rider problems by informal social control. ..... hand, company towns may help to solve free rider problems, because ...... Exchange and Power in Social Life.
Do company towns solve free rider problems? A sensitivity analysis of a rational-choice explanation Andreas Flache, Michael W. Macy, Werner Raub
Abstract Coleman (1979; 1994) has argued that sociological rational choice theory is an appropriate tool to analyze organizations. He emphasizes that the theory combines the analytical power of formal decision analysis with sociology’s attention to informal incentives. Our paper aims to caution against a potential danger in Coleman’s research agenda. Substantively important implications of the theory, namely, propositions about the interplay of formal and informal mechanisms, may be highly sensitive to specifications of the central assumption of goal-directed decision making. To demonstrate this potential sensitivity, we provide a stylized analysis of the effect of company towns on workers’ compliance with production norms, an example discussed by Coleman. Our study starts out with a forward-looking analysis, employing the orthodox rational choice assumption of a “forward-looking” rational actor. For comparison, we then apply a “backward-looking” learning model. It turns out that results are highly sensitive to variation in the underlying decision model. The forwardlooking model suggests that company towns may help workers to solve free rider problems by informal social control. By contrast, the backward-looking model implies that company towns may foster strong bilateral friendships that undermine workers’ willingness to invest in social control. We argue that such sensitivity is of relevance beyond the scope of this particular example. We therefore propose that rational choice analyses of organizations carefully assess model sensitivity to deviations from the assumption of perfect rationality.
1 Introduction The aim of this paper is twofold. Theoretically, we ask whether the implications of sociological models based on the core assumption of goal-directed decision making are in fact – as is often claimed – relatively robust to specifications of this assumption of incentive-guided behavior. We show that, indeed, different specifications of the rational choice assumption yield rather different implications for micro-behavior and its macro-consequences in a social context. Substantively, we focus on employment relations as an application. More precisely, we ask whether employees who are friends are better capable of working together than employees who do not care much about each other. We conceive of work groups (teams) as a social dilemma between the peers. The well-known “density-cooperation hypothesis” states that a tight web of social relations between team members should foster their cooperation in the sense of promoting joint output. We show that the density-cooperation hypothesis is sensitive to different specifications of the decision model. Coleman (1979; 1994) has argued that sociological rational choice theory promises an important contribution to the analysis of firms and organizations. He points out that the strength of the theory lies in its combination of economics’ deductive power with sociology’s focus on informal incentives. Deductive power derives from the “one assumption that most distinguishes neoclassical economics,” the assumption “that individuals are goal-directed, and that once the goals are known, the actions will be those that the individual perceives to be most efficient toward the goal” (1994, 167). Sociological theory demonstrated that the principle is applicable beyond the analysis of market transactions to exchanges of symbolic and nonfungible resources, such as social approval or status (Blau 1964; Homans 1974). Accordingly, Coleman concludes that rational choice theory is an appropriate analytical tool to address “spontaneous or informal social processes that arise within a formal organizational structure and thus makes possible organizational design that shapes and directs these informal processes” (1994, 177; see also Coleman 1979, 84-86). Our paper cautions against a potential danger in such a research agenda. Substantively important propositions about the interplay of formal and informal mechanisms in organizations may be highly sensitive to specifications of the central assumption of goal-directed decision making. We believe that applications of rational choice theory tend to underestimate this problem. Researchers readily admit that “real” individual decision making may be better described by a set of “boundedly rational” (Simon 1982) heuristics rather than
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by the heroic assumption of perfect rationality (Coleman 1990, 14-15). At the same time, it is widely believed that this does not compromise the usefulness of the perfect rationality assumption for the analysis of regularities at the aggregate level (Friedman 1953, 20-21; Stinchcombe 1968; Coleman 1987, 184; Wippler and Lindenberg 1987; Hechter 1988, 31-33). These authors stress that micro deviations from rational behavior fail to affect macro regularities, because deviations may be unsystematic “random errors”. Moreover, theorists refer to “backward-looking” mechanisms supposedly underlying “real” decision making, such as learning, imitation and selective pressure. In the end result, it is claimed, these mechanisms drive actors to behave “as if” they were fully rational decision makers. To question the robustness of macro propositions derived from the perfect rationality approach, we conduct a stylized analysis of the interplay of formal and informal mechanisms in company towns, an example proposed by Coleman. In general, Coleman highlights the interdependence between the formal structure of the organization, such as incentive schemes or authority relations between occupants of different positions in the organization, and the informal, “spontaneous” exchanges between employees (1979, 84). For example, he points out that Japanese firms often create “company towns” and “common recreational facilities” for their employees, “designed to simultaneously strengthen loyalty to the company and social ties among employees” (1994, 173). Coleman then suggests that rational choice theory is capable of identifying conditions under which measures like company towns may effectively foster employees’ compliance with organizational norms. From a rational choice perspective, compliance is problematic when actors’ individual and organizational (collective) interests are partly diverging (Raub and Weesie, Introduction). In the company town example, this divergence centers on the “workers’ dilemma” whether to “work” or “shirk.” Workers share a common interest in maximizing productivity, if, for example, weak performance by the firm leads to the loss of jobs. This common interest is especially strong when workers’ wages are tied to production norms by bonus payments or group piece-rate schemes (Edwards and Scullion 1982, 182). At the same time every worker faces an individual incentive to “free ride” at the expense of his colleagues by “shirking” while others shoulder the burden of maximizing output.1 Company towns may help solving free rider problems, because workers’ higher
1
With this assumption we neglect the complication of quota restriction norms that workers may impose to discourage “rate busters” (Homans 1951). Instead, our analysis follows “agency theory” (Alchian and Demsetz 1972) and views the firm as a group rewarded team facing a free rider problem.
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dependence on social ties inside the firm may increase the effectiveness of informal social control.2 To test this intuition, we first employ an orthodox rational choice analysis of informal control, using the theory of repeated games with complete information. Following Coleman’s research agenda, we apply the notion of utility maximization to exchanges of both formal and informal incentives. Unsurprisingly, the analysis predicts that higher dependence on ties with colleagues both increases social cohesion in the workforce and workers’ compliance with the production norm. In a nutshell, the reason is that fully rational workers identify an optimal equilibrium strategy in which they reward compliant workers with social approval. As a consequence, higher dependence on peer rewards increases incentives to comply. We demonstrate that results of the orthodox rational choice analysis are not robust against variation in the underlying model of decision making. To test robustness, we draw on Flache and Macy (1996) and replace the assumption of perfect rationality with a “backward-looking” model drawing on social learning theory. The backward-looking model assumes that actors follow a “trial and error” rule, gradually adapting their behavior in response to experience. The model relying on game theory, by contrast, assumes that actors rationally anticipate each others’ actions. The model abstracts from learning because complete information of the actors is assumed so that learning is not an issue and actors behave purely “forward-looking.”3 Beyond that, the models are identical in the 2
Coleman (1994, 178) discusses an example where it did backfire. In the coal mining industry in 19th century industrial america, company towns facilitated formation of social ties between employees. However this fostered the formation of strong antifirm organizations rather than workers’ loyalty to the company.
3
Note that learning is of course a crucial element of games with incomplete information, i.e., games played by actors who are less than fully informed on some aspects of the situation, like the preferences or strategic options of others, and who try to infer unknown characteristics of the game from observed behavior of other actors, using Bayesian updating. Hence, under incomplete information, even fully rational actors do rely on experience from the past for present decision making and conventional game theory not at all excludes backward-looking behavior and learning, although rational learning - in the sense of Bayesian learning - is assumed. Recent work in game theory (see, e.g., Fudenberg and Levine 1998) focuses on boundedly rational learning. Evolutionary game theory in particular addresses the behavior of any strategically interdependent organism facing selective pressure, including fish (e.g., Axelrod and Hamilton, 1984). Evolutionary game theory does not require the assumption that fully rational players anticipate each others' actions (or behave as if they do so). Instead, the theory assumes that success and failure in interdependent situations affect the reproduction chances of a particular strategy (or species). All these approaches for incorporating backward looking
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decision problem individuals face. The two models are only distinct in the assumptions describing how actors optimize behavior. To preview, our comparison demonstrates that the variation in micro assumptions radically changes substantive implications. Flache and Macy’s computer simulations showed that backward-looking actors fail to organize cooperation in the collective task, while they succeed in solving the simpler problem of establishing “friendships” in terms of bilateral exchanges of social rewards (cf. Flache 1996). These friendships then undermine group production as actors use approval to reward approval rather than using approval as a “selective incentive” (Olson 1965) for solving free rider problems. The remainder of this paper presents the argument in detail. In the following section, we present the exchange theoretical perspective underlying both the forward-looking and the backward-looking model. Section 3 elaborates this perspective in terms of an iterated game. While Section 4 presents the forward-looking game theoretical analysis of this game, Section 5 describes the corresponding backward-looking simulation study. The concluding section discusses the relevance of model sensitivity for rational choice analyses of organizations.
2 A social exchange perspective Our analysis of informal control draws on a social exchange perspective proposed by Homans (1974). Empirical evidence from studies on group conformity (Festinger, Schachter and Back 1950) led Homans to ask why group cohesion often fosters members’ conformity with group obligations. Homans used social exchange theory to explain the regularity. In line with most theoretical studies, he defined cohesion as the level of interpersonal attraction among the members of a group (Hogg 1992). Homans then modeled interpersonal attraction as the exchange of social approval. In short, a cohesive group is “one in which many members reward one another” (1974, 156) with expressions of approval that affirm a member’s standing in the group. These rewards are then exchanged for compliance with group obligations. Since “some degree of ostracism is the penalty for failing to conform to a norm” (1974, 156), learning in game theoretical analyses show that the contrast between forward- and backward-looking models should not be misconstrued as implying an inconsistency per se between game theory and learning models.
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peer pressure can be an effective instrument of informal social control. The more cohesive the group, the stronger the pressure to conform. Clearly, Homans’ reasoning implies a positive effect of company towns on workers’ willingness to comply with the production norm dominant in the workforce. In Homans’ social exchange perspective, company towns foster the effectiveness of peer pressure, because they increase workers’ dependence on social rewards from their colleagues. We develop a formal analysis of Homans’ argument, because we believe that his reasoning is less straightforward than he suggests. To explain, in using social exchange theory to model informal social control, Homans assumed, correctly, that compliance is traded for approval. However, he erred to therefore assume that approval must also be exchanged for compliance. To illustrate, suppose Ego and Alter each possess only one of two dissimilar resources, call them C and A, with equal unit values. Obviously, Ego and Alter may then only exchange C for A and A for C, as Homans assumed. However, when the exchange problem is applied to informal social control, the assumption that the actors possess only dissimilar resources is violated. Ego can offer both approval and compliance to Alter, and vice versa. That is, Ego can approve and comply, in exchange for Alter doing the same. In this situation, Homans may still be right: Ego and Alter may still exchange C for A and A for C, an exchange that Heckathorn (1993) calls “compliant control.” But now other exchanges are also possible. They may exchange C for C and A for A, two C’s for A plus C, two A’s for C plus A, etc. It is no longer evident what happens when approval can be exchanged for approval instead of compliance. Actors then face the decision of whether to use social ties to enforce group obligations (compliant control) or to build personal relationships that are privately satisfying (relational control). The latter possibility suggests that contrary to Homans’ reasoning high dependence on social approval may even compromise the effectiveness of informal social control. Instead of giving Ego leverage over Alter’s compliance, a mutually beneficial exchange may give Alter leverage over Ego’s willingness to enforce conformity with group obligations. The bilateral exchange of approval introduces a new possibility. Approval must be salient to effectively enforce compliance, yet the more salient it becomes, the greater the temptation to exchange approval for approval rather than for compliance. Homans’ exchange theoretical perspective leaves two possibilities. On one hand, company towns may help to solve free rider problems, because workers’ higher dependence on social ties within the workforce facilitates compliant control. At the same time, this higher dependence may undermine compliance, because relational control allows workers to develop cohesive friendships that
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may effectively insulate participants from peer pressure. To clarify implications, the following sections propose formal analyses of the argument.
3 The repeated game To describe the decision problem individuals face, we specify a repeated game underlying both the backward-looking and the forward-looking analysis. In this game, workers’ payoffs are shaped by both formal payment and informal peer rewards. More specifically, we assume that actors value wage payments and approval of their peers, and they weigh these values against the effort required to obtain them. Wage payments, in turn, are tied to firm output, i.e., the more workers contribute to the collective effort, the higher the payment. Actors must make two decisions: whether to invest in collective effort (“work”) and whether to invest in their relationships with other members of the group (“approval”). To simplify, we assume actors must choose between just two options for each decision: to work or shirk, and to approve or not approve. The exchange of work and approval is modeled as a repeated N-person game where in every iteration every group member selects a decision vector consisting of N components. The first decision component is whether to work or to shirk, the other decisions are whether to approve or not of another group member. In addition, we assume that decisions are taken simultaneously and independently. Formally, the strategy of player i in iteration t of the game, is the vector σit, where ∀i:σ it = ( wit , a i1t ,..., a iNt ) .
(1)
The symbols i,j in (1) index actors, w and a identify each of the two decisions, work effort and social approval. The work decision taken by actor i in iteration t is denoted wit , where wit = 0 for shirkers and wit = 1 for contributors. i’s approval of j is indicated by aijt , where aijt = 1 when i approves of j and
aijt = 0 , otherwise. To preclude narcissism, we use the restriction a iit = 0 . The payoff actor i derives in iteration t of the game, uit , results from the joint effect of all actors’ decisions on i’s payoff (including his own decisions). uit comprises both benefits from wage and approval and the costs of i’s own effort and social actions. The effort or expense from hard work or from giving approval may be offset by two types of benefits: a higher group wage and social approval by one’s peers. For simplicity, we assume that the group wage is a linear function of aggregated individual efforts. Each actor then receives 1/Nth
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of the bonus earned by the group, regardless of contribution. The output of one worker benefits Ego with a wage increase of one unit. The second source of benefit is social approval from one’s peers. We assume that the benefit Ego derives from being approved of is proportional to the number of peers who give approval to Ego. Finally, when Ego invests into the collective effort, his utility is diminished by work costs. In addition, Ego may incur some cost for every unit of approval he gives to one of his peers. Equation (2) formalizes the utility Ego derives from the outcome of the approval and work decisions at iteration t: N
α
j =1
N
uit = ∑ (
N
w jt + β a jit ) − cwit − c ′ ∑ a ijt .
(2)
j =1
In (2), the parameter α captures the wage workers earn per unit of output produced. More precisely, α indicates the maximum wage actors can attain, i.e. the wage that is paid when every worker contributes to the work task. The parameter β represents the value of a unit of approval. This is the parameter central to our analysis. We assume that in a firm where workers live in a company town, they are more dependent on colleagues’ approval as compared to other firms due to, for example, lack of alternative sources of approval. Hence, the unit value of approval, β, is higher in firms with company towns, all other things being equal. Finally, the costs of spending a unit of effort and the costs of giving a unit of approval are indicated by the parameters c and c ′ , respectively. Our interest focuses on cooperation problems. Thus, we conceive of the game as a repeated n-person Prisoner’s Dilemma (see Raub 1988). Accordingly, we assume that cooperation in the exchange of work effort is collectively desirable, but actors face incentives to free ride. We assume that loafing is more cost-effective than working ( α N < c ) and that everyone realizes a Pareto optimal collective benefit when everyone pulls his weight (c < α), or
α N
< c < α.
(3)
Similarly, the exchange of approval for approval is mutually profitable for both members of a dyad, but there is at least some incentive to free ride on others’ approval. Hence, there is a cost of giving approval ( c ′ ) that is positive but smaller than β, the value of approval for the recipient. Formally, 0 < c′ < β .
(4)
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Then, obviously, each iteration of the game has a unique Nash equilibrium, i.e., each player maximizes his utility given the behavior of all others, such that each worker shirks and no approval is given.
4 The forward-looking model To analyze forward-looking behavior in the game, we apply the theory of repeated non-cooperative games. Game theory may be regarded as the appropriate tool for a orthodox rational choice analysis. It is the only model of decision making that fully takes into account the strategic problem maximizing actors face in interdependent situations. We furthermore concentrate on repeated non-cooperative games, i.e. we assume that no binding contracts between players are feasible. This class of games straightforwardly models the emergence of cooperation from “tacit” reciprocity and conditional cooperation in social exchange (Taylor 1987; Voss 1985; for a more detailed discussion of our application, cf. Flache 1996, 66-68). The forward-looking model consists of two components. In Section 4.1, we describe payoffs and information assumptions in the repeated game. In Section 4.2, we formulate a simple solution theory for our game. Finally, Section 4.3 applies this solution theory to derive predictions for the effect of dependence on peer approval, β, on workers’ compliance.
4.1 The repeated game: payoffs and information assumptions Forward-looking actors, we assume, evaluate the consequences of their actions by taking into account the anticipated effect of all decisions they make on the overall expected utility they derive in the game. We follow the standard approach in the literature (Friedman 1986, Taylor 1987) and assume that in making strategic choices actors discount future payoffs. This assumption reflects uncertainty of continuation of the game in the future. Technically, this amounts to exponential discounting of payoffs. The payoff ui that actor i derives in the repeated game is obtained by summation of the discounted payoffs derived in all iterations t, uit . Formally,
∞
ui = ∑ τ it uit t =0
, 0 < τi < 1 .
(5)
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where τ i is the value of the individual discount parameter of actor i. The payoff of iteration t, uit , ensues from the corresponding outcome as defined by (2) above. For simplicity, we assume that the value of the individual discount parameter is identical for all members of the group. In the remainder of this paper we therefore denote this value τ. Finally, the repeated game is assumed to be a game with complete information. Hence, each actor is informed on the number of actors, their payoff functions, and their feasible strategies. In particular, actors’ information is modeled by the assumption that in iteration t, worker i is fully and perfectly informed on both the work actions w jt′ and the approval actions a jkt′ of all group members in previous iterations t ′ < t (including i herself).4 Note that these information assumptions imply that rational actors have nothing to learn about unknown characteristics of other actors or about the game when the game develops. Hence, our game theoretical model captures the idea of pure forward-looking rationality. Note also that the repeated game provides a rational choice model of crucial aspects of reputation effects in social networks (see Raub and Weesie 1990; Buskens 1999): An actor’s behavior in iteration t is observed by others and affects their future reactions.
4.2 A solution theory To make predictions, we specify a theory for “solving” the repeated game. In game theory, a solution of a game is an outcome that is consistent with the assumption that actors are rational decision makers. An outcome of our game is a sequence of compliance and approval decisions of all players in all iterations. Game theory has not yet produced a commonly accepted solution theory that is capable of yielding a unique solution for all repeated non-cooperative games (see, however, Harsanyi and Selten 1988). At the same time, there is considerable agreement that a solution should at least satisfy certain criteria. For our purposes, two widely accepted criteria suffice, subgame perfect equilibrium (spe) (Selten 1965), and payoff dominance (Harsanyi 1977). A spe has the following two qualities. First, it is a Nash equilibrium. Second, the spe satisfies an important condition for the stability of the prediction. If at any point in the game “something goes wrong” and some player takes an action that “deviates” from the equilibrium path, rational actors 4 It may be more plausible to assume that i is only partially aware of approval exchanges between third parties j and k. For simplicity, we do not employ this assumption here. This simplification is not problematic, however. Flache (1996) showed that the results of the game theoretical analysis are not affected when the alternative information assumption is made that Ego is ignorant about approval exchange between third parties.
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nevertheless face no incentive to afterwards deviate from the equilibrium strategy (for a detailed discussion of the spe concept, see e.g. Kreps 1990, 402410). The criterion of payoff dominance further reduces the set of spe’s of the repeated game. Informally, payoff dominance eliminates those spe’s from the set of possible solutions to which all players would unanimously prefer other spe’s (for more details, see Harsanyi 1977, 116-119).
Idealized outcomes To facilitate model analysis, we restrict the set of potential solutions to four idealized outcomes. As a baseline, we take the full defection outcome ( OD ), in which all group members fail to cooperate in the collective task and, in addition, abstain from any exchange of approval. Since payoffs satisfy the Prisoner’s Dilemma conditions (3) and (4), the full defection outcome is the unique solution of the constituent game, i.e., the game which is repeated in every iteration. As a consequence, universal play of the corresponding full defection strategy (the full defection strategy combination) always is a spe in the corresponding repeated game. In addition, the set of idealized outcomes comprises three outcomes in which all workers perpetually and unanimously follow a cooperative strategy. A cooperative strategy is one that entails an outcome Pareto superior to the full defection outcome. These outcomes are the compliance outcome, the cohesion-compliance outcome and the cohesion outcome. In the compliance outcome every actor contributes to the collective effort (C) but he fails to approve of his peers. In the cohesion-compliance outcome, every actor contributes to the collective task (C) and simultaneously approves of all colleagues (A). Finally, in the cohesion outcome, every actor approves (A) of all his colleagues but he fails to contribute to the collective task. To analyze spe conditions for the cooperative outcomes, we use the most extreme and simple form of conditional cooperation, so-called trigger strategies (cf. Friedman 1971). In a trigger strategy, a player always starts cooperatively but changes to a permanent “punishment strategy” as soon as he learns that some other player failed to also cooperate. More formally, trigger strategy combinations σ T of the repeated game are induced by a cooperative strategy combination of the constituent game, σ c* , and the “punishment strategy” which is given by the unique inefficient solution of the constituent game, σ cD (full defection). This definition generates three trigger strategy combinations for the repeated game, corresponding to the three cooperative idealized outcomes. For accuracy, we denote the related strategy combinations of the constituent game σ cC , σ cCA and σ cA , respectively. The corresponding trigger strategy combinations then are 1) the compliance strategy combination, σ C = (σ cC , σ cD ) ; 2) the
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cohesion-compliance strategy combination, σ CA = (σ cCA , σ cD ) ; and 3) the cohesion strategy combination, σ A = (σ cA , σ cD ) . For completeness, we add 4) the full defection strategy combination, σ D , where every actor i plays his full defection strategy σ ciD in every iteration of the game. Actors’ interest in future payoffs, τ, is the crucial condition for a trigger strategy combination to be a spe. When τ is large (close to 1) so that actors are sufficiently interested in the payoff of future interactions, then the long term punishment of players’ eternal defection is severe enough to deter them from unilateral defection. Theorem 1 below provides a well known result of the theory of repeated non-cooperative games that formalizes this condition. In Theorem 1, φi* denotes the payoff that actor i can achieve in the constituent game by unilateral deviation from the cooperative strategy combination σ * to full defection, σ ciD . Furthermore, ui* and uiD identify i’s payoff from universal cooperation and his payoff from universal defection in the constituent game, respectively. Finally, τ * indicates the threshold discount parameter that specifies the minimum interest in future payoffs required to sustain conditional cooperation.
Theorem 1 Let σ T = (σ * , σ D ) be a trigger strategy combination of the repeated game. If
τ > τ* =
φi* − ui* φi* − uiD
(6)
then σ T is a subgame perfect equilibrium of the repeated game. Proof: Friedman (1986, 88-89). Theorem 1 has a straightforward interpretation. The larger the short term gains of defection (numerator) and the more the payoff of unilateral defection exceeds the payoff of the long term punishment (denominator), the greater the weight that actors must place on future payoffs, τ, to be willing to cooperate on basis of trigger strategies. Theorem 1 allows to identify the idealized outcomes supported by a trigger strategy spe of the repeated game. Below we show that for a particular level of τ more than one of the idealized outcomes may satisfy this requirement. In these cases, payoff dominance selects a unique solution. The Prisoner’s Dilemma conditions (3) and (4) immediately imply that the cohesion-compliance outcome always payoff dominates the other idealized outcomes. Furthermore, all
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cooperative outcomes always payoff dominate the full defection outcome. Finally, comparison of the payoffs of the cohesion outcome, OA , and the compliance outcome, OC , shows that OC payoff dominates OA , if and only if exchanging compliance is more rewarding than exchanging approval, i.e. α − c > ( N − 1)( β − c ′ ) . Otherwise, OA payoff dominates OC . To summarize, the solution theory consists of three elements, the concept of a subgame perfect equilibrium, the set of idealized outcomes and the criterion of payoff dominance. More precisely, a solution of the repeated game is an outcome O that satisfies the following requirements: • • •
O is supported by a subgame perfect equilibrium (individual rationality), O is one of the four idealized outcomes OD , OC , OCA , O A , and there is no other individually rational outcome O ′ that payoff dominates O.
4.3 Results The forward-looking analysis confirms the expectation that increasing dependence on peer approval facilitates compliance in a large region of the parameter space. At the same time, the model shows that contrary to Homans’ argument, high cohesion may sometimes arise without compliance. To obtain this result, we start out with an analysis of how actors’ interest in future payoffs, τ, affects the solution of the repeated game. We then address the effect of dependence on peer approval, β, on both workers’ compliance and cohesion. The solution of the game depends on the value τ of actors’ interest in future payoffs relative to the thresholds for the discount parameters of each of the three idealized cooperative outcomes. We denote these thresholds corresponding to τ * with τ C , τ CA and τ A , respectively. Calculation of the threshold values yields Theorem 2 below. The theorem states that for every parameter combination the ensuing game can be assigned to exactly one of three categories. For games in Category 1 actors find it easier (in the sense that the threshold τ A is lowest) to build a highly cohesive network without compliance than to invest in compliance alone or to attain both cohesion and compliance. More precisely, in Category 1 cooperation in the cohesion strategy combination requires less interest in future payoffs, τ, as compared to cooperation in the compliance strategy combination. The order of threshold values is τ A < τ CA < τ C . Conversely, in Category 2 the easiest solution is compliance without cohesion.
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Here the reversed order of threshold values applies. In Category 3, finally, the three thresholds have the same value. Theorem 2
Consider the game generated by the parameter combination N, α, β, c and c ′ . The order of the threshold values for individual rationality of the cooperative outcomes can be obtained as follows.
CA
1) ( 0 < τ < τ
0, otherwise = 0, if α ∂β c′ ∂β c− N
(9)
∂p ′ > 0 ∂β
To illustrate the result of Corollary 1, we visualize the effects of dependence on peer approval, β, for a particular scenario. The scenario assumes that workers face a serious free rider problem in the work game. With N = 10, α = 1 and c = 0.33, the marginal costs of a unit of effort are more than three times as large as the corresponding marginal benefit. Furthermore, we follow Coleman (1990, 277) who has argued that approval may be a particularly effective instrument of peer pressure, because its production is costless or nearly so. Accordingly, we assume c ′ = 0.01 . Figure 1 shows the results.
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1 0,9 0,8
p p'
0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 0
0,1 0,2 0,3 0,4
0,5 0,6 0,7 0,8 0,9
1
Figure 1: Forward-looking model. Effects of dependence on peer approval (β) on compliance (p), and cohesion ( p ′ ). α = 1, c = 0.33, c ′ = 0.01 , N = 10. Figure 1 demonstrates that results of the forward-looking model are by and large consistent with Homans’ argument. In a wide region of the parameter space, higher dependence on peer approval, β, increases both compliance and cohesion. More precisely, dependence on peer approval fosters compliance, p, in the range of β > 0.05. In this range of the parameter space, the game falls into Category 1. Here, the forward-looking model reflects Homans’ intuition. The informal incentive (approval) is sufficiently attractive to support compliance. Hence, cooperation in exchanges of work contribution is easier to obtain when these exchanges are combined with simultaneous exchanges of approval. The possibility overlooked by Homans, bilateral exchanges of approval, does not impede compliance in this range of the parameter space. Payoff dominance ensures that forward-looking actors always choose simultaneous exchange of approval and compliance, as soon as their interest in future payoffs is large enough to make feasible both the cohesion outcome and the cohesioncompliance outcome. At the same time, cohesion may arise without compliance when actors are only moderately interested in future payoffs ( τ A < τ < τ CA ). Accordingly, in this region of the parameter space higher levels of dependence on peer approval render cooperation in the work game more likely, because they increasingly facilitate cooperation in the simultaneous exchange of compliance and approval. The range of β ≤ 0.05, finally, reflects a possibility not addressed by Homans. The free rider problem may be resolved exclusively by conditional cooperation in the work task without exchanges of approval. In this region of the parameter space, approval is so weak an incentive that cooperation in
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simultaneous exchanges of compliance and approval is harder to obtain than cooperation in the work game alone. To summarize, the forward-looking analysis confirms the expectation that increasing dependence on peer approval facilitates compliance in a large region of the parameter space. At the same time, the model shows that contrary to Homans’ argument, high cohesion may sometimes arise without compliance. Accordingly the results of the forward-looking model suggest that company towns help workers to solve free rider problems, at least when their interest in both future payoffs and peer approval is sufficiently large. In the worst case, a company town may fail to foster workers’ willingness to invest effort. At the same time, the forward-looking model suggests that such a measure will at least not backfire against the firms’ interest.
5 The backward-looking model The backward-looking learning model assumes that actors follow a simple decision heuristic that economizes on cognitive effort. In this model, actors optimize by learning and adaptation rather than by calculating the marginal return on individual investment. In other words, actors adjust both their effort level and their attitudes toward other members in response to social cues that signal whether the investment was worthwhile. The actors thus influence one another in response to the influence they receive, creating a complex adaptive system. Such systems lend themselves more readily to computational rather than analytical models (Axelrod 1997; for “backward-looking” computer simulations of collective action and social exchange, see Macy 1989, 1990, 1993) and are often addressed by evolutionary game theory (Skyrms 1996). The computational model consists of three basic components: a decision algorithm, a reward function by which outcomes are evaluated as satisfactory or unsatisfactory, and a learning algorithm by which these evaluations modify choice propensities. We describe these components in turn. Finally, we present results of the backward-looking analysis using an agent-based computational model.
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5.1 Decision algorithm The backward-looking simulation model assumes that the decision process is stochastic rather than deterministic. Learning actors follow choice propensities that are altered after they experience the consequences of their behavior. The outcomes raise and lower propensities, but choices remain uncertain. In short, anything can happen, but not with equal probability. The stochastic decision algorithm assumes that each actor i has some propensity pit representing the probability that i will work at time t ( wit = 1 ). With probability 1− pit , i will shirk ( wit = 0 ). Similarly, pijt′ represents the probability that i will approve of j at time t ( aijt = 1). With probability 1− pijt′ , i will not approve of j ( aijt = 0).
5.2 Reward function: the evaluation of compliance and approval The backward-looking model assumes an actor who economizes on cognitive effort with three shortcuts: reliance on propinquity as a low-cost proxy for causality, “satisficing” as a low-cost proxy for the identification of global optima, and separate evaluation of decisions as a proxy for analysis of the joint effects of simultaneous actions. Beyond that, the backward-looking model is similar to the forward-looking model. Both approaches assume that actors modify their behavior based on the associated outcomes. However, the forwardlooking model assumes that outcomes are causally associated with actions, while learning theory replaces causality with propinquity as the link between behavior and outcome. A successful outcome thus reinforces the corresponding decision even if this decision had no effect on the outcome. “Satisficing” (Simon 1982) implies that rather than calculate the actual probability of further improvement, actors assume that the odds of doing better diminish as outcomes approach optimality. The better the outcome, the more likely the actor will deem it to be “good enough” rather than risk an inferior result by searching for something better. The poorer the outcome, the more likely the actor will be to take the risk. For simplicity, the model formalizes this by evaluating outcomes relative to the midpoint of the payoff distribution. Finally, separate evaluation of actions implies that actors adapt their propensities to work or to approve separately per decision, based on their satisfaction only with some components of the outcome of the preceding iteration. This contrasts with the game theoretic analysis where we assume that actors strive to maximize
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the total utility they derive from the complete sequence of strategy choices for the iterated game. Evaluation of the work decision is modeled by a satisfaction function in which satisfaction increases with the actor’s share of the total group wage and decreases with the costliness of the decision. Actors also take into account the effect of their effort on their relationships with other members of the group. The effort is deemed worthwhile to the extent that it is associated with high levels of approval. More formally, S it =
α
N
N
j =1
j =1
∑ w jt + β ∑ a jit − cwit − S e . N
(10)
S it is i’s satisfaction with current work effort, such that the sign of S it indicates positive or negative evaluation. N, wit , α, β and c are defined in (1) and (2) above. S e is the reference point that determines whether actors are risk averse (as S e declines) or risk taking (as S e increases). A lower reference point expresses a more risk averse attitude in that a relatively small payoff suffices to cause an actor to accept her most recent decision as “good enough,” such that the actor becomes less likely to try other strategies. For simplicity, we balanced risk preferences by fixing S e for all actors at the midpoint of the range of possible satisfaction values, or
Se =
1 (α + β ( N − 1) − c ) . 2
(11)
The decision by i to approve of j, aijt , is evaluated in the same way except that the collective action problem is now disaggregated into a matrix of dyadic Prisoner’s Dilemma games, one for each of the possible dyads. Rather than taking into account overall group effort and overall approval received from the group, i considers only i’s benefit from j’s effort and the approval received from j. Since i’s benefit when all N members work is α, i’s benefit when one individual j works is α N . These benefits are then weighed against the cost of approval, c ′ , and evaluated against the expectation or reference point S e′ : S ijt′ =
α N
w jt + β a jit − c ′ a ijt − S e′ .
(12)
According to (10) and (11), the parameter β represents the weight i places on others’ approval relative to their work effort. With β = α N , i values others’
Do company towns solve free rider problems?
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approval equally with work effort both in evaluating his work decision and in evaluating his approval decisions. With β < α N , others’ approval of i has a stronger effect on i’s satisfaction than work effort. Conversely, with β > α N others’ work effort has a stronger effect on both i’s work behavior and his investment in social relations than others’ approval of i. S e′ , finally, is the reference point that corresponds to the midpoint of the reward distribution in the evaluation of approval: Se′ =
1 α ( + β − c′) . 2 N
(13)
The evaluation of each decision is transformed into a positive or negative reinforcer constrained to the interval [-1,+1]. Let Rit be the reinforcer corresponding to S it . Then Rit =
l S it , S max
(14)
where l is a learning parameter that scales the magnitude of reinforcement and S max is the highest possible work-evaluation. Since c > α N , the maximum work benefit is attained if you shirk and all others work. S max requires that all others work and approve of Ego, while Ego shirks, or S max =
1 α ( N − 2) ( + β ( N − 1) + c ) . N 2
(15)
Analogously we obtain Rijt′ :
Rijt′ =
α N
2 l S ijt′ + β − c′
.
(16)
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5.3 Learning function The final component of the model is the learning algorithm by which propensities to work and approve are modified by satisfaction or dissatisfaction with the outcomes associated with those behaviors. The learning algorithm is adapted from a conventional Bush-Mosteller stochastic backward-looking (Bush and Mosteller 1955). Actor i’s propensity to work, pit , is reinforced when effort seems to pay ( wit = 1 and S it > 0 ) or when shirking is costly ( wit = 0 and S it > 1 ): pi ,t +1 = pit + Rit (1 − pit )wit − Rit (1 − pit )(1 − wit ) .
(17)
The benefits of hard work and the costs of free-riding are indicated in the equation by two adjustments to pit , one positive (when wit = 1 ) and the other negative (when wit = 0 ). Hence, the reward to workers is added to the propensity when wit = 1 , while the penalty for shirkers is subtracted when wit = 0 , causing the propensity to increase in either case. Conversely, if feckless behavior pays off or hard work is suckered, then the propensity to shirk (1− pit ) is reinforced, i.e., 1− pit is substituted for pit on both sides of the equation and 1− wit is substituted for wit , giving pi ,t +1 = pit + Rit pit wit − Rit pit (1 − wit ) .
(18)
The propensity for approval pijt′ is modified in the same way. If aijt = 1 and Sijt′ > 0 , or aijt = 0 and Sijt′ < 0 , then: pij′ ,t +1 = pijt′ + Rijt′ (1 − pijt′ ) aijt − Rijt′ (1 − pijt′ )(1 − a ijt ) .
(19)
Conversely, if aijt = 0 and Sijt′ > 0 , or aijt = 1 and Sijt′ < 0 , then: pij′ ,t +1 = pijt′ + Rijt′ pijt′ aijt − Rijt′ pijt′ (1 − a ijt ) .
(20)
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5.4 Results Computer simulations of the stochastic learning model clearly question Homans’ analysis. The possibility to exchange approval for approval may undermine actors’ willingness to invest in social control. As a consequence, a highly cohesive network may arise in which the group comes to accept a complete failure of collective action. In order to create a fair test of the effectiveness of informal social control, we focus on the scenario discussed in Section 4.3. In this scenario, the group faces free rider problems when exchange of approval is precluded (β = 0). Flache and Macy (1996) showed that with N = 10, α = 1, and c = 0.33, compliance with work norms is difficult to attain but not impossible. In this situation an initial uniform work propensity of pi 0 = 0.5 can typically not be sustained. The reason is that the corresponding group wage is not sufficient to compensate the costs of investing full effort. Hence, workers are dissatisfied. However, shirkers do not pay the cost of compliance, and therefore they are either content with the outcome or, if dissatisfied, then less so than those who paid the cost. Dissatisfaction with working, and either contentment or milder dissatisfaction with shirking, causes overall work propensities to drop until a stable low-productivity equilibrium is reached where work propensities are only approximately p = 0.3. At equilibrium, both working and shirking are punished, but the larger punishment for workers is balanced by the larger proportion of shirkers. Clearly, this group might benefit from social control. To explore whether social control is effective, we increased actors’ need for peer approval from β = 0 to β = 0.2. Now a unit of peer approval is worth twice as much as the contribution of a unit of effort. Again, we assume that the production of approval is nearly costless, i.e., c ′ = 0.01 . Figure 2 shows the pattern that typically obtains. Group cohesion (mean pt′ ) increases to the maximum, while compliance with production norms (mean pt ) plummets, with 9 free-riders. All dyads eventually lock in mutual approval even if both Alter and Ego shirk. This is consistent with the hypothesized effects of bilateral exchange of approval. Peer pressure is no longer an effective instrument of informal social control. To test the reliability of the simulations, we replicated the experiment 50 times. Without informal control (β = 0), the mean rate of compliance at the end of 200 iterations was 0.4. Compliance dropped to 0.16 when need for peer approval was increased to β = 0.2 , a statistically significant difference (p < 0.01).
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Andreas Flache, Michael W. Macy, Werner Raub
1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0
p p'
0
10
20
30
40
iteration Figure model.Effects Change in mean propensities for Figure21: : Backward-looking Forward-looking model: of dependence on peer approval compliance (p) and (p), approval ( p ′ ). α( = c= 0.33, 0.01,c ′β= =0.01 0.2, (β) on compliance and cohesion p′ 1, ), N=10, α=1, cc′ ==0.33, . β ′ = 0.2 , N = 10. These simulation results reflect the cognitive shortcuts applied by backwardlooking decision makers. The learning process quickly leads a dyad to lock in mutual approval. More precisely, satisficing implies that as soon as Ego and Alter “discover” the option of mutual approval, both of them are content with their approval decisions regardless of the compliance of their counterpart. As a consequence, mutual approval is a self reinforcing outcome that eventually drives propensities for approval towards lock in at the equilibrium pijt′ = p ′jit = 1 . The simulations show how this exchange of approval for approval undermines compliance. For a dyad to be in equilibrium, it is not sufficient that Ego works and Alter approves. Shirking lowers satisfaction by only 0.1 (since N = 10), while approval increases satisfaction by 0.2 (since β = 0 .2 ). Thus, Ego can never be satisfied with his behavior toward Alter, even if Alter works, unless Alter also approves of Ego. (Note that c ′ > 0 means that Ego will always be more dissatisfied with approving Alter than ignoring
Do company towns solve free rider problems?
25
Alter.) Moreover, Ego will always be satisfied with his behavior toward Alter if Alter approves of Ego, even if Alter shirks. Of course, both will be much more satisfied if the other works, but since working is relatively costly, compliance tends to be low at the point when mutual approval makes actors satisfied with the work decision they presently take. In principle, the learning process could also lead towards an equilibrium where most actors work and most approve of their peers. Again, satisficing makes every group member in this situation content with both his compliance and his approval decisions. However, compliance involves a multilateral exchange (the pooling of work effort) that is much more difficult to coordinate spontaneously than mutual approval, even in a group with only 10 members. Inevitably, a network of strong ties emerges well before a critical mass of compliant actors, and once the network forms, the strong social rewards preclude further increases in compliance. This bias toward dyadic over multilateral exchange is created by differences in coordination complexity that emerge only in the backward-looking model and are not a factor in the forwardlooking model. The “weakness of strong ties” (Flache and Macy 1996) revealed by the simulations of Figure 2 shapes effects of the variable that is central to our analysis - the need for approval. This is demonstrated with a series of simulations gradually increasing β. Starting with the parameter set used in the previous simulation, we increased β from 0.0 to 1.0, in increments of 0.01. At each step, we measured equilibrium compliance (within a limit of 200 iterations). For reliability, we took mean values from 50 replications at each step. Figure 3 below confirms the hypothesized negative effect of β on compliance, but only for levels of β below approximately 0.15. The graph also shows that above this tipping point dependence increases compliance, despite the opportunity to form strong social ties based on mutual approval. In addition, Figure 3 demonstrates the tendency towards increasing relational control caused by higher levels of β. We measure relational control in terms of the correlation between Ego’s propensity to approve of Alter and Alter’s propensity to approve of Ego, 5 raa . Below β = 0.15, an increase in β causes relational control to soar and compliance to plummet. However, above the tipping point, further increases in β enhanced compliance.
5
To have sufficient variance for computation of the correlation, we measured propensities well before lock-in, in iteration 10 of the game. The strong effect of β on raa in Figure 3 indicates that even with a moderate level of β, this small number of iterations suffices for coordination of dyads on mutual approval.
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Andreas Flache, Michael W. Macy, Werner Raub
1 0,9 0,8 0,7 0,6
p p' raa
0,5 0,4 0,3 0,2 0,1 0 0
0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9
1
β Figure 3: Tipping Point in effect of dependence on peer approval (β) on compliance (p), cohesion ( p ′ ) and relational control ( raa ). α = 1, β = 0.2 , c = 0.33, c ′ = 0.01, l = 1, N = 10. Comparison of model dynamics for different regions of the parameter space shows why groups whose members feel an extreme need for one anothers’ approval can be relatively more cohesive and more compliant. Consider a group with outside sources of social support and no need for in-group approval. Over 200 iterations, compliance gravitates to p = 0.40. Approval is thus ineffective for rewarding either compliance or friendship. When the need for approval is slightly higher than zero (0 < β < 0.1), Ego cares more about whether Alter works ( α N ) than whether Alter approves of Ego. In this region, the value of approval is too low to compensate the costs of working. Strong ties are therefore very difficult to establish, especially if either or both sides are deviant. In their absence, workers receive a smaller wage than shirkers (due to the cost of work effort), which means that the proportion of the group who shirk just balances the larger payoff to shirkers. In our simulations, that generates an equilibrium with only about one-third of the group in compliance.
Do company towns solve free rider problems?
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Once the need for approval exceeds β = 0.1, Ego cares more whether Alter approves than whether Alter works. Bilateral ties can now become mutually satisfying, even among shirkers, and the group can become highly cohesive. As indicated in Figure 3, relational control then quickly approaches unity, which means that approval is exchanged strictly for approval, without regard to compliance. However, below β = 0.15, the value of approval is still only high enough to reward shirkers but not enough to compensate the cost of effort by workers. Hence, the propensities of both decline, as is evident in Figure 3. (Shirkers might say to themselves, “Well, hardly anyone is working, and I am popular with the other shirkers, so why not free-ride like the rest?” Workers might mutter, “Well, hardly anyone is working except me, and yet I am no more popular than the shirkers, so why bother?”) When β is above 0.15, strong social rewards now cause both workers and shirkers to feel satisfied with their work decisions. The group develops a permanent division of labor between workers and shirkers, and everyone enjoys widespread approval, regardless of work effort. As β approaches 1, although shirkers are slightly more satisfied than workers (since they do not pay c), the difference is overwhelmed by the value of approval. (Workers might now say, “I really don’t mind working; all that really matters to me is feeling a part of the group.”) The higher the value placed on approval, the smaller the relative impact of c, and the closer the equilibrium compliance to 0.5. Thus the tipping point corresponds to the cost of effort. As the cost increases, the tipping point can be expected to rise. These simulation results suggest that, contrary to Homans, higher levels of compliance in the region beyond the tipping point are not caused by compliant control. Above the tipping point, relational control becomes universal (raa ≈ 1), driving out compliant control. This means that compliance increased as a byproduct of the bilateral exchange of approval, and not because of the exchange of compliance for approval, as Homans assumed. The result reveals a clear contradiction between the predictions of the forward-looking model and the backward-looking. The forward-looking model implies that dependence on peer approval never undermines workers’ willingness to invest effort, and, moreover, even facilitates compliance in a large region of the parameter space. By contrast, the backward-looking suggests that higher dependence on peer approval may boost relational control and thus undermine peer pressure to work. The forward-looking model confirmed the expectation that company towns may be an effective instrument to solve free rider problems in the workforce. The backward-looking questions that expectation and suggests, to the contrary, that
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Andreas Flache, Michael W. Macy, Werner Raub
this instrument may even backfire against the firms’ interest. Workers in company towns may be so dependent on one another for friendship that they become unwilling to use friendship as an instrument to compel their friends to comply with company norms.
6 Discussion Coleman (1979; 1994) proposed that rational choice theory is an appropriate analytical tool to analyze how formal institutional design shapes, directs and interacts with informal processes in an organization. Our research reveals a potential danger in his research agenda. Substantively important propositions about the interplay of formal and informal mechanisms that follow from the theory may be highly sensitive to how exactly theorists specify the central assumption of goal-directed decision making. Rational choice theorists tends to neglect the problem. They often assume that the micro model of perfectly rational utility maximization captures the macro regularities that arise from the boundedly rational decision heuristics that “real actors” apply. In effect, they assume that departures from perfect rationality at the individual level “cancel out” in the aggregate. We believe that this optimism is unwarranted. To demonstrate the potential sensitivity of theoretical propositions, we provided a stylized analysis of an example discussed by Coleman, the effect of company towns on workers’ compliance with production norms. For simplicity, we assumed that it is workers’ common interest to maximize firm production. Firm performance then is a collective good that is threatened by individual incentives to free-ride. In this situation, company towns may foster workers’ compliance, because they increase workers’ dependence on social ties with colleagues. This, in turn, may facilitate informal social control. To test the intuition, we employed an exchange theoretical perspective on informal control proposed by Homans (1974). Homans viewed peer pressure as an exchange process where group members trade social approval for others’ compliance with collective obligations. However, this perspective is inconclusive with respect to the effect of company towns on workers’ compliance. On one hand, higher dependence on peer approval may increase the effectiveness of peer pressure as an instrument to enforce compliance. On the other hand, dependence on peer approval may foster strong friendship relations between workers. These relations may then undermine social control, because workers exchange approval for approval rather than approval for compliance.
Do company towns solve free rider problems?
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To clarify implications of Homans’ exchange perspective, we used formal modeling. In a first step, we employed an orthodox “forward-looking” rational choice analysis, drawing on non-cooperative game theory. For comparison, we then applied a “backward-looking” model based on social learning theory. The two models are identical in their assumptions about the decision problem actors face. However, the models are distinct in how individuals are assumed to optimize behavior. The forward-looking model assumes that actors rationally anticipate each others’ rational behavior. The backward-looking model assumes that individuals do not try to anticipate effects of their decisions. Instead, they optimize “on the fly,” driven by a simple trial and error mechanism. Comparison of model results shows that, contrary to the widespread optimism of rational choice theorists, the results are indeed sensitive to variation in the underlying decision model. The forward-looking analysis implied that rational actors are not distracted from social control by strong friendship relations. Instead, under a large range of conditions, actors are capable of solving the relatively complicated cooperation problem posed by simultaneous exchanges of approval and compliance. Accordingly, the forward-looking analysis confirms the intuition that higher dependence on peer rewards in company towns may facilitate cooperation between workers. By contrast, the backward-looking analysis based on the learning model suggests that dependence on peer approval may undermine the effectiveness of informal control. Workers may get trapped in satisfactory exchanges of approval for approval, even when simultaneous exchanges of approval and compliance are more rewarding. The reason is the limited capacity of adaptive actors to solve the coordination problem created by the multilateral exchange of approval and compliance. Actors easily learn to build strong friendship relations based on mutual approval, a lesson that blocks their interest in further improvement of payoffs. From a learning-theoretic perspective, company towns may exacerbate the workers’ cooperation problem rather than sustain informal control. Careful attention to the potential limitations of our study is required to assess whether theorists should be concerned by the possibility of model sensitivity. Two restrictions of our analysis might limit generalizability. First, we inspected only one particular stylized example of social interaction and exchange, namely compliance and approval exchange among members of a team. Second, we compared the orthodox rational choice assumption of perfect rationality to only one particular alternative, stochastic learning. Despite these restrictions, we believe that sensitivity to micro assumptions needs to be taken
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Andreas Flache, Michael W. Macy, Werner Raub
into account for a wider range of applications. To support this claim, we discuss the restrictions in turn. In our analysis, only the backward-looking model assumed that actors might get trapped in Pareto inferior bilateral exchanges that undermine multilateral exchange. This conflict between bilateral relations and collective exchanges may occur not only in the particular example of company towns, but also in a variety of other organizational situations. All these situations may confront analysts with potential model sensitivity. For example, in research teams, a “communication dilemma” (Bonacich 1992) may arise, when status gains or bonus payments reward exceptional individual performance. The team as a whole may benefit when all members share their knowledge with the group. At the same time, individuals face incentives to collude in dyadic exchanges or small cliques. Whether members trade knowledge multilaterally or bilaterally, the exchanges require cooperation between participants. However, team performance may suffer because cooperation in collusive bilateral exchanges may be more easily attained. As a consequence, members may be distracted from the Pareto superior solution of sharing knowledge with the group as a whole. A similar problem may arise between subdivisions of an organization. Organizational efficiency may be maximized when all department heads are willing to contribute personnel and services whenever a particular division comes under pressure. However, in a competitive environment this requires a high level of trust that a subdivision will receive some form of reciprocation in the future. Again, trust and reciprocity may develop more easily in dyadic support relations between divisions, precluding multilateral exchanges even when the latter are more efficient. Other models besides the stochastic learning model may challenge the orthodox rational choice analysis. A combination of the forward-looking analysis with assumptions of bounded rationality may yield the same qualitative results as generated by the simulations based on the backward-looking. For example, bounded rationality may be modeled with the assumption that individual actors may occasionally fail to contribute to the collective task or to approve of their peers due to “idiosyncratic disturbances” (Bendor and Mookherjee 1987; cf. Green and Porter 1984). “Erroneous” defections may then reduce efficiency of exchanges, because conditionally cooperative strategies need to impose at least some retaliation in order to credibly deter free riders. However, multilateral exchanges tend to suffer more from idiosyncratic disturbances as compared to bilateral exchanges, because the probability that an error occurs increases with the number of participants. As a consequence, in a noisy environment, bilateral exchanges of approval may no longer be payoff dominated by the simultaneous exchange of approval and compliance.
Do company towns solve free rider problems?
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Increasing dependence on peer approval then makes bilateral approval even more attractive as compared to the fragile multilateral exchange. Less technically, a forward-looking analysis based on bounded rationality may predict that company towns undermine peer pressure rather than foster cooperation between workers. Again, this suggests that results derived from the orthodox perfect rationality approach are highly sensitive. Finally, previous work of Flache (1996, Chapter 5) showed that the prediction of a possible social trap from bilateral exchange not only conflicts with perfect rationality, but is also supported by empirical evidence. Flache translated the exchange theoretical framework into a laboratory game representing the situation of a work team. In this game, subjects’ scores emerged from their own and others’ decisions whether 1) to invest in “work” and 2) to invest in “approval of a colleague”. “Work” was a contribution to the collective welfare (group wage), while “approval” constituted a contribution to the colleague’s personal welfare. The experiment confirmed that bilateral exchanges may undermine compliant control. Flache compared two conditions. In one condition, bilateral exchanges of approval were feasible. In the other condition, feedback on others’ decisions was restricted so that only multilateral exchanges involving compliance could arise. More precisely, subjects only learned how many approvals they received, but not who in the group approved of them. As expected, subjects’ tendency to reward compliance with approval, compliant control, dropped significantly when bilateral exchanges were allowed (184). Accordingly, in this condition compliance was lower and declined faster than without bilateral exchanges (169-179). Our study demonstrated that rational choice analyses of organizations may be highly sensitive to varying specifications of goal-directed decision making.6 This sensitivity to the specification of the underlying “model of man” is ironic, given Homans’ (e.g., 1974) celebrated claim that the theoretical assumptions of rational behavior can be derived from more basic assumptions of learning and reinforcement. Obviously, the solution of this problem is not to replace the assumption of perfect rationality with a highly complex “realistic” model of decision making. The analysis of collective phenomena requires a simple model of action in order to concentrate on the effects of “social organizational” 6
See Voss (1990, Chapter 4) for more general arguments that for strategic situations with interdependence between actors implications of rational choice models can be expected to be sensitive to different specifications of goal-directed decision making like perfectly versus boundedly rational behavior. Raub and Snijders (1997) show that such sensitivity can be expected for strategic situations even if the assumption of perfect rationality is kept constant and only other micro-assumptions, such as assumptions on the actors’ preferences, more precisely, their risk-preferences, are varied.
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components (Coleman 1990, 13-21). The problem can be solved, we believe, when research strategies are employed that both retain parsimony and explore sensitivity. For example, analyses may benefit when they approach one and the same regularity of interest from two different angles. Initial analyses may employ an orthodox model of perfect rationality and compare it to an equally simple analysis based on a learning model. This strategy has the advantage of retaining model parsimony for the first analytical step, while the simultaneous use of both models limits the possibility that phenomena of interest escape the attention of the analyst. Moreover, the comparison of radically different models of action may test the robustness of results against variation in behavioral assumptions. When it turns out that model implications converge across different specifications of the decision process, we may be confident that one of the two simplified models of action suffices for the task at hand. If, on the other hand, model predictions diverge, this is clearly an indication that investments in a more complex model may improve analytical power.
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—, 1993. “Social Learning and the Structure of Collective Action.” Pp. 1-35 in Advances in Group Processes 10, edited by E. Lawler et al. Greenwich, CN: JAI Press. Olson, M. 1965. The Logic of Collective Action. Cambridge, MA: Harvard University Press. Raub, W. 1988. “Problematic Social Situations and the Large Number Dilemma.” Journal of Mathematical Sociology 13:311-357. —, and J. Weesie. 1990. “Reputation and Efficiency in Social Interaction: an Example of Network Effects.” American Journal of Sociology 96:626-654. —, and C. Snijders, 1997. “Gains, Losses, and Cooperation in Social Dilemmas and Collective Action: The Effects of Risk Preferences.” Journal of Mathematical Sociology 22: 263-302. Selten, R. 1965. “Spieltheoretische Behandlung eines Oligopolmodells mit Nachfrageträgheit.” Zeitschrift für die gesamte Staatswissenschaft 121:301324, 667-689. Simon, H.A. 1982. “A Behavioral Model of Rational Choice.” Pp. 239-258 in Models of Bounded Rationality: Behavioral Economics and Business Organization 2. Cambridge, MA: MIT Press. Skyrms, B. 1996. The Evolution of the Social Contract. Cambridge: Cambridge University Press. Stinchcombe 1968. Constructing Social Theories. New York: Harcourt Brace and World. Taylor, M. 1987. The Possibility of Cooperation. Cambridge: Cambridge University Press. Voss, T. 1985. Rationale Akteure und Soziale Institutionen. München: Oldenbourg. — 1990. Eine Individualistische Theorie der Evolution von Regeln und einige Anwendungsmöglichkeiten in der Organisationsforschung. München: Sozialwissenschaftliche Fakultät der Universität München (Habilitation). Wippler, R., S. Lindenberg. 1987. “Collective Phenomena and Rational Choice.” Pp. 135-152 in The Micro-Macro Link edited by Alexander, J.C. et al. Berkeley, CA: University of California Press.
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Andreas Flache, Michael W. Macy, Werner Raub
Appendix Proof of Theorem 2 Equation (2) yields the following terms for the utilities actor i achieves by unilateral deviation from a cooperative outcome, φiC , φiCA and φiA , for the utilities of universal cooperation for i, uiC , uiCA and uiA , and, finally, for the utility i derives from the full defection outcome, uiD :
φ Ci = α −
α N
,
= α + β ( N − 1) − φ CA i
α N
,
φ iA = β ( N − 1), C i
u
(A1)
= α − c,
= α + β ( N − 1) − c − c ′ ( N − 1 ), uCA i A ui = ( β − c ′ )( N − 1), uiD
= 0..
Substituting these terms into the condition for the individual rationality of trigger strategy equilibria in Theorem 1 yields the following threshold values for the individual discount parameters τ C , τ CA , τ A :
φ C − uCi τ C = iC φ i − uiD
τ CA
φ CA − uCA i = i CA φ i − uiD
=
=
c−
α−
c + c ′( N − 1) −
α + β ( N − 1) −
φ A − uiA τ A = iA φ i − uiD
=
α N ,
α
(A2)
N
α
N ,
α
N c′
β
,
(A3)
(A4)
Do company towns solve free rider problems?
37
After substitution of the threshold values by the r.h.s. of Equations (A3) and (A4), the condition τ A < τ CA can be simplified as follows: c + c ′( N − 1) −
α + β ( N − 1) −
α
c′
N
0 .
(A11)
Analogously, p ′ equals the probability 1− τ CA for the cohesion-compliance outcome if τ CA ≤ τ A . Equation (A10) above shows that the corresponding term for the probability of high cohesion, 1− τ CA entails a partial derivative − ∂τ CA ∂β that is larger than zero. In combination, the equations (A9), (A10) and (A11) yield the conditions for the partial derivatives of p and p ′ by β in Corollary 1. Q.E.D.
