A Percolation-Like Process of Within-Organization Collective Corruption: A Computational Approach

Abstract

This study investigates how collective corruption appears, using a computational method. Specifically, acknowledging that the characteristics of collective corruption process are analogous to percolation phenomena, we illuminate that collective corruption is formed by ongoing social interactions in an organizational boundary. By formulating a percolation-based system dynamics model, we consider the behavioral characteristics of collective corruption in terms of individuals’ corruption preferences governed by personal attributes on corruption. We also propose and examine scenarios regarding the formation of collective corruption.

Keywords

collective corruption percolation system dynamics

Corruption is not always the consequence of an individual’s immorality; rather, it is the result of collective misbehaviors of multiple actors (Ashforth & Anand, 2003; Greve, Palmer, & Pozner, 2010; Lin, 2001; Nielsen, 1996; Noonan, 1984; Pinto, Leana, & Pil, 2008). As seen in the cases of insider trading (“Crony Capitalism,” 2004), price fixing (Baker & Faulkner, 1993), financial fraud (Baker & Faulkner, 2003, 2004), and churning (McLean, 2001), corruption often occurs when one actor enables the other actors (e.g., board members, employees, supervisors, or persons from other firms in the same/different industry) to increase opportunities for deceit, deviance, and misconduct (Ashforth & Anand, 2003; Pinto et al., 2008; Smith-Crowe & Warren, 2014). That is, corruption comes up with “collective efforts intentionally orchestrated by a number of interconnected individuals” (Greve et al., 2010, p. 68). Also, Baker and Faulkner (1993) contended that a corruption is “enacted by collectivities or aggregates of discrete individuals in the context of complex relationships and expectations among boards of directors, executives, and managers, and among parent corporations, corporate divisions, and subsidiaries” (p. 842). That is, a corruptive practice occurs not by an atomic individual actor but by a group of actors who perceive it as usual in a certain field (Ashforth & Anand, 2003). In this sense, collective corruption can be defined as “a form of crime that involves the sustained coordination of multiple organizational participants” (Palmer & Maher, 2006, p. 363).

In viewing collective corruption, researchers have examined how corruptive behaviors perpetrated by one or a few individuals can become an organizational phenomenon (Ashforth & Anand, 2003; Brief, Buttram, & Dukerich, 2001), especially focusing on the cause of the corrupted state (except Palmer, 2008; Palmer & Maher, 2006). This research stream, however, has rarely paid attention to the process of collective corruption (Greve et al., 2010; Palmer, 2008; Pinto et al., 2008; Smith-Crowe & Warren, 2014). In explaining how collective corruption occurs within an organization, we postulate that corruption in organizations has an aspect of social construction (Anand, Ashforth, & Joshi, 2005; Baker & Faulkner, 2004; Granovetter, 2007; Greve et al., 2010; Nielsen, 2000; Verbrugge, 2006). Given that a practice in an organization can be accepted through ongoing social interactions in a social structure (Giddens, 1984), even practices which are currently perceived as misconducts by the majority of social actors could get legitimacy if social interactions were engaged. That is, societal evaluation on the misconducts can be negotiated to re-define their social meanings in an organization (Ashforth & Anand, 2003; Greve et al., 2010; MacLean, 2008; Sykes & Matza, 1957). As such, the misconducts previously rejected or stigmatized can be legitimated and collectively mobilized among the organizational members. In particular, given that the interpretive engagement of social actors depends on cultural meanings (Ashforth & Anand, 2003; MacLean, 2008), such a kind of corruption is characterized as being particularistic and contextual (Schweitzer, 2005; Sims & Brinkmann, 2003).

From this standpoint, we pay attention to the social construction characteristic of collective corruption. In particular, we need to understand how a corruption within a firm can appear in a collective way (Anand et al., 2005; Ashforth & Anand, 2003; Brief et al., 2001) through interactions between individual persons within it. As Schweitzer (2005) contended, corruption can occur when “corrupt actions” appear as (largely) normal and as being in conformity by individual actors over a longer period of time. Thus, the more social actors who adopt an unethical behavior in an organization, the more likely corruption which is collectively made in the organization (Baker & Faulkner, 1993; Smith-Crowe & Warren, 2014).

In this study, to make better understanding of collective corruption in terms of its formation process, we develop a computational model of collective corruption at the individual level. Given that collective corruption happens as a corrupt behavior (which might be initially illegitimated among organizational members) is adopted by the organizational members (Ashforth & Anand, 2003; Palmer & Maher, 2006), our computational model is based on percolation models (Duffie & Manso, 2007; Solomon, Weisbuch, Arcangelis, Jan, & Stauffer, 2000). Originally, percolation models were developed in fluid physics to explain the natural phenomena of percolation (Stauffer & Aharony, 1994). The scholars in fluid physics, with the percolation models, have investigated the processes where liquid makes its way to reach the one end from the other end point through paths allowing the liquid to flow (Broadbent & Hammersley, 2008; Hassan & Rahman, 2016; Kesten, 1982). Adopting the metaphor of percolation, scholars in social science, by reframing the processes of percolation as phenomena of information spread, reinvented models of percolation, which are called social percolation or information percolation (Duffie & Manso, 2007; Solomon et al., 2000). That is, percolation models in social science mainly deal with how a certain information or behavior spread throughout a certain organizational boundary (Hohnisch, Pittnauer, & Stauffer, 2008; Ruan, Iniguez, Karsai, & Kertész, 2015).

Accordingly, we explain the collective corruption process as a percolation-like phenomenon, based on multiple characteristics of personal attributes including initial level of corruption tendency, attitude toward risk, and authority. To elaborate our idea on the formation of collective corruption, first, we present the basic mechanism of collective corruption, based on these analogous characteristics of percolation theory to the collective corruption. Then, we translate its properties and theoretical relationships into the system dynamics approach of stocks, flows, and feedback loops (Forrester, 1961; Sterman, 2000). Then, we specify different organizational contexts, which can influence the formation of collective corruption, with scenario analyses using Monte Carlo simulation methods. Specifically, considering different configurations of the factors to enhance or constrain the percolation process, we investigate how different settings lead to diverse formation processes of collective corruption. Then, implications are subsequently presented.

Theoretical Background

Formation of Collective Corruption

The formation of collective corruption has been understood as multistage processes (Ashforth & Anand, 2003; Brief et al., 2001; Palmer, 2008; Palmer & Maher, 2006). First, those who intend to commit a misconduct decide to authorize it (i.e., initiation). Then, they find their supporters in implementing the misconduct (i.e., proliferation). Then, the misconduct is embedded in organizational routines and cultural norms (i.e., institutionalization). Finally, new organizational participants internalize the wrongful course of behavior as an existing norm (i.e., socialization).

This process model of collective corruption indicates that collective corruption is facilitated by interactions among social actors (Palmer, 2008). And it is perpetuated throughout an organization (Ashforth & Anand, 2003; Brief et al., 2001). These natures of collective corruption are, particularly in the perspective of structuration (Giddens, 1984), interpreted as an enactment of social actors for a state where a misconduct is taken for granted in an organizational boundary. Furthermore, given that ongoing social interactions reinforce the current practices (Feldman, 2004; Strauss & Quinn, 1997), the enacted misconduct in an organization can create additional accumulations of corruption opportunities through social interactions. As such, a misconduct is collectively mobilized over time, resulting in collective corruption. Taken together, we can understand that ongoing social interactions are a central mechanism for the formation of collective corruption.

However, collective corruption would not be automatically mobilized even if social interactions are engaged in. There are two main barriers against the formation of collective corruption, particularly in terms of disseminating corrupt actions. First, it is hard for people to engage in wrongful acts which violate their own morality (Smith-Crowe & Warren, 2014). According to the process model of collective corruption, corrupt actions are perpetuated as a rational choice (Palmer & Maher, 2006) or mindlessly (Palmer, 2008). In fact, collective corruption may be intimidated by those who think certain practices are morally wrong. As Smith-Crowe and Warren (2014) acknowledged, if individuals are mindful in doing wrong or conscious to whether such a wrongdoing is consistent with their norms, values, and beliefs, they would not be willing to engage in the wrongdoing (Palmer, 2008). Second, social interactions among actors per se tend to limit the engagement in collective corruption, as they comply with social expectations among other people (Palmer, 2008). As evidence, Manz, Joshi, and Anand (2005) observed that employees tend to hesitate to affiliate and bond with corrupt actions due to social pressures. Also, social relationships often play a role as monitoring devices and punishment regimes to de-incentivize corrupt actions. Specifically, individual actions are constraint by shared expectations regarding how one will act in organization, and this constraint is amplified through social interactions (Medina, 2007; Ostrom, 1998).

Despite these barriers, corporate corruption can occur as misconducts are diffused through a social structure in which social actors interact one another as direct and close as possible. In fact, to avoid the constraints drawn from social expectations, individuals are reluctant to share corrupt actions with those who they cannot trust. As such, corrupt actions tend to diffuse with extreme secrecy between close relationships (“Crony Capitalism,” 2004).

From these standpoints, we specify the characteristics of collective corruption occurring in organization. First is the path dependence. As corrupt actions are allowed to be disseminated only when the other individuals accept the corrupt actions (Smith-Crowe & Warren, 2014), one tends to pass his or her corrupt action on the person nearest to him or her. This makes corrupt actions conveyed along with his or her existing social networks (Baker & Faulkner, 2003, 2004; Brass, Butterfield, & Skaggs, 1998). In particular, given that social networks are created and persist based on trust or reciprocity (Uzzi, 1997), corrupt actions would be introduced to only those who are trustworthy (“Crony Capitalism,” 2004). As such, if a person who has a corrupt action had no social ties, collective corruption could not take place. This suggests that there is a path which can lead to collective corruption. And the path is drawn from existing social ties of the person who has an original corrupt action. In other words, collective corruption, which is formed, by definition, when multiple actors share a certain corrupt action, is dependent on existing social ties, which creates a path for collective corruption (Baker & Faulkner, 2003, 2004).

Second is diffusion. According to the process model of collective corruption, corrupt actions can be exchanged and shared within an organization (Brief et al., 2001; Palmer, 2008; Palmer & Maher, 2006). An original corrupt action is passed on the other person; once he or she decides to accept the action, a social tie (or a path) to convey the corrupt action is created and the action is legitimized through the path; then, the person who accepts the corrupt action, in turn, can play a role as another disseminator of the action. As such, a certain corrupt action, originated by only one organizational member, is disseminated throughout an organization (Ashforth & Anand, 2003). As a result, collective corruption is formed in an organizational boundary. This indicates that as more people are involved in the corruption exchange, corrupt actions can be diffused throughout the organization; thereupon, collective corruption unfolds.

The final aspect is phase transition. Given that a corrupt action cannot be easily conveyed to others (Palmer, 2008; Smith-Crowe & Warren, 2014), collective corruption is invisible until it reaches a certain level for an observer to become aware of it. This implies that, to be formed, collective corruption carries a moment that a particular behavior which has been perceived as unethical or unacceptable becomes legitimate throughout the organization (Ashforth & Anand, 2003). And thus, we can discern two phases in the formation of collective corruption: One phase indicates that an action is perceived as morally wrong and the other phase indicates the action as acceptable. Given that the moment that a corrupt action becomes legitimate throughout the organization is determined by the decisions that each organizational member to whom a corrupt action introduced evaluates that this action is acceptable (Palmer, 2008; Smith-Crowe & Warren, 2014), the moment that previously perceived as wrongdoings can become normal is understood as the transition of the former phase into the latter phase.

Percolation as a Behavioral Representation of Collective Corruption

Based on these three characteristics in the process of its formation, collective corruption can be understood as a process of percolation. In fluid physics, percolation refers to the movement and filtering of fluids through porous materials (Saberi, 2015; Stauffer & Aharony, 1993). Percolation is a natural phenomenon that we can see, such as the development of forest fires and the penetration of oil or gas into porous rocks, which would turn into oil reservoirs. To explain these natural phenomena, theories on percolation, developed in fluid physics, deals with connective characteristics of fluid flow (or any other similar process) in random media (Fortunato, 2003; Stauffer & Aharony, 1994). As such, the percolation metaphor helps explain how a spanning cluster emerges which connects the two sides of the lattice, for example (Fortunato, 2003; Saberi, 2015). In fact, other than the natural phenomena, by formulating a simple stochastic model for such a situation, percolation theory has been applied to a wide range of social science to explain various social phenomena (Ahmed & Abdusalam, 2000; Goldenberg, Libai, Solomon, Jan, & Stauffer, 2000; Gupta & Stauffer, 2000; Hohnisch et al., 2008; Proykova & Stauffer, 2002; Ruan et al., 2015; Solomon et al., 2000).

The applications of percolation theory to social phenomena have been made in terms of how information spreads through within a certain setting (which can be a lattice in physics or a social network in social sciences, for example). The information spread implies (a) how individuals adopt new knowledge or (b) who will be the information sender or information receiver (Strang, 1991). In particular, many studies on information spread or social percolation delved into the question of what structure can convey a new information or a certain behavior more easily (Burt, 1987; Strang, 1991). As such, social percolation reveals a process which has the stages as follows: (a) that there is initial information to be delivered through social structure and (b) once a new idea is generated, it flows through existing structures.

Following the research stream of social percolation models, we postulate that percolation phenomena are analogous to the collectively formed corporate corruption. First, collective corruption deals with corruption exchange (Brief et al., 2001). According to Baker and Faulkner (2004), through social ties, corruptive practices can be diffused by each member within organizations (Baker & Faulkner, 2004). As such, individuals, inside of the organization, collude for their own benefits through their social relationships. Similarly, percolation finds how a locale in a fixed structure is adopted by a material from the other proximal locale (Stauffer & Aharony, 1994). This implies that a material is shared between two proximal locales. And the connected locales by sharing the material are clustered in the whole structure (Fortunato, 2003). Likewise, according to collective corruption, a misconduct initiated is shared among individuals (Palmer & Maher, 2006). And such corruption exchange discerns a group of organizational members who adopt a corruptive behavior, indicating that the misconduct spreads out through clustering in an organization. In other words, clustering, as percolation reveals as its outcome (Fortunato, 2003), occurs among organizational members in terms of the adoption of a misconduct. And this can be an initial signal that makes a collective corruption.

Second, each individual in an organization makes his or her own decision on whether the misconduct is adopted or rejected. Given that collective corruption is formed when multiple social actors are jointly engaged in a corrupt action, it is crucial how acceptable the corrupt action is to those who are requested to engage in the action (Ashforth & Anand, 2003; Palmer, 2008; Palmer & Maher, 2006). According to percolation theory formalized in fluid physics, materials cannot flow in a structure until a certain threshold level for the material flow is reached in the structure (Stauffer & Aharony, 1994). The threshold levels vary according to the quality of structure in which liquid flows, the type of liquid, and the pathways within the structure (Stauffer & Aharony, 1994). In terms of collective corruption, the notion of threshold levels can be understood as the moment that one adopts another’s unethical behavior or one’s behavior which has been understood as illegitimate in an organization becomes accepted by another organizational member (Ashforth & Anand, 2003; Palmer & Maher, 2006). Also, the notions of the threshold determinants can be interpreted as what individual or organizational conditions under which a corrupt action can spread throughout the organization. In particular, as percolation theory emphasizes the structure in which liquid flows, any structural characteristics in the organization, such as the leader–follower relationships or any relational structure among organizational members (Brass et al., 1998; Greve et al., 2010), as well as individual characteristics, such as individual tendency on corruption (Greve et al., 2010; Palmer & Maher, 2006), will play critical roles in the formation of collective corruption.

Third, the corruption exchange unfolds spatially. Percolation phenomena are about how liquid flows in a fixed structure. According to percolation theory in physics, percolation unfolds when the two nearest neighbors are tied in a structure, as close relationships can constitute a path for the media flow (Fortunato, 2003; Saberi, 2015). This is analogous to how unethical intention or practices are conveyed in an (existing) social structure. As collective corruption indicates, misconducts would be diffused if individuals are standing close to one another (Brief et al., 2001; Palmer, 2008). Furthermore, all the misconducts start to diffuse with extreme secrecy because the corruption exchange usually takes place between close neighbors.

In sum, given that percolation is based on connective characteristics between locales in a structure, it can explicate how corruption is formed, developed, and saturated in a collective way within an organization. Suppose that there is a certain social structure within an organization, constituted by social relationships, and each organizational member is located in each locale in the social structure (Chang, Stauffer, & Pandey, 2002). When one actor is corrupted (or has a corrupt action), his or her nearest neighbors are vulnerable to the corruption, as the focal actor disseminates the corrupt action through his or her social structure (Radicchi & Castellano, 2016; Zhukov, Khvatova, Lesko, & Zaltcman, 2017). When the corrupt action is delivered to the neighbors, collective corruption will take place unless the neighbors reject the action.

Table 1 presents how different are the models based on the percolation as a natural phenomenon, as a physics formulation, social percolation as an application to social science, and as a phenomenon around collective corruption.

Table 1.

Percolation in Different Domains.

	Natural percolation	Social percolation	Percolation-like collective corruption
Phenomena	Movement of media in a certain environment	Information spread in an organizational setting	Spread of corrupt acts in an organization
Media	Physical materials (e.g., liquid)	Intellectual materials (e.g., information)	Corruption opportunities (e.g., acts or ideas)
Paths	Lattice	Social network	Social network in an organization
Nodes	Objects (e.g., atoms, ions, and metals)	Social entities (e.g., individuals or organizations)	Actors within an organization boundary
Phase transition	Change in the objects’ states	Adoption of a new information	Normalization of corrupt acts

Percolation models in physics capture the movement of physical materials (e.g., liquids) in an environment. The environment for the percolation process is defined as the arrangement of particular objects (e.g., atoms, ions, and metals) called a lattice. In particular, the neighboring objects in the lattice make paths through which the materials flow. As a result, the state of an object is changed. Percolation phenomena are found when the object’s state has been changed through the material flows.

On the contrary, social percolation models focus on information spread in a social structure. The social structure, which is the environment in which social percolation takes places, is made up of social relationships among social actors (who can be individuals or organizations). That is, social percolation models capture how information flows through social relationships. When an information is adopted by the other through social ties, social percolation can be identified.

Along with the social percolation models, the percolation-like collective corruption indicates the process where corrupt acts diffuse through social relationships within an organization. Organizational members actively convey corruption opportunities (e.g., corrupt acts or any ideas on corruption) to the other organizational members who are connected to them. As the other organizational members accept the corruption opportunities, the corruption opportunities become legitimated and normalized throughout the organization. This transition forms a percolation-like collective corruption.

Methodological Approach

Percolation-Based System Dynamics

The purpose of our effort is to move toward a general explanation of how collective corruption can have percolating processes or properties. We choose formal modeling as a tool for theory development because while there is a rich array of narratives and case-specific theories of collective corruption, there have been fewer efforts to develop a theory that abstracts from different domains (Lambsdorff, Taube, & Schramm, 2005). Drawn from percolation theory, we postulate that connective characteristics of material flow (e.g., corruption information for this study) either maintain or modify the connected actors’ current activities (Zhukov et al., 2017). This means that social actors, once connected, influence each other in transmitting materials.

Those recursive relationships between actors can be reframed as feedback loops, which can be easily formulated in system dynamics (Black, Carlile, & Repenning, 2004; Rudolph & Repenning, 2002). System dynamics models enable to understand how an individual actor changes his or her attitudes and behaviors through interactions with other actors over time (Sterman, 2000). In this sense, the system dynamics methodology sheds light on the recursive feedback process with dynamic and system thinking perspectives (Richardson, 1998), in a holistic view (Senge, 1990; Sterman, 2000). Accordingly, we treat percolation theory as our basic platform and translate its concepts and properties into the system dynamics language of stocks, flows, and feedback loops (Forrester, 1961; Sterman, 2000). With this mapping, we apply our diagrams and frames to constructs and relationships in other collective corruption cases in an iterative process of model elaboration and revision.¹

Percolation-Based Model of Collective Corruption Formation

Given that percolation signifies how new information is conveyed from the one end to the other (Khvatova, Block, Zhukov, & Lesko, 2016; Radicchi & Castellano, 2016; Ruan et al., 2015; Zhukov et al., 2017), we specify the percolation-based formation process of collective corruption in terms of (a) initiation of corruption (i.e., an opportunistic and self-interest seeking nature), (b) its dissemination, and (c) feedback from the dissemination. To model this process, we hold three assumptions. First, there are a focal actor (called ego) and his or her neighbor (called alter), who are connected to each other within an organization. Second, the alter has a relationship with the ego so that each party can share corruption-related ideas with the other. Third, interactions between the ego and the alter continuously happen. These assumptions imply that a dyadic relationship between ego and alter is a minimum unit of collective corruption. That is, a collective corruption starts with the ego’s initiation to implement a corruption opportunity, but its growing is affected by the alter, who accepts, validates, and even participates in the implementation of the corruption opportunity.

Based on these assumptions, we build up a model to explain the process where both the ego and the alter update their preferences on corruption in their own ways in response to the ongoing interactions with them. Specifically, through the relationship with the alter, the ego disseminates a corruption-related information and the alter evaluates the information to decide whether to adopt it. In response to the alter’s response to the ego’s dissemination of corruption, the ego and the alter update their corruption preferences, respectively. If both have a high level of corruption preference, this would result in a collective corruption. That is, collective corruption is initiated depending on how likely a corruption opportunity is diffused through social interactions between the ego and the alter. Figure 1 presents the recursive relationship between the ego and the alter with respect to corruption preferences.

Figure 1.

Causal loop diagram.

Figure 1 is constituted by reinforcing loops, which lead to exponential behaviors, as well as balancing loops, which indicates goal-seeking behaviors (Sterman, 2000). The combination of those feedback loops determines how a collective corruption is formed over time: Social actors’ corruption preferences are simultaneously updating, such as one is collapsing and the other is increasing, or both collapsing. Within this recursive, closed system in Figure 1, the model yields time paths of the ego’s corruption preference as well as the alter’s corruption preference. Given that the ego and the alter are, by nature, situated in a relationship, the trajectories of corruption preferences of the ego and the alter indicate how both actors change their own likelihood of involvement in corruption behaviors.

In this sense, the percolation-based model of collective corruption needs to illuminate the relationship between the ego and the alter and then unfolds the process including formation and diffusion of corruption. Given that the ego and the alter are formally or informally related to each other, we focus on the likelihood of committing corruption of the ego. Assuming that the ego faces a continual (and potentially varying) stream of novel corruption-related tactics (called corruption opportunity), we postulate that the ego’s evaluations of the corruption opportunities over time constitute his or her corruption preference. In other words, the streams of incoming and outgoing corruption opportunities over time will formulate the likelihood of committing corruption of the ego by adjusting the corruption preference. Accordingly, we propose that the ego’s corruption preference accounts for the accumulation of the evaluations regarding the corruption opportunities he or she faces over time. And we formulate the equation for corruption preference for both ego and alter as follows:

\begin{array}{l} Corruption Preference (t_{0}) = [\begin{array}{l} Increasing CP (s)_ \\ Decreasing CP (s) \end{array}] d s \\ + Corruption Preference (t - 1) \end{array}

(1)

Here, the left-hand side presents an actor’s tendency to accept corruption or information about corrupt actions from the other actor in the current time (i.e., t₀). As seen in the equation, there are three factors that affect this corruption preference. The first term in the right-hand side indicates the extent to which corruption preference is enhanced at the given time period. Meanwhile, the second term is the decreased level of corruption preference at the given time period. The last term in the right-hand side shows the level of corruption preference at the prior time period (i.e., t − 1).

In Equation 1, the parameters which can influence the corruption preferences of the ego and the alter are considered in terms of how different the social interactions for a corruption opportunity are engaged in. Specifically, acknowledging that percolation-like collective corruption is constructed through ongoing social interactions, a percolation process is modeled with Bayesian evolutionary algorithm (Zhang, 1999). That is, the ego’s corruption preference is influenced by the evaluation of his or her prior corruption preference and the newly coming corruption opportunity. If the evaluation is positive, which means that the corruption opportunity is feasible, the ego’s corruption preference would increase, and vice versa. In this sense, we consider personal attributes that govern the percolation process (Duffie & Manso, 2007; Søreide, 2009). The detailed elaboration of the percolation-based system dynamics model is presented in the appendix.

Results

Computational Settings

To investigate the changes in corruption preferences of the ego and the alter under the condition of the continuously generated corruption opportunities over time, we adopt a Monte Carlo simulation method. The Monte Carlo method is a computational approach which specifies a behavior of the focal variables by infusing a randomly generated condition (Berg, 2004; Fishman, 1995). Given that the corruption opportunity is randomly generated over time, we generate a series of random numbers over time, which are uniformly distributed. The time frame for this simulation is set to 1,000 with an increment of 1, which means that the system dynamics model is repeatedly run 1,000 times.

Co-dynamics of Corruption Preferences

Given that the formation of collective corruption unfolds when the alter adopts the corruption opportunities introduced by the ego, we consider that the formation of collective corruption is represented when both the ego and the alter have high corruption preferences. Drawn from social percolation models (Duffie & Manso, 2007), we assume that the initial information on corruption is given (or randomly generated) and the ego is willing to disseminate the corruption opportunities. Based on this assumption, our computational model focuses on how the alter adopts the corruption opportunities. From this standpoint, we focus on how the alter responds to the corruption opportunities with the conditions of the personal attributes between the ego and the alter.

To do this analysis, we run our system dynamics model to find out how the initial corruption preference of the alter influences the participation in corruption opportunities according to the personal attributes of the ego and the alter. For the personal attributes, we pay attention to the initial corruption preference and risk propensity. Figure 2 presents the alter’s corruption preferences by his or her initial corruption preference. For this simulation, the other variables in the model are set constant, whereas only the initial corruption preference (i.e., Corruption Preference t₀) of the alter is incrementally changed between 0 and 1.

Figure 2.

Corruption preferences depending upon alter’s initial value: (a) ego and (b) alter.

As can be seen from Figure 2, at the extremely low levels of the initial corruption preference (i.e., less than the level of 0.1), the alter’s corruption preference is not changed. This indicates that the alter with a strong ethical will is not willing to adopt the corruption opportunities. Yet, once the alter has a likelihood of allowing a certain level of corruption opportunities (i.e., the initial corruption preference is greater than 0.1 or near 0.5), his or her corruption preference becomes stronger as the number of cases increase. This means that the alter who is relatively flexible to corruption opportunities may eventually adopt the corruption opportunities. In addition, we can find out that the ego, in response to the change in the alter’s corruption preference, also can enhance his or her corruption preference over time.

Next, we consider risk propensity of the alter. The risk propensity of the alter refers to the extent to which the alter is willing to take risks of corruption opportunities introduced by the ego (Søreide, 2009). Figure 3 presents how the corruption preferences of the ego and the alter are changed over time depending on the risk propensity of the alter. For this simulation, the other variables in the model are set constant, whereas only the risk propensity of the alter is incrementally changed between −1 and 1 (depicting Lines 1 through 5 in Figure 3). When the risk propensity has a negative value, it means that the alter is risk averse. If the risk propensity has a positive value, it indicates that the alter has a risk-taking tendency. In Figure 3, from Lines 1 to 5, the risk propensity is proportionally distributed from being risk-loving to being risk averse. Figure 3 shows that if the alter has a risk-taking tendency (i.e., Line 1) and he or she is likely to adopt the corruption opportunities faster. And in response to the adoption of the corruption opportunities, the ego’s corruption preference also increases over time. This suggests that with the risk-taking preference of the alter, the collective corruption can be formed more rapidly.

Figure 3.

Corruption preferences depending upon alter’s risk propensity: (a) ego and (b) alter.

Furthermore, the personal attributes including initial corruption preference and risk propensity can be examined together as how favorable the alter responds to the ego’s introduction to a corruption opportunity. To discern the favorable response of the alter to the ego’s suggestion on participating in a corruption opportunity, we consider the initial corruption preference and the risk propensity simultaneously. Figure 4 shows the trajectories of the alter’s corruption preference corresponding to that of the ego with respect to the combination of the alter’s initial corruption preference and risk propensity. Each line in Figure 4 indicates how the ego and the alter change their corruption preferences over time when they have a certain level of initial corruption preference. Specifically, the longer lines mean that one has a drastic change in his or her corruption preference due to the other’s preference; the shorter lines indicate that both rarely influence each other.

Figure 4.

Co-dynamics of corruption preferences of ego and alter with respect to the initial corruption preference and risk propensity: (a) high risk propensity and (b) low risk propensity.

Figure 4a shows the alter’s corruption preferences corresponding to that of the ego when he or she is risk-taking; Figure 4b shows the alter’s corruption preferences when he or she is risk averse. In Figure 4a, all the trajectories of the corruption preferences move upwardly. That is, once the alter has a tendency of risk-taking, his or her corruption preference increases with that of the ego over time. This dynamic pattern suggests that at any circumstances in terms of initial corruption preferences, the alter’s risk-taking propensity will induce a collective corruption. On the contrary, Figure 4b shows the corruption preferences of the alter corresponding to that of the ego when the alter has a risk-aversion tendency. As can be seen from Figure 4b, the trajectories of the corruption preferences go downward. That means, the alter tends to reject participating in a corruption opportunity introduced by the ego, regardless of his or her initial corruption preference.

Two Scenarios for the Formation of Collective Corruption

Based on the understanding of the percolation-like process of collective corruption, the formation of collective corruption within an organization is determined by ongoing social interactions. This suggests that with the computational model, we can explore how collective corruption is formed under diverse contexts of social interactions. Drawn from the well-received metaphor of “bad apples in bad barrels” (Trevino & Youngblood, 1990), we propose and examine the following two scenarios to determine the causal mechanisms of collective corruption. First, collective corruption can be initiated with people who are originally bad or have a positive attitude on corruption (i.e., rotten apples). Just as rotten apples make the whole apples decayed, the social actor who appreciates a corruption opportunity will mobilize the whole process of collective corruption. The second scenario for collective corruption formation is a process where social actors become bad, influenced by social situations which can facilitate bad behavior (i.e., apples rotten). Particularly, this scenario conjectures that collective corruption is formed by inducing more people whose corruption preferences are enhanced by their relational structure. Specifically, given that collective corruption can be formed when a corruption opportunity is forced to adopt through asymmetrical power relations (Ashforth & Anand, 2003; Greve et al., 2010; Pinto et al., 2008; Vaughan, 1999), we focus on power imbalance as a situational factor which influences the corruption preference of the ego and the alter.

To examine the different formation processes of collective corruption depending on different scenarios, we investigate how the alter’s willingness to participate in collective corruption can be enhanced under the influence of the ego. Specifically, through the percolation-based system dynamics model, we analyze how the alter and the ego’s corruption preferences change over time depending on their attitude on corruption over time.

Scenario 1: Rotten apple effect

With the percolation-based model, we examine whether “good” people can be involved in the process of collective corruption. One way to categorize the causes of corruptive behaviors is to focus on individual-level causes of corruptive behaviors—rotten apples (Greve et al., 2010; Tenbrunsel, 1998; Tenbrunsel & Messick, 2004; Trevino, 1986, 1992; Trevino & Victor, 1992; Wathne & Heide, 2000; Wisemen & Gomez-Mejia, 1998). This group of studies pays attention to finding the reasons for corporate corruption in personal, ethical problems.

To demonstrate the rotten apple effect in the formation of collective corruption, we set four different situations built up by the combinations of initial corruption preference and risk propensity in our simulation model. Figure 6 specifies four different “rotten apple” combinations. In Figure 5, a good person (either ego or alter) indicates a person who is risk averse with a low level of initial corruption preference (i.e., initial CP). On the contrary, the bad person (either ego or alter) refers to a person who is risk-taking with a high level of initial corruption preference.

Figure 5.

Typology of rotten apples.

According to the typology of “rotten apples,” we trace the changes in corruption preferences of the ego and the alter over time. In Figure 6, the simulation results corroborate what the prior literature argued: A bad ego makes its alter (even who is not previously bad) likely to commit a corruptive behavior. Specifically, given that the “good–good” combination of the ego and the alter helps refrain from forming a collective corruption (Line 1), an ego who is originally bad (i.e., the initial corruption preference is high enough) makes the alter who is originally bad further commit corruptive behaviors (Line 4) and the alter who is originally good less likely to reject the corruption opportunity the ego introduced (Line 2). This is true for the alter. When the alter is bad, the ego’s corruption preference gets reinforced (see Lines 3 and 4). This suggests that not only the ego (or the originators) but also the alter (or the recipients) can initiate the rotten apple process. Thus, for the formation of collective corruption, if any corruption opportunities readily exist, all social actors can influence one another to facilitate a collective corruption. Given that the attempt for collective corruption, as a rent-seeking behavior, is routinely situated in the corporate environment (Greve et al., 2010), we can understand that all social actors are susceptible for collective corruption. This can further explain how a corruptive behavior can be committed in the entire firm (Ashforth & Anand, 2003).

Figure 6.

Rotten apple effect: (a) ego and (b) alter.

Scenario 2: Apples rotten effect

Besides the roles of bad individuals in facilitating a collective corruption, their relative positions also promote or attenuate a collective corruption (Allinson, 2004; Crane, Matten, & Moon, 2004; Langenberg, 2004; Pinto et al., 2008; Shleifer & Vishny, 1986; Tenbrunsel & Messick, 1999; Williamson, 1981, 1996). Researchers postulate that the cause of corporate corruption lies in the surrounding factors of individual actors as well as their personal attributes (Klitgaard, 1988; Noonan, 1984). That is, the collective corruption can be further developed with the pressures from positions and authority which influence actors’ decisions to participate in the collective corruption. To delve into this issue, we consider the level of power difference or power imbalance between the ego and the alter. Given that power is determined by the extent to which one influences the other (Emerson, 1962), we assume that one’s power can determine or affect at least the level of one’s corruption preference. That is, if the ego can smoothly convey his or her corruption opportunity to the alter without any resistance, the ego has a power to manage the corruption opportunity.

Given such, to demonstrate the apples rotten effect in our model in terms of power imbalance, we consider the ego’s ability to enable the alter to adopt a corruption opportunity (called pass-on) and the alter’s ability to resist the corruption opportunity the ego disseminates. Figure 7 specifies the four different “apples rotten” cases between the ego and the alter. In Figure 7, the balanced relationship between the ego and the alter is identified twofold. Cell 1 indicates that while the ego disseminates a corruption opportunity very actively, the alter also actively resists it. Cell 4 shows a situation that both the ego and the alter are not active to disseminate or accept any corruption opportunities. The unbalanced relationships are presented as Cell 2 with passive ego and active alter, and Cell 3 with active ego and passive alter.

Figure 7.

Typology of apples rotten.

Based on the typology of “apples rotten,” presented in Figure 7, we trace how the corruption preferences of the ego and the alter are changed over time. Figure 8 depicts the apples rotten effects in the formation of collective corruption. First, in the balanced power relationship between the ego and the alter, the alter has no change in his or her corruption preference (Lines 2 and 4 corresponding to Cells 2 and 4, respectively, in Figure 8b). Under the balanced power relationship, the ego’s corruption preferences can be reinforced if the alter is active. On the contrary, in the unbalanced power relationship, the alter is likely to accept the corruption opportunity the ego attempts to convey (see Lines 1 and 3 corresponding to Cells 1 and 3, respectively). In particular, when the ego has more power over the alter, the corruption preference of the alter increases very rapidly (Line 3 for Cell 3). These results reveal that apples are rotten by their power difference between them.

Figure 8.

Apples rotten effect: (a) ego and (b) alter.

Discussion

Percolation-Like Collective Corruption

Collective corruption initiated and reinforced through ongoing social interactions could enlarge its scape even more if it happens within an organizational boundary, because the communication channels are well established and thus spreading it out is not difficult. In this sense, collective corruption can be started with a small initiation but ultimately becomes pervasive through the whole company, as in the case of Enron (Sims & Brinkmann, 2003). Then, as unethical behaviors derive through certain patterns with corruption preferences, constant diffusion, some might ask why people could not recognize the disaster coming. As is with Enron case and other corruption cases, unethical behaviors latently exist and are passed on from one employee to another within an organization—though very subtly (Pinto et al., 2008). In this process, collective corruption prevails slowly but gradually. For example, if we are standing within a forest when fire starts, we could not notice the fire until it reaches close to us or grows into an enormous conflagration. If we are outside the forest, and not above it, we still could not identify the fire spreading out. In terms of percolation theory and percolation-like process, this situation is explained with critical points for phase transition (Stauffer & Aharony, 1994) or proliferation presented in this article.

Myriads of corruption cases, including Enron, take place in a corporate managerial setting. More or less, most individual actors possess a tendency of opportunistic behaviors, or quasi-rent, internally. This opportunism functions as a seed of corruption and unethical behaviors, and thus every actor has a likelihood of accepting and committing one (Greve et al., 2010; Hill, 1990; Williamson, 1981). This seed of collective corruption does not grow unless actors have preferences for taking risk of accepting it. Such preference or guile is critical as a flame of fire—and this is how the collective corruption process ignites. In terms of percolation theory, the space where collective corruption can occur could be explained as a “lattice” on which all the social actors stand. On a lattice, one can only be randomly stimulated by its nearest neighbors. Likewise, in an organization, the probability of one being initiated by his or her nearest neighbors is very high and therefore a fire could grow into a conflagration explosively. As such, collective corruption percolates within an organization that has a proper control system.

Normalization of Deviance

The percolation-like phenomena of collective corruption are framed as the normalization of deviant organizational practices, which describes how the practices occur through coordinating actors and eventually become institutionalized within an organization (Ashforth & Anand, 2003; Earle, Spicer, & Peter, 2010; Gaba, 2000; Vaughan, 1996). As a process model of collective corruption discerning four stages, initiation, proliferation, institutionalization, and socialization (Brief et al., 2001; Palmer & Maher, 2006), there are three stages for the normalization of deviant organizational practices, institutionalization, rationalization, and socialization (Ashforth & Anand, 2003). Ashforth and Anand (2003), first, as a deviant act appears and is accepted by organizational members, it becomes embedded in organizational structures and processes (i.e., institutionalization). Then, new theories to justify and valorize the deviant act are developed (i.e., rationalization). With the rationalization, the deviant act becomes acceptable through the organization (i.e., socialization).

Furthermore, based on this process, the normalization of deviance can be interpreted as a percolation process. As a deviant behavior is normalized, prevailing practices are discarded, and their boundaries are blurred by social pressures (Oliver, 1992). That is, social actors accept the (previously) deviant practices as right and proper by changing their belief system. Despite its clarification of normalization process as transitioning initial appearance to establishment of deviant practices, this perspective does not fully consider how social actors involve in making deviant practices as pervasive. In achieving the transition of one’s belief system, social actors should overcome structural barriers of the deviant behavior, such as stigmatization (Goffman, 1963), structural inertia (Oliver, 1992), and internal costs of collective action for the deviant behavior (Snow & Soule, 2010). As percolation processes concern the mechanisms of phase transition, the normalization of deviance can be further understood by examining when social actors start accepting the deviance (i.e., the threshold of phase transition mechanisms).

In this study, we particularly specify the proliferation stage in the process of collective corruption by investigating how corruptive behaviors perpetrated by one or a few individuals can become an organizational phenomenon. As such, we can understand how the normalization of deviance can be facilitated as transitioning initial proposal to acceptance by other organizational actors.

Prevention From Collective Corruption

Many studies have acknowledged that corruption controls have not been successful (Bukovansky, 2006; Gong, 2002; Johnston, 2011; Smith-Crowe & Warren, 2014). One of the reasons is that through collective commitment, corrupt actions are legitimized and rationalized (Gong, 2002; Persson, Rothstein, & Teorell, 2013). The percolation metaphor, however, provides how and what we should consider to control the formation of corporate corruption. Based on the analysis and findings from a computational model based on percolation-like process, we suggest practical implications on how collective corruption can be intervened and prevented from for responsible and sustainable corporations as follows.

First, given that the percolation metaphor of collective corruption implies that corruption exchange can be made through coordination, anti-corruption efforts can be developed with regard to ongoing social interactions among organizational members (Smith-Crowe & Warren, 2014). This suggests that it is not enough to incentivize or monitor organizational members not to engage in corrupt actions. Also, it may not be effective to hire employees who are morally motivated at the recruiting stage. Through interactions with their colleagues or their supervisors, they can consider a corrupt action legitimate. Thus, to prevent such socially constructed corruption, organizations can identify informal interactions and encourage them to be developed in healthy and sound ways.

In addition to this, one of the salient characteristics in collective corruption is clustering: networked social actors jointly commit a corruptive behavior (Greve et al., 2010; Palmer, 2008; Smith-Crowe & Warren, 2014). Through such social relationships, social actors can be forced to adopt a corruption opportunity. This implies that social actors’ attitudes on corruption are co-varied with their relational structures. To prevent these clustering situations, leadership behaviors that foster speak-up behaviors can be considered. Otherwise, internal whistle-blowing can be another means to make the work atmosphere to make the social interactions within an organization morally motivated.

Second, given that percolation-like collective corruption unfolds when one starts adopting a corrupt action, in this study, we find that there is a phase transition in the process of collective corruption (Schweitzer, 2005). This finding is relevant to the issue why many firms perceive corruption as a sudden, unexpected disaster and start to panic (“Crony Capitalism,” 2004). If this phase transition were accurately identified, collective corruption could come up with a proper control system. Organizations, thus, need to find ways to reduce the corruption preference of each individual, such as motivating them to explicitly share their organizations’ ethical values among their organizational members.

Conclusion

This study contributes for understanding collective corruption in three ways. First, we illuminate that collective corruption is formed as a percolation-like process. Specifically, we identify three aspects that collective corruption is analogous to percolation phenomena: path dependence, diffusion, and phase transition. To elaborate the percolation process of collective corruption, we adapt a methodological framework of system dynamics. The system dynamics model provides various patterns of collective corruption formation according to individual and organizational characteristics.

Second, we analyze the process of collective corruption by considering personal attributes. In particular, we focus on the change in corruption preference between ego (i.e., the focal actor who attempts to disseminate a corruption opportunity) and alter (i.e., the neighboring actor who is supposed to be a first target of the corruption dissemination). This setting indicates that our findings reveal how collective corruption can be facilitated at the earlier stage of the whole process.

Although contributions can be identified in this study, limitations also exist, which may suggest future studies. First, our arguments are examined with computational methods. The computational approach is useful to understand the dynamic patterns of collective corruption, but it is not enough to explain the percolation-like phenomena of collective corruption. Through empirical investigation of collective corruption based on the percolation mechanism, we can further elaborate the formation of collective corruption. Second, we assumed a dyadic relationship between ego and alter in our computational model to present the formation of collective corruption. This assumption can be relaxed to further understand the formation of collective corruption. If we set up a network structure, the percolation process of collective corruption formation could be further elaborated. Third, we considered the formation of collective corruption at intraorganizational settings only. To further understand the formation process of collective corruption, future research can profit from a focus on understanding collective corruption as a percolation process under different structures. For example, corruptive behaviors can be disseminated beyond the boundaries of organization or interorganizational collective corruption. That means, even without formal authority, corporate corruption could be collectively made through social networks. Accordingly, future studies will expand the social structure for the percolation process into a multi-actor structure (or a network structure). Third, as personal attributes, we considered only corruption preference. Given that percolation theory is useful to analyze individual behaviors embedded in a certain structure to explain social dynamics, future studies can examine various individual characteristics in the formation of collective corruption. Finally, given that the percolation-based model of collective corruption is assumed with a fixed relational structure (i.e., the dyadic relationship between ego and alter), structural aspects of percolation are not fully specified. For example, how close is the relationship between ego and alter or their hierarchical positions can be considered in developing the model. Accordingly, to further understand the percolation-like process of collective corruption, the structural attributes of the collective corruption can be specified in the future studies.

Footnotes

Appendix

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Notes

ORCID iDs

Sang-Joon Kim

Jegoo Lee

Author Biographies

Sang-Joon Kim (PhD, University of California, Irvine) is an assistant professor of management and organization at Ewha School of Business, Ewha Womans University, Seoul, South Korea. His research interests center on understanding social construction aspects of social phenomena, especially knowledge creation, entrepreneurship, and technological and social innovation, including corporate social responsibility (CSR) and sustainability. His research appears at Academy of Management Journal, Journal of Business Ethics, Strategic Management Journal, and other management-related journals.

Jegoo Lee (PhD, Boston College) is an associate professor of management and ethics at Stonehill College’s Leo J. Meehan School of Business and a research fellow at Boston College’s Center for Work and Family. His research focuses on how firms and organizations manage their relationships with various stakeholders, and how their strategies and efforts create values for stakeholders and influence their performance. His work has been published in Academy of Management Learning & Education, Business & Society, Business and Society Review, Journal of the Operational Research Society, Social Responsibility Journal, and Sustainability.

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