The dynamics of personal norms and the determinants of cultural homogeneity

Abstract

This article studies the emergence of cultural homogeneity in personal norms when the behavior of heterogeneous individuals is driven both by economic incentives and by personal norms. Agents participate in a team production game by choosing their level of costly effort. Norms evolve along the life cycle of the individuals according to two psychological forces: cognitive dissonance or consistency and informational conformity. The model sheds light on how primitive economic and behavioral parameters such as the distribution of skills, the income distribution, and the levels of materialism, conformism, and consistency in the group determine the long-run culture and its degree of cultural homogeneity.

Keywords

Cognitive dissonance conformity cultural homogeneity personal norm dynamics team production

Introduction

Cultural homogeneity in values or personal norms concerning effort is by now an important challenge for the management of an organization or the leaders of a society. The reason is that the behavior derived from a more or less homogeneous culture has a strong influence on the performance of a society or organization (see, for example, Ellison and Mullin (2014) and Van den Steen (2010a). Our goal in this article is to study the impact on an organization’s cultural homogeneity of primitive economic and behavioral parameters such as the distribution of skills in the population, the sharing rule on total income that determines remunerations and income distribution, and the levels of materialism, conformism, and consistency displayed by agents in the organization.

Culture is the degree to which members of a group, organization, or society share similar behavior and values or beliefs. A society faces the important task of building a culture where its characteristics deeply influence its levels of aggregate performance and welfare (see Fernandez, 2008, 2013; Guiso et al., 2006; Landes, 1998). Similarly, any long-lived group or organization that is involved in a long-run activity deals with the challenge of designing an organizational culture, and the features of this culture seem closely related to the levels of satisfaction or welfare of its members and its levels of performance (see Ellison and Mullin, 2014; Kotter and Heskett, 1992; Nadler and Tushman, 1997; Schein, 1985; Schwartz and Davis, 1981).

Cultural homogeneity concerning values and behavior has deserved much attention in the management science. In fact, the most common definition of corporate culture in this field views it as a situation with a high degree of homogeneity in values of the members of the organization, that is, shared values (Schein, 1990; Schwartz and Davis, 1981; Van den Steen, 2010a). For instance, Van den Steen (2010a) defines a strong culture as an homogeneous one. Van den Steen (2010b) shows that an homogeneous culture leads to more delegation, higher utility, less monitoring, higher effort, faster coordination, less influence activity, and less biased communication. These are the benefits of homogeneity. But there are also costs associated with homogeneity: less information collection and less experimentation. Summarizing there are costs and benefits coming from the homogeneity of an organizational culture. But definitely homogeneity matters.

According to Bednar et al. (2010), empirical research on cultural organizational differences reveals four broadly accepted findings:

Cultures exhibit homogeneity both in behavior and in beliefs or preferences.

Behavior and preferences exhibit coherence.

Despite the previous findings, cultures exhibit substantial within-group diversity or heterogeneity and behavior and preferences also exhibit varying levels of incoherence.

Cultures differ (inter-group diversity).

A candidate for a good theory or model on the emergence and formation of organizational cultures should explain all these findings and show the determinants of the levels of homogeneity and incoherence of different cultures.

We analyze the emergence and evolution of a culture in an organization in which its members participate each period in a team production game by choosing their level of costly efforts. Agents are guided both by economic incentives and also by personal norms of behavior, that is, individuals have an internal standard for a particular conduct concerning the “good” effort to exert. We allow for heterogeneity in the initial condition of the group concerning not only the individuals’ personal norms (or intrinsic motivation) but also their levels of materialism, that is, the weight they assign in their utility function to their material interest. Heterogeneity also concerns their individual skills or productivities, and their shares according to the total income distribution rule (in short, their remunerations).

We take materialism, skills, and remunerations as given, but personal norms evolve along the life cycle of the individuals according to two psychological forces: cognitive dissonance or consistency and informational conformity. Consistency is an individual force that drives personal norms toward actual behavior. People tend to seek consistency in their norms and behavior. When there is a discrepancy between them, something must change in order to eliminate or reduce the dissonance (Akerlof and Dickens, 1982; Festinger, 1957; Kuran and Sandholm, 2008; Nordblom and Zamac, 2012). Conformity, by driving personal norms toward the average actual group behavior, captures how social interaction impacts homogeneity. Conformity is a type of social influence involving a change in norms or behavior in order to fit in with a group (Akerlof, 1997; Bernheim, 1994; Fischer and Huddart, 2008; Kandel and Lazear, 1992). In the next section, we will analyze and justify in a more detailed way the role of personal norms and the forces that make them change along time.

We characterize the long-run outcomes of the group (the steady states of the dynamics of personal norms) and study how the levels of homogeneity in personal norms and in behavior and the level of incoherence between both variables are determined by the primitives of the model. Our main findings are the following.

We first characterize the Nash equilibrium (NE) of the team production game played each period. Agents, maximizing their instantaneous utility, exert an effort which is a weighted average of their individual marginal revenue and their personal norm where the weight is given by their level of materialism. If the dynamics of personal norms is exclusively governed by consistency, both personal norms and equilibrium behavior converge to the Nash equilibrium of the team production game in material payoffs. There is complete coherence between behavior and values with each individual having a personal norm that dictates an effort that coincides with her individual marginal revenue. Norm and behavior heterogeneity reflects the dispersion of the individual marginal revenues in the society, which is in turn determined by the distribution of skills and the income distribution rule. Alternatively, if the dynamics of personal norms is exclusively governed by conformism, all agents’ personal norms converge to the same value which coincides with the average marginal revenue of the members of the organization. Therefore, the group tends to complete homogeneity in values.¹ But notice that each agent performs a different action given the different incentives derived from skills, income sharing rule, and materialism. Thus, there is heterogeneity on behavior and consequently high levels of incoherence. This result drives us away from standard findings obtained when conformism is part of the utility function via peer effects. In that case, if only conformism is at work, then a complete homogeneity in behavior is shown. However, we obtain behavior heterogeneity even if agents form norms in a fully conformist way.

We also analyze, for the case of a dynamics with only conformism, the effects derived from the presence in the group of a subset of either non-conformists individuals or non-materialistic agents or finally completely materialistic (selfish) individuals. In all these cases, an homogeneous culture in personal norms still arises in the long run but not in behavior. The presence of non-conformist agents, non-materialistic agents, or selfish agents only affect the particular value of the homogeneous personal norm in the steady state.

We turn next to the general case when the personal norms dynamics displays positive levels of consistency and conformity. Each agent’s personal norms in the steady state is a convex combination between her individual marginal revenue and the average marginal revenue in the group. We characterize the level of homogeneity of norms and behavior in the long run, making use of their respective variances in the steady state. We also define the level of incoherence of a culture as the variance of the distances between values and behavior in the steady state. Our model establishes some clear predictions on these variables. According to the stylized facts stated above, we find that behavior and norms heterogeneity are correlated and that behavior is always more heterogeneous than norms.

Looking at the determinants of cultural homogeneity (stylized facts 1 and 3 of Bednar et al., 2010), our article highlights how the income and skills distribution in a group or society and the levels of deep behavioral social features such as materialism, conformism, and consistency determine the diversity and coherence of a culture. In particular, a more unequal distribution of skills yields a culture with less homogeneity in behavior and norms and more incoherence. Similarly, a more unequal sharing distributional rule which increases income inequality will also yield a culture with less homogeneity in behavior and norms and more incoherence. Finally, we find that conformism increases the level of homogeneity, while consistency and materialism increase heterogeneity.

A closely related work to our article is Bednar et al. (2010). These authors analyze the formation of a culture when agents try to maintain consistency across domains in a multi-dimensional model. Besides this internal desire to be consistent, there exists also a social pressure to conform. Our work can be seen as complementary to theirs. On one hand, we explicitly propose a dynamic model of culture formation while they work with a static model. On the other hand, we focus on a single individual decision and study consistency between personal norms or values and behavior, instead of analyzing consistency across actions in a multidimensional setting.

The rest of the article is organized as follows. Section “Personal norms and their dynamics” discusses with more detail conformity and consistency as the main driving forces behind the dynamics of personal norms. Section “The static model” describes the team production game played in each period and the utility function of any member of the group. In section “Dynamics of personal norms,” we first study the evolution of personal norms exclusively governed by a dynamics of consistency and second when these are exclusively governed by a dynamics of conformity. In section “The determinants of cultural homogeneity, personal norms and behavior,” we analyze the dynamics when both forces work together and characterize the determinants of cultural homogeneity and incoherence. Finally, section “Conclusion” concludes.

Personal norms and their dynamics

In order to analyze how a culture becomes homogeneous or heterogeneous, it is now crucial to discuss in depth the role of personal norms and the forces that make them change in time. We can take for granted that each agent has personal norms, innate or derived from some form of social pressure or internalization of society’s stimuli. Deci and Ryan (1985), Ryan and Deci (2000), and Thogersen (2006) provide some additional evidence for the existence of this internalized norms as forces for behavior. When choosing for an action, together with material incentives, each agent also considers what her own personal norms dictate since they may provide some intrinsic motivation to act in a certain way. More specifically, intrinsic motivation can be seen as a way to take into account self-punishments and self-rewards that may derive from acting coherently with the norm (Schwartz, 1977). Frey (1997) introduced intrinsic motivation and personal norms in the economic debate, not considering them as negligible elements (see Lindenberg (2001) for a review on intrinsic motivations).

Personal norm evolve

The internalization process of personal norms opens the road to the possibility of the evolution and change of the norms themselves. We consider intragenerational transmission of personal norms: agents update their own norms depending on what happens in the surrounding environment, and this mechanism implies that norms, and thus preferences, are not stable over the lifetime. Some examples can be derived from Cialdini and Trost (1998) for the psychological literature, Postlewaite (2011) for the economics literature, and Matthied et al. (2012) for the evolution of norms in pro-environment settings. Furthermore, the recent literature on cultural evolution and transmission, starting with Bisin and Verdier (2001), also relies on the endogeneity of preferences or values. Bednar et al. (2010) identify two main forces that are at work while norms are formed: conformity and consistency. Nordblom and Žamac (2012) also implement these two forces for studying the evolution of norms for tax evasion. We also use them as driving forces for the analysis of the evolution of personal norms and for the study of the emergence of a culture.

Conformity

Conformity relates to the way personal norms depend on others’ norms and behaviors. If others’ personal norms are considered in the own personal norm formation process, then we can talk about normative conformism, while if others’ observed behavior is taken into account, then we can talk about informational conformism (see Nordblom and Žamac, 2012). From an economist’s point of view, we find informational conformism to be more plausible since it does not assume agents to inspect others’ minds and infer their true norms, but just observe others’ choices and get influenced by them. Bernheim (1994) was the first one to introduce informational conformism in economics. However, the first formalization is due to Manski (1993) who introduced it using the peer effects concept. In Manski’s framework, peer effect is the result of the influence of the more prevalent behavior in the environment on agents’ choices.

Our model departs from these papers and the rest of literature on conformity and peer effects (see additionally, Akerlof, 1997; Fischer and Huddart, 2008; Kandel and Lazear, 1992) in that this literature puts the conformity part directly into the utility function of the individual and directly influences her behavior, whereas in our approach, conformity or peer effects influence the process of preference evolution and thus indirectly affects behavior.

Consistency

Consistency is the second mechanism we consider for the personal norms formation scheme. In particular, consistency assumes that agents would like to have their own personal norms and behaviors to be positively correlated, otherwise they experience a psychological cost for not having followed their personal norm. As Bednar et al. (2010) and Bednar and Page (2007) suggest, consistency finds its roots in the desire of reducing a potential cognitive load agents may experience if behavior and norms happen not to be in line. Festinger (1957) was the first one to formalize this phenomenon using the notion of cognitive dissonance. Notice that avoiding cognitive dissonance can be the result of two distinct processes: agents updating values considering their own past behavior and agents behaving taking into account their own values. However, while the first process regards the norm formation mechanisms, the second one is captured by the specific decision process modeled. In our framework, we consider both these forces to hold: the former in the way norms evolve and the latter the way behavior is influenced by their own norms. The behavior-to-norm force can be again rooted in the cultural evolution evidence since, when forming their own attitudes and norms, agents tend to be partially stuck to their own past choices, as argued in Aronson (1999), Beauvois and Joule (1996), Harmon-Jones and Harmon-Jones (2002), and McGuire (1966). Bednar et al. (2010) also provide exhaustive literature on this topic. Notice finally that some links between cognitive dissonance and the self-signaling theory (Bem, 1972; Benabou and Tirole, 2004, 2006, 2010) have been proposed. Self-signaling theory assumes that agents, by observing their own behavior, progressively discover their own true norms and update them in the direction of past behavior so that norms and behavior progressively converge because of the behavior-to-norm force.

The static model

Consider a social group or an organization composed by N agents acting simultaneously. Each agent i chooses a level of non-verifiable effort $e_{i} \geq 0$ to participate in a team production game, where effort is costly and this cost is given by $c (e_{i}) = (1 / 2) e_{i}^{2}$ . The total revenue is given by the function $y = \sum_{i = 1}^{N} s_{i} e_{i}$ , where $s_{i} \geq 0$ is the productivity of each agent, being related to an idiosyncratic skill level. We assume that the total revenue generated by the team is divided according to a sharing rule w, being w a vector of real numbers that assigns to each agent a share $w_{i} \in 0, 1]$ of the total revenue, with $\sum_{i = 1}^{N} w_{i} = 1 .$

Besides the economic incentives, each agent i has a personal norm $ê_{i} \geq 0$ assessing the level of effort that should be chosen by the agent according to the norm. In this sense, all agents have an internal standard for a particular conduct concerning the “good” effort to exert, and any deviation of actual behavior from their personal norms will yield disutility. We assume that the loss function is given by $(1 / 2) (e_{i} - ê_{i})^{2}$ . This loss depends on the difference between the actual agent’s effort and her personal norm. Therefore, each agent is motivated to act by two forces: economic incentives and personal norms. Each individual may assign different levels of importance to these two factors putting a weight $β_{i} \in (0, 1)$ to the material payoffs and $(1 - β_{i})$ to the intrinsic motivation (personal norms $ê_{i}$ ). Therefore, we will denote $β_{i}$ as the level of materialism of player i.

Summarizing, the utility of a player in the team production game is given by the following linear quadratic function

u_{i} (e) = β_{i} [w_{i} \sum_{j = 1}^{N} s_{j} e_{j} - \frac{1}{2} e_{i}^{2}] - (1 - β_{i}) \frac{1}{2} {(e_{i} - ê_{i})}^{2}

(1)

where e is the vector of efforts of the N agents. Note that agents differ not only in personal norms $ê_{i}$ but also in the weights assigned to material incentives and personal norms $β_{i}$ , in the shares of income $w_{i}$ and in the skills $s_{i}$ . The standard case with no intrinsic motivation is obtained as a special case of equation (1) when $β_{i}$ tends to 1.

The NE of the simultaneous game in each period t is given by

ē_{i}^{t} = β_{i} (w_{i} s_{i}) + (1 - β_{i}) ê_{i}^{t}, for i = 1, 2,..., N

(2)

Notice that the equilibrium action $ē_{i}^{t}$ is the dominant action of player i.

Once we have defined the static problem, we now introduce the possibility for personal norms $ê_{i}^{t}$ to evolve over time. We consider a two-speed dynamics: gradual changes in preferences (personal norms) are accompanied by immediate behavioral adjustment in each period’s equilibrium play. In the following sections, we assume that individuals may change their personal norms through two psychological mechanisms: consistency (or cognitive dissonance) and informational conformism (or conformity). In the next section, we will analyze these two motives for the evolution of behavior and personal norms, separately in order to get a better understanding of the influence of each mechanism.

Dynamics of personal norms

Consistency

In this section, we assume that only consistency holds so that, when there is a discrepancy between personal norms and behaviors, something must change in order to reduce the dissonance. In particular, we assume that this dissonance is reduced by making preferences of each agent i to evolve in the direction of her own NE behavior, with the following rule

ê_{i}^{t + 1} = γ_{i} ē_{i}^{t} + (1 - γ_{i}) ê_{i}^{t}

(3)

where $γ_{i} \in (0, 1)$ is the weight that agent i assigns to her equilibrium behavior, and $1 - γ_{i}$ indicates how much the agent is anchored to her own past personal norm. Using the continuous time limit of the dynamics in equation (3), we get the following differential equation system

\frac{d \hat{e_{i}}}{d t} = γ_{i} (ē_{i}^{t} - ê_{i}^{t}) for i = 1, 2,..., N

(4)

Substituting, in each period, the NE of equation (2) into equation (4), we get a set of independent linear ordinary differential equations (ODE)

\frac{d \hat{e_{i}}}{d t} = (γ_{i} β_{i}) (w_{i} s_{i} - ê_{i}^{t}) for i = 1, 2,..., n

(5)

Then, calling $ê_{i}^{\infty}$ and $ē_{i}^{\infty}$ the long run values of personal norms and equilibrium behavior, we obtain the following result.

Proposition 1. If the dynamics of personal norms is exclusively governed by consistency, personal norms $ē_{i}^{\infty}$ and equilibrium behavior $ê_{i}^{\infty}$ converge to a level equal to the NE of the team game in material payoffs ( $ê_{i}^{\infty} = ē_{i}^{\infty} = w_{i} s_{i}$ ). Moreover, $ê_{i}^{\infty}$ is a globally stable steady state Proof. See Appendix 1.

Proposition 1 states that, if consistency is the unique driving force for the evolution of personal norms, then personal norms will tend to the NE in material payoffs of the team production game. This means that each agent’s personal norm evolves to a specific effort level equal to her individual marginal revenue which is determined by the product of her own skills and the share of total income she obtains. For example, even if agents start with personal norms for efficiency ( $ê_{i}^{0} = s_{i}$ ) in the steady state, personal norms get eroded and will tend to the individual marginal revenue $w_{i} s_{i}$ . Clearly, when there is no influence of behavior on the norm $(γ_{i} = 0)$ and/or the material payoffs are not important $(β_{i} = 0)$ , then $ê_{i}^{t} = ê_{i}^{t + 1}$ , and thus in the steady state personal norms coincide with the initial personal norm of each agent, $ê_{i}^{∞} = ê_{i}^{0}$ , since no dynamics at all is shown.

Let us now introduce the concept of the degree of incoherence between behavior and personal norms of a culture. Formally,

Definition 1. The degree of incoherence of an organizational culture is

θ (w, s) = \frac{1}{N} \overset{}{\underset{}{\sum_{i = 1}^{n} {(ē_{i}^{\infty} - ê_{i}^{\infty})}^{2}}}

(6)

In this case, notice that both individual personal norms and behavior converge to the same value. Therefore, there is complete coherence between behavior and personal norms, that is, $θ (w, s) = 0 .$ In other words, there is no cognitive dissonance in the steady state. Heterogeneity of both behavior and personal norms reflects the dispersion of the individual marginal revenues in the society which is, in turn, determined by the distribution of skills and the income distribution rule.

Finally, it is important to notice that, since equations in system (5) are all independent, if some agent has $γ_{i} = 0$ , $β_{i} = 0$ , or $β_{i} = 1$ , this only has an effect on her own dynamics maintaining unchanged the dynamics of personal norms and behaviors of all other agents.

Conformity

We now consider what happens if conformity (or informational conformism) is the unique force driving the change of personal norms. By conformity, personal norms tend to move toward the average of the actual behavior of the organization, this average being considered what one “ should” do in that specific social context.

Hereafter, we will denote by $〈 x 〉$ the average of variable $x_{i}$ , that is, $〈 x 〉 = (1 / N) \sum_{i = 1}^{N} x_{i}$ . The difference equations that characterize the evolution of personal norms in this case take the following form

ê_{i}^{t + 1} = α_{i} 〈 ē^{t} 〉 + (1 - α_{i}) ê_{i}^{t}, for i = 1, 2,..., N

(7)

where $α_{i} \in (0, 1)$ is the parameter that measures the degree of conformism and $〈 ē^{t} 〉$ is the average of the NE of the group in period t.

Taking the continuous time limit of the dynamics and substituting the NE of equation (2), we get the following set of coupled ODE

\frac{d \hat{e_{i}}}{d t} = α_{i} [〈 β w s 〉 + 〈 (1 - β) ê^{t} 〉 - ê_{i}^{t}], for i = 1, 2,..., N

Then, we can state the following.

Proposition 2. If the dynamics of personal norms is exclusively governed by informational conformism, all agent’s personal norms converge to the same value, $ê_{i}^{\infty} = ê^{\infty} = 〈 β w s 〉 / 〈 β 〉, \forall i$ Proof. See Appendix 1.

The main message of Proposition 2 is that, if only informational conformism is at work and all individuals display positive levels of conformism, then the group tends to a completely homogeneous culture in values. Moreover, note that the steady state common personal norm is entirely independent of the initial distribution of personal norms and is only grounded on the levels of skills, sharing rule and preference parameter $β .$ We can simplify this result, assuming that the random variables $β_{i}$ and $(w_{i} s_{i})$ are statistically independent. We will use this case along all the paper. Thus, we can approximate $〈 β w s 〉 ≃ 〈 β 〉〈 w s 〉$ . Then,

Corollary 1. If personal norms are governed by a dynamics of informational conformism, and the variables $β_{i}$ and ( $w_{i} s_{i}$ ) are statistically independent, then the personal norm of each agent in the steady state is $ê_{i}^{\infty} = 〈 w s 〉, \forall i$ and the equilibrium behavior is $ē_{i}^{\infty} = β_{i} w_{i} s_{i} + (1 - β_{i}) 〈 w s 〉$ , for $i = 1, 2,..., N$ .

This result states that having just informational conformism, each agent personal norm converges to a common value that is the average marginal revenue of the group. Notice that with this dynamics, even if all agents have the same personal norm, each agent performs a different action given the different incentives derived from skills, sharing rule and the level of materialism. Therefore, there is a strong culture concerning values but there is heterogeneity concerning behavior.

This is a major difference with respect to models that include conformism into the utility function by inserting some sort of complementarities in behavior. In those models, if only conformism holds, then complementarities act to the point of making all agents’ behaviors converge to the same level. In our case, however, even if conformism is maximal, we still keep some degree of heterogeneity in behavior, in line with most of the empirical findings about culture homogeneity and behavior, as highlighted in section “ Introduction.”

Moreover, there is perpetual cognitive dissonance or incoherence, $ē_{i}^{\infty} \neq ê^{\infty}$ , since in the steady state the equilibrium action will be different from their personal norm. Notice that

if w_{i} s_{i} ⋛ 〈 w s 〉, then ē_{i}^{\infty} ⋛ ê^{\infty}

so that when agents have higher (lower) individual revenue than the average of the group, they will choose a higher (lower) level of effort than the one prescribed by the common personal norm. Only if agents are in the average of the group in terms of individual revenue, then their equilibrium effort choice will coincide with the personal norm.

With respect to the degree of incoherence, note that when there is only conformism and applying Definition 1 for the case of a constant $β$ , then $θ (w, s) = β^{2} σ^{2} (w s)$ , where $σ^{2} (w s)$ denotes the variance of marginal revenues. Therefore, the degree of incoherence in the group increases with the level of materialism and the dispersion of skills and/or remunerations.

We have assumed in the previous results that all agents have a positive level of conformism. We relegate to Appendix 2 the analysis of different cases in which not all agents have positive values for conformism, $α_{i}$ or they have a extreme value 0 or 1 in the weight assigned to the material payoff, $β_{i}$ .

We show that the presence of non-conformist and/or non-materialistic and/or fully materialistic agents in the group only affects the particular value of the homogeneous personal norm in the steady state. Obviously both non-conformist and fully materialistic agents display a different behavior in steady state, but the rest of the organization is culturally homogeneous and its common personal norm might be strongly influenced by these types of agents.

Let us next analyze the evolution of personal norms and the equilibrium behavior in the group when the dynamics of the personal norms is a mix between consistency and informational conformity.

Dynamics with consistency and conformity

We assume that with a weight $(1 - τ_{i})$ the personal norm $ê_{i}^{t + 1}$ of individual i moves toward the average equilibrium behavior in the group, and with a weight $τ_{i}$ the personal norm moves in the direction of the individual equilibrium behavior. In summary, people update their norms influenced by their own past behavior and/or by the attitude of their peers, with different weights. Thus, the law of motion of personal norms is given by the following expression

ê_{i}^{t + 1} = \underset{Consistency}{\underset{︸}{τ_{i} (γ_{i} ē_{i}^{t} + (1 - γ_{i}) ê_{i}^{t})}} + \underset{Informational Conformism}{\underset{︸}{(1 - τ_{i}) (α_{i} 〈 ē^{t} 〉 + (1 - α_{i}) ê_{i}^{t})}}

(8)

We denote by $a_{i} \equiv τ_{i} γ_{i}$ the weight associated with consistency and by $b_{i} \equiv α_{i} (1 - τ_{i})$ the weight associated with conformism for each player, where both $a_{i}, b_{i} \in (0, 1)$ . For simplicity, we allow for individual heterogeneity of these weights, while the level of materialism $β$ will be the same for all players, that is, $β_{i} = β, \forall i$ . Then the following result on steady state personal norms and behavior is shown in the following.

Proposition 3. If personal norms are governed by a dynamics that is driven by both consistency and informational conformism as in equation (8), the steady state personal norm of each agent is

ê_{i}^{\infty} = (A_{i}) (w_{i} s_{i}) + (1 - A_{i}) 〈 w s 〉, for i = 1, 2,..., N

(9)

Moreover, the equilibrium behavior is

ē_{i}^{\infty} = (β + (1 - β) (A_{i}) (w_{i} s_{i}) + (1 - β) (1 - A_{i}) 〈 w s 〉, for i = 1, 2,..., N

(10)

where $A_{i} = (a_{i} β / (a_{i} β + b_{i}))$ Proof. See Appendix 1.

By Proposition 3, we know that steady state personal norms are a convex combination between individual marginal revenue and population average marginal revenue. Using previous results, note that the first part is driven by consistency and the latter by conformity. The main consequence in terms of the resulting culture can be seen by looking at the steady state behavior. Note that there is no consensus among agents on how to form behavior, since each agent weighs differently the information derived from her own material incentives $(w_{i} s_{i})$ and from the overall society $〈 w s 〉$ and this weight depends on her levels of materialism, conformism, and consistency.

With respect to the degree of incoherence and assuming that the random variables ( $a_{i}, b_{i})$ and $(w_{i} s_{i})$ are statistically independent, the reader can check that it is given by

θ (w, s) = 〈 {(\frac{β b}{a β + b})}^{2} 〉 σ^{2} (w s)

(11)

Notice that the level of incoherence of a culture represents a social psychological cost and increases with the variance of the group marginal revenues $σ^{2} (w s)$ , with the level of materialism $β$ , and with the level of conformism b and decreases with the level of consistency a.

In the next section, we will analyze the homogeneity of behavior and personal norms arising from this process. Nevertheless, it is interesting to obtain the average effort of the group in the steady state and discuss its determinants. By taking averages in the expressions (9) and (10), we have the following result.

Result 1. The group average personal norm and the average effort in the steady state is equal to the average marginal revenue of the group, $〈 ê^{\infty} 〉 = 〈 ē^{\infty} 〉 = 〈 w s 〉 .$

Therefore, average norm and behavior coincide in the long run and will be higher if the average of the marginal revenue of the group is higher. So, it is fully determined by the remunerations and the skills of its members while the levels of materialism, conformism, and consistency in the group do not have any influence. We know that $〈 w s 〉 = 〈 s 〉 / N + Cov (w, s),$ but if we assume statistical independence between variables $w$ and $s,$ then $Cov (w, s) = 0$ and thus $〈 w s 〉 = 〈 s 〉 / N$ . Therefore, $〈 ê^{\infty} 〉 = 〈 ē^{\infty} 〉 = 〈 w s 〉 = 〈 s 〉 / N .$ In an organization where remunerations and skills are not correlated, the group average long-run effort increases with the average skill and diminishes with the size of the group.

However, average effort does not measure the degree of cultural homogeneity, since we can have two very different societies, a very homogeneous one and a very heterogeneous one with exactly the same average effort. In the following section, we propose a measure of cultural homogeneity.

The determinants of cultural homogeneity, personal norms, and behavior

Now we are ready to define a general measure of the homogeneity of an organizational culture in the long run and study its determinants.

The lower the variation of personal norms in steady state, the more homogeneous (the stronger) is the group culture. The natural candidate for this measure of dispersion is the variance of the personal norms in steady state. The higher this variance, the lower is the homogeneity of the culture and vice versa. We will denote by $σ^{2} (x)$ the variance of variable $x_{i}$ , that is, $σ^{2} (x) = (1 / N) \sum_{i = 1}^{N} {(x_{i} - 〈 x 〉)}^{2} .$

Assuming statistical independence between both $a_{i}, b_{i}$ , and ( $w_{i} s_{i}$ ), we can approximate the variance of personal norms in a culture as (see Appendix 3 for details)

σ^{2} (ê^{\infty}) = 〈 {(\frac{a β}{a β + b})}^{2} 〉 σ^{2} (w s)

(12)

Note first that $(a_{i} β / (a_{i} β + b_{i})) < 1$ , then $〈 {(a β / (a β + b))}^{2} 〉 < 1$ , therefore $σ^{2} (ê^{\infty}) \leq σ^{2} (w s)$ .

Analogously, a good measure of the dispersion of behavior in the long run would be the variance of the equilibrium actions in the steady state.

Assuming again statistical independence between $a_{i}$ and $b_{i}$ and $w_{i} s_{i}$ , we obtain

σ^{2} (ē^{\infty}) = 〈 {(\frac{β (a + b)}{a β + b})}^{2} 〉 σ^{2} (w s)

(13)

Note also that $σ^{2} (ē^{\infty}) ⩽ σ^{2} (w s)$ .

Let us now compare both variances, if we rearrange terms we have

σ^{2} (ē^{\infty}) = \frac{〈 {(\frac{β (a + b)}{a β + b})}^{2} 〉}{〈 {(\frac{a β}{a β + b})}^{2} 〉} σ^{2} (ê^{\infty})

(14)

Notice that $σ^{2} (ē^{\infty}) ⩾ σ^{2} (ê^{\infty})$ . We can summarize the above results in the following proposition.

Proposition 4. In the steady state, the variance of individual marginal revenues is always greater or equal than the variance of behavior which in turn is greater or equal than the variance of personal norms. That is, $σ^{2} (w s) ⩾ σ^{2} (ē^{\infty}) ⩾ σ^{2} (ê^{\infty})$ .

Notice that if $b = 0$ , so that the dynamics of personal norms is only governed by consistency, then $σ^{2} (ē^{\infty}) = σ^{2} (ê^{\infty}) = σ^{2} (w s)$ . Clearly in this case, the only way to reduce the variance of personal norms and behavior is reducing the dispersion of “technical” factors like productivity or distributional factors like the income distribution. On the other hand, when the dynamics is only governed by conformity, that is, $a = 0$ , then $σ^{2} (w s) > σ^{2} (ē^{\infty}) = β^{2} σ^{2} (w s) > σ^{2} (ê^{\infty}) = 0$ . Therefore, conformity, as we already know, creates a tendency toward homogeneity in personal norms, although the variance of behavior is determined again by the distribution of marginal revenues and also by the level of materialism in the society.

This proposition allows us to state as a Corollary a first result concerning cultural homogeneity.

Corollary 2. Cultural homogeneity of personal norms and behavior is always greater or equal than homogeneity in individual marginal revenues, and homogeneity in norms is always greater or equal than homogeneity in behavior.

Thus, our model establishes a strong empirical prediction: societies and organizations will always exhibit more homogeneity in norms than in behavior. Moreover, the cultural dynamics will make always norms and behavior less diverse than the mere variance of marginal revenues which is determined by technical and social factors. We thus get the rough intuition that the dynamics of personal norms actually helps in creating some sort of homogeneity in the population.

Next, we analyze the influence of several parameters on the variance of personal norms, and consequently, on the homogeneity of the culture of an organization.

Effects of skills and income distribution

Notice that an increase in the variance of the individual marginal revenues, $σ^{2} (w s)$ will yield an increase in the variances of personal norms and behavior, as can be easily observed from expressions (12) and (13). Generally, if $w_{i} and s_{i}$ are not statistically independent, the variance $σ^{2} (w s)$ depends on the average and variance of the distribution of skills in the population, on the variance of the income sharing rule but also on the covariance between the sharing rule and the skills, $cov (w, s)$ ². Clearly, if the two variables are correlated, it is hard to determine, ex ante, how $σ^{2} (w s)$ changes when the mean or the variance in variables $w_{i} or s_{i}$ is considered.

We focus in the rest of this section in the usual team situation where individual remunerations cannot be linked to effort as we have assumed so far, but neither to individual levels of skill because of the standard non-verifiability problems of these variables. In this kind of situation, only joint production is verifiable. This lack of correlation between remunerations and skills might appear even if skills were observable, when the group (or any external authority or leader) decides purposely not to link remuneration and individual skills. For instance, according to the anthropological evidence in most hunter-gatherer societies, the distribution of food (i.e. team revenue) is governed by a social norm that is independent of the skills of its members (see, for instance, Alvard and Nolin, 2002). In modern team production, management sometimes prefers a more compressed remuneration structure because cooperation among team-mates could be harmed because of fairness or inequality aversion concerns (see, for instance, Englmaier and Wambach, 2010). These previous situations would be observationally equivalent to assume statistical independence between skills and remunerations.

Thus, following Goodman (1960) and assuming statistical independence between the variables $w_{i} and s_{i}$ , we have that the variance of individual marginal revenues $σ^{2} (w s)$ is given by

σ^{2} (w s) = σ^{2} (w) σ^{2} (s) + (\frac{1}{N^{2}}) σ^{2} (s) + {〈 s 〉}^{2} σ^{2} (w)

(15)

It is straightforward to check that an increase in the average skill $〈 s 〉$ in the society will lead to an increase in $σ^{2} (w s)$ so that a society with a higher average productivity (due to innate or acquired skills) will give place to a less homogeneous culture. If skills are thus a function of previous economic outcomes, it follows that the more a society invests in skills and rise the average skill, the less homogeneity in norms and behavior will be observed. An increase in the variance of the distribution of skills will have a similar effect, reducing the cultural homogeneity.

On the other hand, a change in the income sharing rule can be captured by its variance and yields a change in income (revenue) distribution. Notice that the variance of income distribution is given by $R^{2} \cdot σ^{2} (w),$ where R is total revenue, that is, $R = \sum_{j = 1}^{N} s_{j} e_{j}$ . Therefore, $σ^{2} (w)$ is a good proxy of the dispersion of the population income distribution. A more unequal distribution of income due to a change in the sharing rule will cause an increase in $σ^{2} (w s)$ and, in turn, a less homogeneous culture.

Concluding, the “ technical” conditions (distributions of skills) and the “ social” conditions (distribution of income) have an impact on the resulting culture so that a culture is more homogeneous both in norms and behavior if there is higher equality in skills and remunerations. Notice that in most organizations, these distributions can be corporate-driven. Thus, the management’s target on corporate culture homogeneity is strongly influenced by management’s decisions on the dispersion in the organization of remunerations and skills. We can sum up by stating the following.

Proposition 5. Cultural homogeneity of personal norms and behavior decreases with the variance of skills, the average group skill level and the variance of the income sharing rule.

Effects of conformism

Consider now the influence of changes in the weight that agents assign to conformism. We will call a change on the size of the levels of conformism a situation where some elements of the vector b simultaneously increase (or simultaneously decrease) while the rest of the elements remain fixed. Then we can state unambiguously that the level of conformism in the group is higher (or lower, respectively).

An increase in the level of conformism has the effect of decreasing the variances of personal norms and behavior. Clearly, a rise in the level of conformism in the group will lead to most of the agents to adopt similar personal norms reducing their variance. In this case, the society will show a more homogeneous culture.

Second, we will analyze the effects of a change in the dispersion of the individual levels of conformism. In order to make meaningful comparisons, we analyze the impact of Mean Preserving Spread (MPS) changes in the dispersion of the distribution of the parameter $b_{i}$ . There is a well-known result from Rothschild and Stiglitz (1970) that states that a MPS increases the expected value of a convex function. It is easy to check that the matrix of second derivatives of equation (10) with respect to b_i is definite positive, thus the function is convex and, consequently, an increase in the dispersion of the distribution of $b_{i}$ will increase the variance of the personal norms and this in turn implies a reduction of the homogeneity of the culture. In other words, suppose two groups with a distribution of conformism with the same average, then the less dispersed distribution yields a more homogeneous culture in the long run. We summarize the above results in the following proposition.

Proposition 6. Cultural homogeneity of personal norms and behavior increases with the level of conformism and decreases under MPS in the distribution of conformism.

Effects of consistency

Consider now an increase in the level of consistency in the group, using the same definition employed for conformity in the previous subsection. An increase in the level of consistency in the group raises the variances of personal norms and behavior, reducing the homogeneity of the culture. This is due to the fact that, by consistency, each agent will have her own personal norm moving toward the level predicted by her own material incentives, as found in section “Consistency.” If the force of consistency rises, the weight of factors like the productivity of agents or their remunerations increases. If these factors are unevenly distributed, then the homogeneity of the culture is reduced. Cognitive dissonance weakens the strength of a culture.

Next, we analyze the effects of an MPS in the distribution of the levels of consistency, $a_{i}$ . The reader can check that the sign of the matrix of second derivatives of equation (10) with respect to $a_{i}$ is unclear, so we cannot have a clear prediction neither on the variance of the personal norms nor on the strength of the culture when there is an increase in the dispersion of the distribution of the weights of consistency.

Proposition 7. Cultural homogeneity of personal norms and behavior decreases with the level of consistency.

Effects of materialism

Finally, an increase in the weight of the level of materialism in the utility function of agents will lead to an increase in the variances of personal norms and behavior. An increase in the weight assigned to the material payoffs is equivalent to a reduction in the influence of personal norms and hence, a reduction in the pressure of the dynamics, resulting in a greater influence of the distribution of individual productivity and/or the income sharing rule. Summarizing, for a higher $β$ , the individuals are more selfish and less influenced by personal norms, weakening the culture, that is resulting in a less homogeneous culture. Note that in the opposite case when $β$ tends to 0, then $σ^{2} (ê^{\infty})$ tends to 0. In this case $ē_{i}^{t} = ê_{i}^{t},$ $\forall t$ and, therefore, only conformism matters. Societies with very low levels of materialism will display very homogeneous cultures. The very same processes happen for behavior homogeneity.

Proposition 8. Cultural homogeneity of personal norms and behavior decreases with the level of materialism. If the level of materialism is null, long-run norm and behavior homogeneity are maximal.

Conclusion

This article has presented a theory on the evolution of personal norms and the degree of homogeneity of organizational cultures when agents’ personal norms follow a dynamics driven by a combination of cognitive dissonance and informational conformism. Individual behavior in each period is motivated both by material incentives and each individual’s personal norm. The main finding is that an individual’s personal norm in the long run consists of a combination of her action in the NE in material payoffs (that depends on her own productivity and her share in the income distribution rule) and the average action of the population in this NE (that depends on the average of the productivities weighted by the shares of the income distribution rule). As a consequence, a prediction of the model is that organizations will always exhibit more homogeneity in personal norms than in behavior since each agent weighs differently the information derived from her own material incentives and from the overall society and this weight depends on her levels of materialism, conformism, and consistency. Moreover, the cultural dynamics will make always norms and behavior less diverse than the mere variance of marginal revenues which is determined by technical and social factors.

It is also analyzed, for simplicity for the case of a dynamics with only conformism, the influence of the presence in the group of a subset of individuals that are non-conformist or non-materialistic or are completely selfish. In all these cases, an homogeneous culture in personal norms for the rest of the organization still arises in the long-run but not in behavior. However, the presence of this type of agents influences the particular value of the homogeneous personal norm in the steady state. On the one hand, the convergence value also depends on the initial and fixed along time personal norms of non-conformist individuals. On the other hand, non-materialistic agents, that is, agents motivated exclusively by their personal norm, have no influence at all in the resulting common norm that will only depend on the skills and remunerations of the agents that display positive levels of materialism. Moreover, although fully materialistic agents do not have a personal norm, they strongly influence the resulting homogeneous culture for the rest of the group.

An important insight of this research is that it is possible to identify the factors that determine the degree of cultural homogeneity. For instance, with respect to the behavioral parameters of the individuals, cultural homogeneity is higher, the higher the level of conformism, the lower the dispersion of the group distribution of the levels of conformism and the lower the level of consistency and materialism in the society.

Furthermore, a culture is more homogeneous both in norms and in behavior if skills are more evenly distributed in the population. Thus, management’s decisions on the recruitment of personnel with different skills may affect the cultural homogeneity of the organization. Similarly, a more unequal distribution of income due to a change in the sharing rule of total income will cause a decrease in the cultural homogeneity of personal norms and behavior. Thus, again we observe that management can play a key role to achieve an homogeneous corporate culture manipulating the dispersion of the remunerations in the organization.

Our model has also implications for public policies concerning the integration of minorities or even the design of immigration policies. Social integration of immigrants into a host society is a crucial problem in most western societies. Obviously, governments might have different integration policies which reflect different goals concerning the desired homogeneity of the society’s culture. In particular, there is a hot debate between diversity or assimilation. Our model highlights the limits in the effectiveness of any assimilation policy, which pursues an homogeneous culture, if it is not accompanied by additional measures. Namely, tax-planning or regulatory measures that reduce income inequality and/or the dispersion of skills (for instance, through investment in human capital).

Similarly, our theory sheds light on possible unexpected effects of a restrictive immigration policy. Societies that only admit immigrants with high skills or high level of human capital will face a tendency to cultural heterogeneity caused by the increase in the average skill in the population. This might conflict with other possible goals of the government regarding cultural homogeneity.

Footnotes

Appendix 1

Appendix 2

Appendix 3 Acknowledgements

This paper has benefited from comments of the participants of the following conferences: 4th Workshop on Dynamic Games and Management Strategy in Padova in December 2012, PET 2013 in Lisbon in July 2013, and a Seminar in the University of Middlesex London in May 2014.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Spanish Ministry of Economia y Competitividad project, EC0-2011-29230, ECO-2014-58297-R, and the ERC project—TECTACOM, “The Economics of Cultural Transmission and Applications to Communities, Organizations and Markets.”

1.

This directly links to standard results in cultural transmission literature with continuous cultural traits, as Cavalli-Sorza and Feldman (1981), Bisin and Verdier (2001), Panebianco (2014), and .

2.

The precise formula is as follows:

σ^{2} (ws) = σ^{2} (w) σ^{2} (s) + (1 / N^{2}) σ^{2} (s) + {〈 s 〉}^{2} σ^{2} (w) + cov (w^{2}, s^{2}) - {[cov (w, s)]}^{2} + 2 〈 w 〉 〈 s 〉 cov (w, s) .

*

In an abuse of notation, we will denote by No $N_{o}$ both the set of players and its cardinality when there is no confusion.

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