce and complement each other. References
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ndez was born in Sevilla in 1972 and Elena Olmedo Ferna got her Bachelor of Science in General Economics by the University of Sevilla in 1995. She was honored with the Real Maestranza de Caballería Award for having the highest G.P.A. among 1995 graduates of the School of Economics and Business of University of Sevilla. She received her Ph. D. from the University of Sevilla in 2001 with the Doctoral Thesis entitled “Time Series Analysis in Nonlinear and Chaotic Economic Dynamics. Application to Spanish Economic Data”. At the present, she is working as Assistant Lecturer of the University of Sevilla where she has worked since 1995. From 2001 to 2004 she worked in a group using statistical tools to analyze the evolution of tourism in the province of Seville. She has published different works about theory and practice in nonlinearity and chaos in Economics and Management such us “From Linearity to Complexity: Towards a New Economics” and “Nonlinear Characterization of Spain's Unemployment”, in Complexity International (2004), “The New Complex Perspective in Economic Analysis and Business Management” in Emergence: Complexity and Organization (2002), “Complexity and Chaos in Organizations: Complex Management” in International Journal of Complexity in Leadership and Management (2010), “Is there chaos in the Spanish Labour Market?” in Chaos, Solitons and Fractals (2011) and “Forecasting Spanish Unemployment Using Near Neighbour and Neural Net Techniques” in Computational Economics (2014).

Ruth Mateos de Cabo is an associate professor in Marketing Research at the University CEU San Pablo in Madrid. She earned her PhD in Business Administration at the University CEU San Pablo, Madrid (Spain). Her research areas are implications of chaos theory and complexity in business and management, and corporate governance and diversity. She is author of several articles, and she has co-presented various reports at different congresses, such as, Conference on Board Diversity and Economic Performance (Copenhagen Business School, 2011), Gender Economics Cycle, (Banco de ~ a, 2009), 5th European Consortium for Political Espa n Research General Conference (Potsdam Univesit€at, 2009), 10th Women's World Conference (UCM, 2008).