Introduction

It is currently commonly understood that public policies should be formulated by arrangements with varying degrees of comprehensiveness, interdependence, and commitment, characterized by the interaction of different types of actors, which can be perceived from the various concepts that have been discussed in the literature as public policy subsystems, networks, public policy communities, epistemic communities, and governance, among others. Sabatier (2007, p.8) recognizes this complexity by stating that "the political process involves a wide range of extremely complex elements that interact over time." A series of relationships underlie this phenomenon, such as "knowledge of the goals and perceptions of many actors, the role of decision-making institutions, power relations, ideas, values and time." (Sabatier, 2007, p.8) It is from this process that public policies emerge and are shaped over time.

Sabatier and Jekins-Smith developed the advocacy coalitions framework in the early 1990s, precisely seeking a more comprehensive theorization that could incorporate these relationships, criticizing Lasswell's (1951) model of stages (Sabatier, 2007; Weible, Sabatier & McQueen, 2009). In the mid-1980s and early 1990s, some frameworks emerged that counterposed the sequential or stage view, such as John Kingdon's Multiples Streams Model, the Advocacy Coalitions Framework proposed by Paul Sabatier and Jekins-Smith in 1993 (later revised and expanded by the authors in 1999), and the Punctuated Equilibrium Model elaborated by Frank Baumgartner and Brian Jones in 1993. The three frameworks understand the policy process by which public policies originate, as complex, unstable, and subject to power relations among diverse actors. In addition, they include important variables in their analyses, such as ideas, the media, and public opinion, considering them important influences on the consolidation of a policy.

However, due to the high degree of complexity inherent in the policy process, some authors have recently criticized these models for their inability to comprehend this process holistically, simultaneously integrating the dimensions of agency and structure (Morçöl, 2010; Budd, Charlesworth & Paton, 2006; Ferlie, Lynn & Pollitt, 2005; Goodin, Rein & Moran, 2006). Others have also criticized these models because they favor the explanation of the stability of the political process rather than its instability (Eppel, 2016, 2009; Haynes, 2009, 2008).

Morçöl (2010) highlights the fact that traditional models [1] [2] of public policies, such as those mentioned by Sabatier (2007) among which are the advocacy coalitions framework, multiple streams, and punctuated equilibrium, cannot overcome the dichotomy between agency and structure. Morçöl argues that a vision that transcends the duality between micro/macro, that is, between agency and structure, like Giddens’ (1984) structuration theory, is needed. In this sense, Haynes (2009) argues for the need to have a “helicopter” view, which provides a panoramic view and makes it possible to look back at the structure, which according to him becomes as important as the analysis of micro behavior.

Parallel to these criticisms, recent studies have warned of the potential contribution of complexity theory to the field of public policy as a way to achieve a vision that would not prioritize agency, structure, instability, and process stability (Morçöl, 2012, 2010, 2005; Eppel, 2016, 2009; Haynes, 2009). In addition, there are discussions pointing out that complexity theory can contribute to the public policy field in general, although with some caveats, because there is no consensus on complexity theory itself since there are different jobs agglutinated under the same complexity, as noted by Cairney (2012). This questions whether there is a theory of complexity or whether "we must speak of many theories of complexity?" (Cairney, 2012, p.354) The same discussion also appears in Geyer and Rihani (2010), who note that "the theory complexity may complicate the study of public policy without offering something new or its insights can be described as 'obvious and common sense'.” (Geyer & Rihani, 2010, p.186) In addition, other authors, such as Koppenjan and Klijn (2014), Koliba (2014), Gerrits and Marks (2015), Rhodes et al. (2011), Teisman, van Buuren and Gerrits (2009), Teisman and Klijn (2008), and Klijn (2008), have warned of its potential application in various fields of public administration, including or excluding public policy processes.

The objective of this study is to identify the extent to which the concepts of complexity theory and complex systems are incorporated into the theoretical perspectives of public policy analysis, comparing the theoretical movement of the mid-1980s and early 1990s with the new theories, and seeking to identify differences or similarities. Thus, the question is: To what extent have public policy analysis models incorporated aspects of complexity theory to understand the policy process characterized by an increasingly complex and uncertain environment? The contribution of this study is to the field of policy process research in verifying how the new theories have responded to the call of the research that affirms that complexity could aid in the study of public policy. It is hoped that this analysis will situate the evolution of the use of the concepts of complexity in the theories of public policy in order to provide subsidies to expand the discussion itself about public policy analysis.

To achieve this objective, this paper is divided into five sections. First, complexity theory and its main concepts are reviewed. In the second part, there is a brief review of the evolution of the theorizing of the political process, which proceeds from a technical decision-making process, marked by stages, to its understanding as a complex process. Next, the discussion proceeds to the extent to which the three frameworks developed in the mid-1980s and early 1990s, namely, Multiple Streams (MS), Advocacy Coalitions (ACF), and Punctuated Equilibrium (EP), incorporated concepts of complexity theory into their structures. In the fourth section, we discuss how the most recent theoretical perspectives, the Robustness framework (RF) and Ecology of Games (EG), work with complexity thinking, and to what extent they use their concepts and methodologies. Finally, we present the differences or similarities between the two theoretical generations regarding the incorporation of aspects of complexity theory, seeking to reflect on the state of the field of policy process research.

Complexity Theory and complex systems

The purpose of this section is to present the concept of a complex system and its characteristics, because as discussed in the introduction, the authors argue that complexity theory can contribute to the study of public policies because the policy process from which public policies originate is in fact a complex system. Therefore, this section seeks to raise the main concepts of a complex system. In the following sections we will analyze how they are incorporated (by citing or implicitly) in traditional and new theories in the field.

Although the idea of “complexity” is not considered to be fully developed to achieve the status of a theory, there are undeniably a series of theories and concepts related to complex thinking that is applied in several areas of knowledge. Mitleton-Kelly (2003, apud Klijn 2008, p.301) distinguishes five different areas of research encompassed by the label of complexity: adaptive complex systems, originating from Kauffman's work (1990); dissipative structures, originating from the work of Prigogine (1996); the theory of autopoiesis (Maturana & Varela, 1991); and chaos theory. Criticism about the validity of complexity theory varies between arguments that there is no unification of theory with an organized set of testable propositions (Horgan, 1995), to claims that they constitute a set of tooling concepts rather than a definitive theoretical body (Bousquet & Curtis, 2011). In general, all theories encompassed under the label of complexity are concerned with how the nature of a system can be characterized from its constituent parts in a non-reductionist way (Manson, 2001), accepting disorder, uncertainty, and unpredictability (Goulielmos, 2005).

Regarding the definition of complex systems, Casti (1994) states that it is those types of systems that have the "fingerprints" of complexity. It is important to note that there are many different definitions of a complex system, but in general it has the following elements: (i) several heterogeneous agents; (ii) the agents act locally and have limited rationality; (iii) the agents interact with each other, which changes the system (emergence of patterns at the macro level that cannot be predicted from individual behavior); (iv) there is not necessarily equilibrium but a dynamic process of constant change with the possibility of more stable periods; (v) agents change their behavior in response to the emerging pattern; and (vi) an evolutionary process that selects or eliminates the emergent patterns (Wu & Marceau, 2002; Cilliers, 2005; Holland, 1995; Prigogine, 1987). Thus, concepts such as non-linearity (the consequence of emerging properties), adaptation, and co-evolution are essential concepts for understanding the behavior of a complex system. Each feature is explained below.

Emergent properties are the most obvious features that distinguish a complex system from a simple system, and explain why it is not linearity, but rather the unpredictability and inability to exercise control that defines a complex system. This means that abrupt changes can arise from simple actions of parts of the system. Emergence is linked to the idea of a "whole greater than the sum of the parts" (Morin, 2003); that is, the interaction of agents in the system forms more complex patterns of an organization than the agents' own patterns (Agar, 1999). In addition, emergency exists because of the interaction between the components of the system, and not because of the simple overlap between the parts.

Emergence is exemplified by Baranger (2000) as follows: the human body is able to walk. This is an emerging property. However, by studying only the head, only the trunk, or only the limbs of a person, there will be no understanding of the ability to walk. It is the emergent property of complex systems that precludes their prediction and control, since changes in a subsystem aiming at the change of the whole may not obtain the expected result, since the other components of the system change to adapt to the intervention, in addition to other changes in the environment (Manson, 2001).

Associated with the concept of emergency, there is the concept of feedback, as its role is of particular importance, since it is about non-linear relationships between changing entities (Manson, 2001). This differs from general systems theory where the notion of feedback is linked to linearity; that is, a change in A causes a proportional change in B. In a complex system, the fact that the parts of the system interact generating unintentional and different feedback scales is precisely the factor that explains the non-linear change; that is, that a change in A can have unpredictable effects.

As for adaptation, this is another striking feature of complex systems. Many authors use the term "adaptive complex systems” (i.e., Stacey 1996; Holland, 1995; Cohen & Axerold, 2000; Leite, 2004; Allison, 1998; Daft, 2002; Gellman, 1996), because these always look for a pattern. They interact with the environment, "learn" from experience, and as a result, adapt themselves (Gellman, 1996). According to Stacey (1996), the interactions between and the learning of agents in systems occur individually by means of a process involving discovery, choices, and action. Agents have "autonomy to guide their actions according to what they learn from their interaction with the environment - which is largely formed by the other agents." (Agostinho, 2003, p.33) In short, adaptation is the feature that allows systems to adjust to contingencies.

When considering an organization as a complex system, Stacey (1996) relates the concept of adaptation to organizational learning. According to the author, learning is characterized as a self-organized process capable of producing radically unpredictable emergent results (Stacey, 1996). In Stacey’s view, the learning process can take place in a linear way, in a process of direct learning through information, or in a non-linear way, in which the acquired knowledge undergoes a process of interiorization and reflection and is then processed (1996). Likewise, Lewin et al. (1999) state that organizations as complex systems can adapt in response to changes in environmental conditions in two ways: a) in the face of an uncertain environment, performing an incremental adaptation of the organizational form; and b) in an environment of great turbulence, generating new patterns of organization.

Evolution is a consequence of the process of adapting the systems. Kelly and Alison (1998) identify different levels of adaptation which correspond to different evolutionary stages of the system. Adaptation leads to a process of evolution, which is another striking feature of a complex system, linked to the fact that the system does not reach a state of equilibrium but continues to evolve. Evolution here must be understood from the notion of irreversibility in a complex system; that is, evolution does not imply progress, but simply that the system cannot return to its previous state, always changing to states that may or may not be considered "best" by the groups that influence the system. Co-evolution means that all subsystems that affect the system are also influenced by it, forming an evolutionary network system (Murray, 1998). In short, a complex system has some constitutive and behavioral characteristics that differentiate them from simple systems, as shown in the chart below:

Many researchers have used the concepts of complexity theory to understand and explain social systems. Complexity applies to systems with multiple agents interacting and changing according to such interactions; thus, it can be applied to many types of systems, including social ones, as they are composed of several members who interact consciously with one another (Byrne, 1998; Cilliers, 1988). These characteristics make complexity theory potentially applicable to the study of the policy process insofar as there are actors heterogeneously interacting with each other in the struggle to print their objectives in a given policy, and being affected by diverse influences and adapting to it over time (Eppel, 2009, 2016; Morçol, 2010; Haynes, 2008).

The following is a brief description of how theorization about the policy process has evolved over time, considering it as a plural decision-making process that is subject to the influence of diverse elements, such as the ideas, interests, and beliefs of the actors and contextual conditions, such as the rules of the political system.

Evolution of policy process theorization

The first instance of theorizing about the policy process came from the application of neoclassical economic theory to the world of politics. The so-called rationalist model assumed that the policy process was confined to the decision-making process in which a rational actor (decision maker) possessed sufficient information and resources from which to strategically analyze problems and alternatives, and choose the best option from all available options. Public policies would be the result of a decision by a public authority or an authority vested with public authority and governmental legitimacy (Sabatier & Weible, 2007). This theory was harshly criticized in the 1940s by Herbert Simon who emphasized the need to incorporate the limitations in the cognitive capacity of the actor, assuming that it has a limited rationality operating with incomplete information, and making not the best possible decision, but the most satisfactory decision within the conditions operated (Simon, 1947).

In parallel to the discussion about the nature of the process, emerged the Laswell approach, which understood the policy process as consisting of sequential phases. In this sense, the author proposed seven functional stages that would apply to the progress of any policy, which he termed intelligence, promotion, prescription, invocation, application, termination, and evaluation (Lasswell, 1951). Driven by Lasswell's work, models that comprised sequential stages or policies were popular in the 1970s and 1980s, and typically considered public policy to include the phases of agenda formation, policy formulation, implementation, and evaluation. However, they were criticized for failing to understand causal relationships, being imprecise from a descriptive point of view, and underestimating the role of analysis and learning for public policy (Sabatier, 2007).

Lindblom (1959, 1979) criticized the rationalism of Laswell and Simon and proposed incorporating other variables into the analysis of the decision-making process (Souza, 2006). In this sense, it was assumed that the decision-making process was centralized, but it was not based on large rational decisions based on the analysis of the listed alternatives and the costs involved, but rather on "incremental" decisions about existing policies, since decisions could be reversed at a lower cost compared to the costs of reversing substantial changes (Souza, 2006).

In the mid-1980s and early 1990s, some theories emerged seeking to understand the policy process by which public policies originate as complex, unstable, and subject to power relations among various actors. In addition, they began to include important variables in their analyses, such as ideas, the media, and public opinion, considering them important influences on the consolidation of a policy. Among these models, three stand out: the Multiple Streams model (Multiple Streams) proposed by John Kingdon in 1984, the Advocacy Coalition (Advocacy Coalitions Framework) proposed by Paul Sabatier and Jekins-Smith in 1993 (later revised and expanded by the authors in 1999), and the Punctuated Equilibrium model elaborated by Frank Baumgartner and Brian Jones in 1993.

The Advocacy Coalitions framework was developed precisely with the clear concern of providing an alternative to models of policy analysis according to stages, which according to their idealizers would lack conceptual robustness for the construction of empirically testable causal hypotheses. In addition, the authors were also concerned with formulating a public policy framework based on systems theory that summarized some of the key contributions of debates on top-down and bottom-up management, as well as analyzing the influence of technical information on public policies (Weible, Sabatier & Mcqueen, 2009). By emphasizing the role of values and ideas, the model, based on the beliefs of the defense coalitions, seeks to construct an overview of the functioning of the subsystem of public policies. A subsystem would be composed of diverse actors actively concerned and involved with a problem or policy issue. All the actors who play important roles in the formulation and implementation of public policies, as well as those who act in a relevant way in the generation, dissemination, and evaluation of ideas related to them, belong to the subsystem (Jenkins-Smith & Sabatier, 1993, 1999). External to the subsystem of public policies, stable factors would be present that are difficult to change, which can be understood as structural factors that would internally constrain individual action in the subsystem. These factors would be the basic attributes of the problem area, the distribution of natural resources, sociocultural values, and social structure, and the structure of the basic rules of the political system (Jenkins-Smith & Sabatier, 1999; Sabatier & Weible, 2007).

The Punctuated Equilibrium, developed by Baumgartner and Jones in 1993, is also an example of the evolution of public policy theorization beyond the rational choice model or stages. The model draws on elements of biology to explain the occurrence of long periods of stability, occasionally interrupted by abrupt changes that mark most public policies (Baumgartner & Jones, 1993).

The Multiple Streams also emerges with the purpose of providing a more comprehensive explanation for the process of public policy formulation, especially the construction phase of the governmental agenda, as opposed to the sequential or stage model; it is even considered the most complete model, insofar as it deals with different variables- external agents, ideas, institutions and processes-in the process of formulating public policies, tends to be a more integrative approach (John, 1998).

The objective of the Multiple Streams is to help understand the reasons why a topic becomes the focus of public policymakers and ascends to the agenda, and conversely, why some are abandoned. Kingdon analyzed the US federal government in extensive empirical research, interviewing several actors in the health and transportation sector between 1976 and 1979. He concluded that the process of formulating the agenda is highly competitive, and that changes in the agenda occur when three streams converge, each of which has its own dynamics and moves relatively independently: the political stream, solutions (policy stream), and the problem stream. In addition to the dynamics of the three flows, Kingdon also emphasizes the importance of the different agents in the process of formulating the agenda, especially the policy entrepreneur who is a skilled negotiator and has the ability to unite the three flows, providing the opportunity for new agenda items.

The three models in question have been extensively applied to different political realities, including in Brazil, as demonstrated by the studies of Brazil and Capella (2016) and Capella, Soares, and Brazil (2014). The three models are considered enshrined in the policy analysis field (Petridou, 2014; Schlager & Weible, 2013); however, other theories have been proposed from the joint efforts of several researchers, as shown by Schlager and Weible (2013) in a special 2013 issue of Policy Studies Journal, who consider them to be the new theories of the political process (2013).

Next, we will present the methodological procedures that were covered in this study in order to comply with the research objectives.

Methodological procedures

This study is characterized as exploratory and descriptive and seeks to investigate how the theoretical perspectives of public policy analysis have incorporated the concepts of complexity theory and complex systems, specifically the concepts of emergence, dynamic equilibrium, adaptation, and coevolution (see Table 1). The idea is to investigate how these concepts are explicitly or implicitly found in these theories. We sought to compare the theories considered as "established” (Petridou, 2014; Schlager & Weible, 2013), developed in the years 1980-1990, namely, the Advocacy Coalition Framework (ACF), Multiple Streams, and Punctuated Equilibrium, with the new theories in the field, seeking to highlight possible differences between them. In addition, we selected these three frameworks as they are also the most widespread and are the most applicable to the study of the formulation and implementation of public policies in Brazil, as demonstrated by the work of Brazil and Capella (2016) and Capella, Soares, and Brazil (2014).

This comparison is justified by the changes in the political process from the 1980s to the present, which are due to changes in public administration itself, changes in institutional arrangements, the influence of globalization, and the increasing complexity of public problems. This is expected to possibly bring forth new theoretical insights in which complexity theory could make sense.

The so-called new theories have been presented in a special edition of the Policy Studies Journal and all attempt to utilize their perspective to elucidate different aspects of the political process. The new theories are: The Institutional Collective Action Framework, proposed by Richard Feiock; The Ecology of Games Framework by Mark Lubell; the Policy Regime Perspective, developed by Peter J. May and Ashley E. Jochim; the Robustness Framework, proposed by John M. Anderies and Marco A. Janssen; The Collective Learning Framework, devised by Tanya Heikkila and Andrea K. Gerlak; and finally, the Narrative Policy Framework, which is the fruit of the work of researchers Elizabeth A. Shanahan, Michael D. Jones, Mark K. McBeth, and Ross R. Lane.

Two of the six presented in the special issue were chosen: the Ecology of Games (Lubell, 2013) and the Robustness Framework (Anderies & Janssen, 2013). The choice is justified by the fact that the authors of the frameworks themselves have made it clear that they understood the policy process as a complex system and that traditional theories did not account for explaining it in all its complexity; thus, these frameworks were designed precisely to overcome this gap.

In the next section, we seek to analyze how complexity has been incorporated in traditional theoretical models, especially in the Advocacy Coalition framework (ACF), Multiple Streams, and Punctuated Equilibrium, seeking to identify in each one if or how dynamics, adaptation, and co-evolution were explicitly or implicitly addressed. The same analysis will then be applied to the new theories, namely, the Robustness and the Ecology of Games Frameworks.

Traditional frameworks and tangential complexity

In the Advocacy Coalition framework (ACF), the policy process was characterized as an open system subject to change with the environment, and whose primary unit of analysis is the subsystem of public policies. These subsystems—in the plural, as each subsystem relates to a specific area of public policy—would be composed of diverse actors actively concerned and involved with a political problem or issue. All actors who play important roles in the formulation and implementation of public policies, as well as those who play a relevant role in the generation, dissemination, and evaluation of ideas related to them, would belong to the subsystem (Sabatier & Jenkins-Smith, 1999). These actors would effectively be involved with the problem and in the construction and defense of intervention alternatives (Sabatier, 2007).

External to the public policy subsystem, "Relatively Stable Parameters" would be present, which are stable factors that are quite difficult to change, even over the course of a decade or more, such as the basic attributes of the problem area, the distribution of natural resources, sociocultural values, and social structure, and the structure of the basic rules of the political system. These factors would be responsible for creating a series of constraints to the insertion of new themes in governmental agendas (Sabatier, 2007).

The ACF pays attention to the moments of change, establishing hypotheses about the conditions necessary for them to take place. Sabatier and Weible consider that inputs from the external environment to the subsystem, internal shocks, negotiated agreements, and the political learning built by the interaction of actors in the subsystem over time are responsible for changes in the process of the formulation and implementation of public policies (2007).

Events outside a certain subsystem would present stimuli for generating changes in a public policy, such as changes in social, economic, and political conditions, decisions on other public policies, and the impact of other policy subsystems. Internal shocks are of greater disturbance and impact the beliefs of the dominant coalition, and can therefore initiate a change in the understanding of a problem and its conduction. Negotiated agreements are also seen as a path to change when there are no internal or external shocks to the subsystem, but rather when there are situations of impasse (Sabatier & Smith, 1999; Sabatier, 2007).

As already discussed, a striking feature of complex systems is the fact that there is not necessarily equilibrium but a dynamic equilibrium with constant changes. Although the ACF considers the idea of an open system as being subject to environmental influences, moments of change and stability are seen as distinct moments and are "separated" from the explanation of the policy process. Haynes (2009) and Morçöl (2012) argue that a coherent view of complexity should not see change and stability as distinct moments, but should rather consider that the system lives in constant change, in a dynamic equilibrium. The ACF on the other hand places more emphasis on understanding the change and its importance as a stimulus (which can change the distribution of actors' resources) that may influence coalition performance.

Another striking feature of complex systems is adaptation. At this point, the ACF seems to implicitly dialogue with complexity theory insofar as it considers the need for an analysis of public policy over time. According to Sabatier and Jenkins-Smith (1993), policy-oriented learning affects aspects of the subsystem over extensive periods of time. Thus, it assumes that the interaction of actors within the subsystem where members of various coalitions would seek a better understanding of reality to enhance their political objectives (Sabatier & Smith, 1999; Sabatier, 2007), would favor the accumulation of knowledge about the characteristics of a problem and factors that affect it, promoting the evaluation of the adopted alternatives and impacting the realization of changes in certain public policies. Therefore, the concept of "policy-oriented learning" refers to the concept of the adaptation of complex systems, since the ACF assumes that the interaction of coalitions and the role of information can change behaviors based on the experience acquired in a given policy problem.

Unlike the ACF, the Multiple Streams model (MS) is concerned with a specific type of change; that is, the change in the governmental agenda either through the inclusion of new themes or even the abandonment of previously considered strategic themes. In this case, the unit of analysis is not a system or subsystem but "streams" that occur in a parallel and spontaneous way, namely, the problem, political, and policy streams. The stream of solutions, or the policy stream "[...] occurs without necessarily being related to the perception of the problem." (Calmon & Marchesini, 2007, p.8) Alternatives are generated in policy communities or communities that generate alternatives. In these communities, ideas are generated about solutions which float in a "primitive broth," which, similar to the process of natural selection, adapt and combine with one another, either remaining intact or being discarded. Alternatives that are technically feasible and cost-effective generally survive. From then on, these alternatives become diffused, not in an automatic way, but through a dynamic of persuasion in which individuals come to defend the idea not only for the political communities, but also for the general public, progressively building acceptance of the idea (Kingdon, 2010).

The third stream, the political stream, is composed of elements such as public opinion, pressure groups, election results, partisan or ideological distributions in Congress, and changes in the administration. In this stream, three elements are influential to the governmental agenda: the national mood, organized political forces, and changes within the government itself. National humor "creates a kind of 'fertile soil' for some ideas to germinate." (Capella, 2007, p.29) Thus, a favorable mood can encourage the promotion of some issues and at the same time discourage the promotion of others (Capella, 2007).

The three mentioned flows have their own dynamics and are relatively independent and sometimes converge, generating an opportunity for change in the agenda. Kingdom calls this windows of opportunity that occur in transient moments, allowing us to open "windows" at certain times as well as close windows at other times. When you open a window of opportunity, it is the moment when a condition succeeds in attracting the attention of policy makers; at the same moment, there are changes in the political stream which allow for changes in the agenda. Thus, formulators start to look for alternatives to the problems that have already been developed in parallel in the solution stream. In this way, Kingdon points out that the opening of windows of opportunity is influenced mainly by the problem and the political streams (Capella, 2007).

In order for the three streams to connect and for the window of opportunity to open, it is fundamentally the figure of the policy entrepreneur who defends an idea and acts in a timely political moment, linking ideas about problems to the solutions, and being responsible for promoting political changes (Kingdon, 2010; Capella, 2016).The great skill of this type of actor is to perceive the timing and to then act. These entrepreneurs do not have a specific profile, being able to be governmental or non-governmental actors who invest their resources in the defense of proposals with a view of obtaining future benefits. Thus, the entrepreneur plays a central role in policy change, but does not alone have the power to change the agenda (Kingdon, 2010; Capella, 2016)

The change in agenda from the opening of a window of opportunity comes close to the concept of emergence in complex systems, because when a topic rises to the agenda, we then have changes in relation to the previous agenda. The phenomenon of emergence in complex systems is characterized as a change in patterns from the emergence of a new pattern of system behavior to which the agents adapt and which cannot be predicted if only individual behavior is analyzed. Similarly, in the MS model, if we analyze only the dynamics of each stream, we cannot understand the opening of a window of opportunity, and consequently the rise of a theme to the agenda. Although the policy entrepreneur assumes a role that leads to change in the agenda, he/she cannot predict when a window of opportunity will open, or when the meeting of the three streams will take place.

In the same way, the Punctuated Equilibrium (PE) resembles that of the multiple streams model regarding the understanding of the dynamics of the policy process. Instead of flows, the model refers to the "processing" of problems at two levels, at the governmental (macro) level and at the non-governmental (micro) level. Small changes, considered incremental, would be the result of decisions made in the microsystem or political-institutional subsystems, in which the different issues are processed in parallel. Radical changes would be the result of the decisions made in the macro-political system, where issues are dealt with in series (Baumgartner & Jones, 2010).

The Punctuated Equilibrium assumes that many competing policy issues would survive simultaneously, waiting for the right moment to expand (Baumgartner & Jones, 2010). Here there is a similarity to Kingdon`s model that considers that problems exist while solutions are simultaneously developed independently of the recognition of problems; in other words, solutions and problems would be parallel and independent. In relation to change and stability, the model proposes that when an issue is captured by a microsystem, there is a period of equilibrium or near equilibrium. On the other hand, when an issue enters the macro political agenda, there are periods of imbalance in which the public policy agenda can change very rapidly, contrary to the consensus of established ideas (Baumgartner & Jones, 2010).

Contrary to microsystems, macro political systems are characterized by intense and rapid changes, different understandings of the same policy (different policy images), and positive feedback. According to Baumgartner and Jones, "The macro policy is the policy of punctuation - the politics of large-scale changes, competing images, political manipulation, and positive reaction." (2010: 137) The Multiple streams and Punctuated equilibrium models have a procedural view and emphasize abrupt, significant change, or in other words, the emergence of new issues in the governmental agenda.

The three frameworks analyzed here implicitly incorporate some concepts of complex systems. The ACF implicitly brings forth the concept of adaptation (in policy: oriented learning idea). In the MS, the concept of emergency stands out (in the idea of opening the window of opportunity and the ascent of new issues to the agenda) as well as the dynamic balance of the system (in which each flow has its own dynamics). Just as in the MS, the concept of emergency is also implicit in the PE framework (in the idea of the image captured by a macrosystem) and dynamic equilibrium (by assuming the existence of two systems, the micro and macro, which operate on different questions of differentiated forms). Traditional frameworks touch on complexity in a tangential way, using some concepts as a metaphor to explain certain situations in the policy process, such as the rise of issues to the agenda. However, some concepts such as evolution and adaptation are infrequently used in the narratives of these frameworks.

New theoretical developments and assumed complexity

According to Petridou (2014), the Robustness framework and the Ecology of Games framework approach complexity and uncertainty in different ways. In this section, we sought to identify how such models explicitly or implicitly incorporate the concepts of emergence, dynamic equilibrium, adaptation, and coevolution.

Anderies and Janssen (2013) argue that traditional models are still insufficient to understand policy processes in an increasingly complex environment, although they acknowledge that progress has been made in this regard, mentioning Sabatier's model of advocacy coalitions as an example. However, they argue for the need to develop other theoretical tools insofar as the environment in which public policies are constructed is marked by fluidity and globalization.

The ACF assumes that "relatively stable parameters" external to the subsystem influence the policy process and are composed of factors that would be quite difficult to change, such as the basic attributes of the problem area, the distribution of natural resources, sociocultural values, and social structure, and the structure of the basic rules of the political system (Sabatier & Smith, 1999). However, Anderies and Janssen (2013) state that in reality this does not always occur; sometimes changes in these parameters are faster than the progress of policies in the subsystem. They cite the example of the issue of climate change, stating that the effects felt on the environment are faster (melting glaciers, social movements, or both) than the progress of the construction of a climate policy, which can be seen in the fact that there has been little development in international negotiations on climate change.

Therefore, the assumption of slow changes and stable system parameters assumed by the ACF is not always the case. Anderies and Jensen argue that there must be a systematic approach to understanding the dynamic interaction between what they call the "political context"—equivalent to the notion of "relatively stable parameters" in the ACF—and the "intervention processes"—equivalent to the actions developed in policy subsystems—in the ACF (2013). By analyzing the Robustness framework, it can be inferred that the intervention processes represent the actors' space of action (micro) and the political context (macro), representing the structural aspects that influence the behavior of the actors. In making this distinction, the authors try to break with the dichotomy between agency and structure as proposed by Morçol (2010).

The Robustness framework is an extension of Ostrom's Institutional Analysis and Development (IAD) model (2009), and aims to understand key issues in the context of natural resource management. The framework makes explicit that public policy in this case is understood as a component of a complex adaptive system, which they call the socio-ecological system (SES), where politics affect and are affected by the biophysical processes of the context in which it is served. Examples of such biophysical processes would be soil degradation and climate change, among others (Anderies & Janssen, 2013).

The socio-ecological system is composed of a set of actors (resource users), a governance structure, and a resource system that are continually evolving and adapting at different scales and levels of the system. Thus, the policy process itself is seen as the emergent property of a dynamic socio-ecological system. The structure of these relationships is what Anderies and Janssen term "aptitude" between biophysical conditions, actors, and rules. A system with good aptitude is one that takes advantage of biophysical and social structures to reduce the costs of monitoring, sanctioning, and conflict management (Anderies & Janssen, 2013).

Anderies and Janssen argue that while it is not possible to understand all aspects of a complex system, researchers need to learn how to manage them. They point to the fact that in an ever-changing world, policies that are appropriate in one context may be vulnerable in another (Anderies & Janssen, 2013).

Experimentation would be a mechanism to increase the probability of achieving a good fit between policies and local conditions, which could be done by studying large systems to identify those aspects that are robust to the size of the system and those that are not. The idea is to reach an optimal point between vulnerability and robustness (Anderies & Janssen, 2013). However, Anderies and Janssen do not propose what the appropriate methodology would be to do this. They argue that one should not think of policy processes "driven by coalitions that uphold the 'right policy', but rather that directions should be devised that stimulate experimentation, adaptation and learning." (Anderies & Janssen, 2013, p.532)

The Robustness framework clearly assumes that it understands the policy process as fundamentally complex, especially when one considers the rapid changes promoted by globalization. In considering the dynamic interaction between "political context" and "intervention processes," the model assumes one of the characteristics of a complex system, which is the constant interaction between the parties in a dynamic equilibrium. However, it does not clearly address the issue of evolution or emergency, understood as naturally expected characteristics of the interaction between the two dimensions, and does not make explicit reference to them. In the same way, the idea of the aptitude of the system leads to the conclusion that evolution is a characteristic of the system as a whole; however, the framework does not clarify how evolution would be operationalized.

The idea of system management is one of the reasons for the proposition of the framework, because according to Anderies and Janssen even if it is not possible to know the entire operation of a complex system due to uncertainty, it is possible to manage it.

As for the Ecology of Games framework, Lubell (2013, p.357) clearly states that "institutional complexity is not a hypothesis, it is a fact" and that policy science needs a theoretical model to empirically analyze "the structure, process, evolution and outcomes of such complex adaptive systems." (Lubell, 2013, p.537) In order to fill this gap, Lubell updated the Game Ecology (EG) model developed by Norton Long (1958).

The main characteristic of the EG framework is to simultaneously provide analysis of the interaction of several policies (governance), considering that the result of a policy is due to decisions made in multiple "games" over time. A political game consists of a set of political actors who participate in a collective decision-making process governed by formal or informal rules—which it calls a "political institution"—that takes place within a geographically defined political arena called "systems." (Lubell, 2013) Policy systems are territories with public problems, multiple institutions related to the problem, and various actors. Systems can be defined at different scales: local, regional, state, national, and global. The assumption is that institutions are linked at various levels, and a decision in one institution affects the set of possible solutions of another institution (Lubell, 2013). For example, a federal-based decision will shape the dynamics of "political ecology" at lower levels, such as at the state and municipal levels. Policy outcomes also depend on how individuals make decisions about resource use in each issue. Actors can also engage in strategic behavior in different systems, from local to global, in order to reshape institutions at different levels to better pursue their interests (Lubell, 2013).

The change in the game may be induced by internal or external factors. The first is based on the strategies of the actors involved who can go through different scales and engage in processes of policy learning, creating and destroying institutions. The second may be due to the change in existing resources and to decisions by higher-level institutions that would impact decisions in the local game. The changes would be difficult to predict and may sometimes be significant. The system that is able to adapt to the ever-changing environment and continue to promote solutions to collective action problems over time would be considered efficient or resilient (Lubell, 2013). Lubell (2013) clearly assumes that he relied on the literature of adaptive complex systems, assuming that global system standards are the result of innumerable local interactions between heterogeneous components and the self-organization of actors at different scales.

The components of the evolution of the model would be represented by the survival of the institutions which depend on the political support of the actors. Thus, institutions that are most effective in solving problems of collective action and that distribute resources in ways that powerful actors perceive as just are more likely to survive (Lubell, 2013). The EG framework intends to produce empirically testable hypotheses about the structure and function of systems involving the interdependence of various policies and processes that influence individual behavior and institutional change, and to understand how different types of institutional arrangements are linked to the outcomes and effects of policies to provide recommendations on how to manage the system. For Lubell, academics and policy analysts should provide policymakers with recommendations to help them achieve their goals; the proposed framework would play that role (2013).

The notion of interaction between components, which is central to the concept of a complex system, is broader here than in the Robustness Framework, since in addition to understanding the interaction between the "political process" and the "political context," the model considers interaction on political decisions at various levels as causal factors for the explanation of a given policy. This is because institutions are considered interconnected. At this point, the model proposes to perform both a longitudinal analysis as well as the vertical interactions (between the different levels, from the international to the local).

As in the robustness model in which a system is considered adequate, in this case, the system is also considered efficient or resilient according to its adaptability and to continue to promote effective solutions to problems. Institutions are the cornerstones of evolution, since those considered more effective from a problem-solving point of view would survive over time. In the same way, Anderies and Janssen justifies that the idea of understanding a complex system is fundamentally to manage it.

In short, the concept of dynamic equilibrium is implicit in the idea of dynamic interaction between the "political context" and the "intervention processes" of the Robustness framework. The model does not address the issue of evolution, rather its focus is on understanding the interactions of ever-changing components, which in some ways are imbued with the idea of adaptation. However, it does not clearly address the issue of evolution or emergency and does not make explicit references to these concepts.

The EG framework seems to encompass all the concepts of a complex system; however, the interaction for it is more detailed than in the RF. The unit of analysis is broadened beyond the two levels of the Anderies and Janssen (2013) model, assuming that the policy process occurs at different levels from the international to the local, and that this interaction influences the formulated and implemented policy. Thus, in addition to the longitudinal interaction, over time, the framework also lends itself to analyzing the vertical interaction (between levels).

The notion of adaptation is also present when considering that a system could be more or less resilient or efficient in that it can to a greater or lesser extent adapt to constant changes. Institutions in this case would be the component in which evolution operates, insofar as the model considers that the most effective institutions would evolve. As in the Robustness framework, the notion of system management is also present. However, the two frameworks do not propose a specific methodology to conduct the analysis according to their assumptions. Lubell (2013) suggests that social network analysis may contribute; however, this assumes that other methodological directions still need to be thought out.

Final considerations

From the discussion undertaken in this paper, it has been shown that the new theories of public policy that have been analyzed have the explicit concern of incorporating the concepts of complexity, unlike traditional theories that did not have such a concern, or at least did not have such an explicit concern. In traditional theories, the concepts of complex systems were implicit in the construction of the frameworks and were used almost metaphorically to explain certain phenomena of the policy process, such as the change in the agenda and the learning of the actors. However, tools were not offered that could capture this dynamic interdependence between agents and structure.

In the new theories analyzed in this study, the dynamic interdependence between agent and structure appears more explicit, starting from the idea of interaction between "political context" and "intervention processes" (in the Robustness framework), and between political institutions and “systems” (in the Ecology of Games). The Robustness, like the traditional models, did not incorporate other important aspects of complexity, such as emergence and evolution. In this sense, the EG seems more complete, incorporating the main concepts of a complex system, such as dynamic balance, emergence, adaptation, and coevolution,

However, the new theories do not present the methodologies of analysis; that is, they do not explain how it would be possible to analyze these interactions. This is perhaps because the goal is not to understand these interactions, but to choose the best solution which makes the system more efficient. In these new theories, it is implied that a vision of the formulation of policies with a more technical character seems to leave aside the conflict, argumentation, and the politics of the political process itself. An example of this is the fact that the RF assumes that experimentation may be able to find a good fit between policy and local conditions by identifying factors that are robust or vulnerable in the system. Moreover, it is possible to manage this system (as stated by the Robustness), and/or provide advice to decision makers, as proposed by the EG. Thus, through the analysis undertaken here, it is possible to suppose that a greater or lesser incorporation of the concepts of complexity, or in other words, complexity assumed or tangentiated, serves an explanatory purpose in the very understanding of the policy process under which public policies are formulated and implemented, and of the role that public policy analysis must fulfill, namely, a prescriptive or descriptive function.

The analysis of this study made it possible to visualize a movement towards an effort to think about other theoretical and methodological approaches that are capable of understanding the public policy process, which is characterized by constant change, uncertainty, and instability. However, we cannot assert that there is a single perspective when trying to analyze the policy process as a complex system, since the very concept of complexity has multiple interpretations. Researchers in the field of policy analysis seem to find themselves in this engagement in the face of an increasingly complex reality.

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Elements that constitute the complex system	Behavior of the complex system	Related concepts
Agents that act locally and have limited rationality	They emerge from macro-level patterns that cannot be predicted by individual behavior.	Emergency/non-linearity
The agents who interact with each other and with the environment in which they are inserted (system subject to environmental influences)	There is not necessarily a balance but a dynamic process of constant change with the possibility of more stable periods.	Dynamic equilibrium
	Agents change their behavior in response to the emerging pattern.	Adaptation
	There is an evolutionary process that selects or eliminates the emerging patterns.	Co-evolution