The compliance you need for a cost you can afford: How to use individual and collective sanctions?

Social

Science RESEARCH

Social Science Research 31 (2002) 630–652

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The compliance you need for a cost you can afford: How to use individual and collective sanctions? q Joseph M. Whitmeyer

*

Department of Sociology, University of North Carolina, Charlotte, NC 28223, USA

Abstract In many naturally occurring situations, actors (agents) use individual sanctions or collective sanctions or both to obtain compliance from members of a group. Individual sanctions are sanctions applied to each individual based on that individualÕs perceived behavior; collective sanctions are sanctions to all group members based on perceived behavior by some group members. Often, there are constraints on the amount of sanctions an agent may use. I use HeckathornÕs (1990) sequential decision model of group-mediated social control to analyze the power of an agent concerning compliance by group members under such constraints. Results show that whether positive or negative sanctions are considered, the amount of group compliance is an increasing but non-linear step function of the looseness of the constraints. Moreover, it appears that the most cost-effective use of power entails using only collective sanctions when lower levels of compliance are sought, only individual sanctions when higher levels of compliance are sought, and never mixing the two. Ó 2002 Elsevier Science (USA). All rights reserved.

q I thank Douglas Heckathorn, Rosemary Hopcroft, Satoshi Kanazawa, Tatsuya Kameda, Alan Miller, Murray Webster, Toshio Yamagishi, and anonymous reviewers for useful comments and suggestions. * Fax: +704-547-3091. E-mail address: [email protected].

0049-089X/02/$ - see front matter Ó 2002 Elsevier Science (USA). All rights reserved. PII: S 0 0 4 9 - 0 8 9 X ( 0 2 ) 0 0 0 1 7 - 0

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1. Introduction In Japan, some years ago, a high school soccer team won the national high school championship. At the celebration party, many members of the team illegally drank beer. In response, rather than punishing the errant team members or even the entire team, educational authorities banned the school from national sports events for two years. In Japan, this is a typical sanction for such situations: for the transgressions of a few members, the entire group is punished rather than just the transgressors (Miller and Kanazawa, 2000). This type of sanctioning occurs in the US as well, although perhaps less commonly. My sonÕs fourth-grade teacher often kept the entire class inside for recess when a few in the class acted up. The use of sanctions, positive (rewards) and negative (punishments), in social control has long been of interest in sociology (e.g., Coleman, 1990; Durkheim, 1982 [1907]; Gibbs, 1975; Hechter, 1987; Heckathorn, 1990). Typically, analyses of effects of sanctions have focused on individual sanctions, which are rewards or punishments applied to each individual based on that individualÕs perceived behavior. However, Heckathorn (1990) argues that we should also consider collective sanctions, which are punishments or rewards applied to a group based on the perceived behavior of one or more of its members. The two examples above are of collective sanctions. As I discuss below, there are many naturally occurring situations in which actors—whom I call agents, following Heckathorn (1990)—use individual or collective sanctions or a combination of both to obtain compliance from others. Some theorists (e.g., Coleman, 1990; Hechter, 1987; Heckathorn, 1990; Kanazawa, 1997) have analyzed formally some aspects of this process. However, many important questions have not been addressed in any systematic, analytic way. In this study, I begin to look at some of those questions. I address two questions in particular. First, I look at whether it is better to use individual sanctions, collective sanctions, or some combination of the two, and under what circumstances. Second, I investigate the effectiveness of individual and collective sanctions under limitations that are frequently present in such situations. Specifically, I look at how much compliance an agent can obtain given constraints on the agentÕs budget (if positive sanctions are applied) or on how much punishment can be applied to a given individual (if negative sanctions are applied). These are questions of both sociological and practical importance. The level of compliance is likely to be important for the outcomes in social phenomena as diverse as education, collective action, and organizations and for social order generally. In many if not all of these phenomena, sanctions, positive or negative, are an important tool of obtaining compliance. Moreover, typically there are constraints on the use of those sanctions. In this study, I

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extend HeckathornÕs (1990) simulation method to address those questions analytically.

2. Background 2.1. Collective sanctions The study of social control—how and how effectively some actors obtain compliance on the part of other actors—has tended to focus on direct effects on individuals and to ignore mediating effects of the group context for individuals (Gibbs, 1975; Heckathorn, 1990). However, in many situations, an agent may use collective sanctions instead of or in addition to individual sanctions to obtain compliance from others. Some uses of collective sanctions have been recognized and analyzed as such in some scholarly literature. Many have not. Here, I discuss some areas of social control where collective sanctions are used. One such area is classroom management in education. Schoolteachers may use individual sanctions; they may reward or punish each individual student according to that studentÕs perceived behavior. However, they also may use collective sanctions. They may punish an entire class for the misbehavior of one or a few class members, reward the entire class for the improved behavior of one or a few class members, or give the whole class a reward if and only if every student or nearly every student cooperates in some way. Use of collective sanctions in the classroom has been advocated by professional educators and studied extensively. For example, a textbook on managing problem behaviors in the classroom summarizes numerous studies showing effective use of what it calls ‘‘interdependent group-oriented contingencies.’’ This is a practice in which ‘‘consequences are applied to the group contingent upon each member reaching a specified level of performance’’ (Kerr and Nelson, 1998, p. 169)—clearly a use of collective sanctions, as defined here. Sanctions include contingent recess time and privileges such as being able to listen to popular music or extra gym or break time. The textbook recommends using positive rather than negative sanctions to avoid creating ‘‘negative peer pressure’’ (Kerr and Nelson, 1998, p. 211). Another book on classroom management explicitly discusses the choice between collective and individual sanctions in terms of cost, my concern in this study. ‘‘The ultimate limitation for the use of any incentive system in the classroom is cost.’’ Based on that criterion, it concludes, ‘‘Our incentive systems will have to be group incentive systems rather than a collection of individual incentive systems’’ (Jones, 1987, p. 154). For the sanctions, it recommends time spent on preferred activities.

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Thus, the classroom management literature raises issues of individual versus collective sanctions and the relevance of cost. However, it does not consider a number of important, logically ensuing questions. These include whether to mix individual and collective sanctions and if so in what proportions; and whether the choice between individual and collective sanctions, or their mix, depends on the total amount of compliance desired. Another area where collective sanctions are used is in organizations and the workplace. Bosses may respond to misuse of resources such as telephones and photocopiers, or even to pilfering, through punitive restrictions on all employees, instead of or in addition to punishment of particular miscreants. Likewise, they may reward entire groups for exceptional achievements of a few group members or for the combined achievement of the group. There is little explicit discussion of use of collective sanctions in the literature on social control in organizations and work (see, e.g., Simpson, 1985). However, more substantively focused studies often reveal their use. For example, case studies suggest that use of collective sanctions in addition to or lieu of individual sanctions is a standard tool of modern business management in the US (see, e.g., Collins and Porras, 1994). Rational choice scholars studying in Japan have explicitly recognized the importance of collective sanctions in business management there (Hechter and Kanazawa, 1993; Miller and Kanazawa, 2000). Here again, the implication is that collective sanctions can be a cheap, effective means of obtaining compliance, but more specific analysis of when and how to mix individual and collective sanctions is lacking. Intentional groups such as cults and communes are yet another area where collective sanctions are used. Leaders of intentional groups may produce group solidarity through direct sanctions to non-complying members but also through sanctions to the group based on the compliance of members. Hechter (1990) analyzes the mechanisms of how collective sanctions work, but again does not analyze precisely the effectiveness of individual and collective sanctions. Historical literature shows that governments have frequently used collective sanctions as means of social control over members of the societies they rule. Rulers have often levied taxes and tribute at the community level, punishing a community as a whole if it does not yield the stipulated amount for the community. That is common throughout the history of Russia, an aspect of the practice of what Hosking (2001) calls ‘‘joint responsibility.’’ The British also followed similar practices in much of colonial India, although in places their use predates British rule (Ludden, 1985; Marriott, 1955; Stokes, 1978). Rulers have used collective sanctions for more than just obtaining revenue. For much of Russian history, Russian rulers used collective sanctions to deal with crime in rural communities. Communities had to investigate serious crimes themselves and hand over the criminal or else

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they had to pay a collective fine (Hosking, 2001). Similar practices have been followed by Mexican governments with regard to crime in indigenous communities in Mexico (Nader, 1990). During StalinÕs regime, the Soviet secret police (NKVD) obtained work out of inmates of labor camps they ran using collective sanctions. If a work-gang did not meet its output norm, all work-gang members received reduced food rations (meaning an inadequate diet). In the 1960s, Soviet authorities would punish an entire intellectual institute, if even one of its members signed a protest letter (Hosking, 2001). Those historical examples—and there are many more—illustrate widespread use of collective sanctions. This suggests that both collective and individual sanctions are seen as effective tools for obtaining compliance, at least under some circumstances. Finally, studies of social capital have noted the availability of collective sanctions as a type of social capital that can be used for rule enforcement. Portes (1998) cites Zhou and BankstonÕs (1996) study of the Vietnamese community of New Orleans as an example. The community sanctions a family for the transgression of a family member. Here, the community as a whole constitutes the agent seeking compliance from members of families (who are also community members). Petee et al. (1994) find similarly that high levels of integration within a group, which make collective sanctions more effective, negatively affect deviance. 2.2. Social control and power As work cited above makes it clear, we know that agents use collective as well as individual sanctions to obtain compliance, with at least some effectiveness. Some theorists, notably Hechter (1987) and Heckathorn (1990), have analyzed some aspects of this system formally. For example, Heckathorn (1990) includes the possibility of social control through collective sanctions in his simulation analysis of sanctions and social control. Recall that my purposes here are to investigate how best to combine individual and collective sanctions, and to investigate the effectiveness of individual and collective sanctions as a function of limitations present in the situation. Answers to especially the second of these questions will be most valuable if conceptualized in ways that facilitate comparison with other processes of obtaining compliance and cooperation. For that, I turn to concepts of control and power. The most recent comprehensive theoretical examination of the concept of control is by Gibbs (1989, 1994). Gibbs defines control, or attempted control, as a behavior. Thus, if an agent administers sanctions in an attempt to obtain compliance, we have an example of attempted control. Using individual sanctions would qualify as proximate control. Gibbs does not discuss collective sanctions explicitly and it is less clear how he would

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classify their use. It seems most likely that he would put their use under sequential control, with the agent essentially telling the group what the agent wants group members to do, and the group then passing that along to group members. It seems less likely that their use would fit social control as Gibbs defines it, which involves a third party ‘‘but not in the way of sequential control’’ (Gibbs, 1994, p. 51). Note that Gibbs defines (attempted) control as a behavior, whereas what I investigate here is an ability—the ability to affect group compliance—and how that ability is affected by levels and allocation of sanctions. I do not consider or attempt to predict the extent to which an agent will use that ability. Hence, I have nothing to say directly about control or attempted control directly. In line with my use here, Gibbs defines the ability related to control as ‘‘power,’’ although he adds a perceptual character, defining power as ‘‘perceived ability’’ (Gibbs, 1994, p. 59). I avoid this perceptual element (see below). Nevertheless, there is a clear relationship between power and control, as Gibbs suggests. Namely, an agent has a certain amount of power, conferred by the situation. The agent uses that power to a certain extent. That use, in turn, yields a certain amount of control, measurable by the amount of group compliance. In the social sciences, the concept of social power has been defined and used in myriad ways. In this study, I follow Whitmeyer (2000, 2001), who not only provides a definition but also numerical measures for social power (and power use, a distinct concept). Those numerical measures can be easily applied to the quantitative results of the simulations in this study. Whitmeyer (2000, 2001) differentiates social power (henceforth just ‘‘power’’) and power use. Power is the ‘‘ability to affect some social phenomena.’’ It must have a referent, namely, the social phenomena being affected, for example, ‘‘power concerning salary levels at company X,’’ ‘‘power concerning political beliefs of own children,’’ or ‘‘power concerning group compliance.’’ Power use is the extent to which power holders use their powers to bring about some specified outcome. Returning to the concept of control, we can take the amount of control to be the effect of combining a certain amount of power with a certain amount of power use. In this study, I do not need the concept of power use, since I am concerned with what agents can do with available sanctions, not what they will or do do. As a measurable quantity, power P is the proportion of the possible total change in the referent phenomena that we expect that the power holder could bring about. The word ‘‘expect’’ means that we must take into consideration possible events and likely responses to actions of the power holder. The word ‘‘could’’ means that we are evaluating an ability, not expectation or prediction of behavior.

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Formally, we may express the measure of power as   maximum DQ actor can cause P ¼E ; total DQ possible

ð1Þ

where Q denotes the outcome of the referent phenomenon, DQ denotes the change in the outcome of the referent phenomenon, and E denotes the expected value function of probability theory. When we evaluate the expected value (the operator E), we should take into consideration what all actors except the power holder and all other elements in the situation are likely to do. In its probabilistic sense, when computing the expected value, we should weigh outcomes by the probability that they occur. Two important properties of P are that 0 6 P 6 1 and that powers (Ps) of those who hold power concerning a given social phenomena typically will not sum to 1. For a given power holder, P ¼ 0 denotes complete inability to affect the social phenomenon in question when all circumstances are as expected. P ¼ 1 denotes the ability to produce all extremes of the outcome, again given what we would expect from surrounding circumstances including behavior of other actors. For some purposes, it may be desirable to have a measure of relative power, such that all power holdersÕ powers sum to 1. This measure may be obtained by summing the powers (Ps) of all power holders and then dividing each power holderÕs power by that sum. 2.3. Heckathorn’s model Heckathorn (1990) mathematically analyzes a scenario in which an actor can use individual and collective sanctions, separately or in combination, to get compliance out of members of a group. In HeckathornÕs scenario, collective sanctions work by getting the group to produce compliance internally. Hechter (1987) in his theory of group solidarity treats a very similar situation, although less mathematically. In the situation Hechter considers, the agent seeking group compliance may be the leadership of the group in question or even the group itself. Although both Heckathorn (1990) and Hechter (1987) recognize the power of the agent seeking group compliance, neither gives us a full, formal analysis of that power. In the situation analyzed by Heckathorn (1990), the agent is exercising power concerning group compliance in part through direct exchange and in part indirectly, by using exchange to get group members to get each other to comply. Group members get compliance from each other by removing the opportunity for non-compliance. However, the power of the agent is not the focus of HeckathornÕs analysis. He does not address the question of the maximum amount of compliance the agent can obtain nor what the agent needs to do to realize that maximum. His simulation model focuses on how different values of a number of important parameters affect the amount of group compliance. Later work (Heckathorn,

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1993, 1996) drops the idea of the agent (except in the form of the entire group) entirely, using the model to examine how group membersÕ sanctions of each other affect collective action. Nevertheless, HeckathornÕs simulation model is a useful method for analyzing an agentÕs power through use of individual and collective sanctions as a function of cost to the agent. Assumptions of the model reflect conditions of natural situations, albeit greatly simplified. The modelÕs output is the amount of compliance, which allows determination of the agentÕs power concerning group compliance. In short, with the model we can analyze an agentÕs ability to get compliance from group members, when the agent can take advantage of group membersÕ control over each other. In the situation modeled, the agent can affect compliance through its control over two factors, individual and collective sanctions. The agent applies individual sanctions to each group member, based on whether the agent detects non-compliance on the part of the individual group member or not. The agent applies collective sanctions identically to all group members, based on whether the agent detects non-compliance by any group member or not. Collective sanctions thus provide incentive for group members to get each other to comply. In HeckathornÕs model, they do this by removing the opportunity for others not to comply with a certain efficacy that is a parameter of the model. Other model parameters are characteristics of the situation much less under an agentÕs control. Hence, they are taken as given, interesting to the extent that they affect the agentÕs power over group compliance. These parameters are the efficacy of the agentÕs monitoring, the efficacy of control of group members over each other, the cost of compliance for individual group members, and costs of sanctioning other group members. With the model, I can analyze two questions concerning the agentÕs power. First, what gives the agent maximal power, that is, under what combination of individual and collective sanctions can the agent obtain maximum compliance for minimal cost? Second, how do certain constraints on use of sanctions affect the agentÕs power? According to HeckathornÕs model, as collective and individual sanctions rise, eventually group compliance rises to 100%, except under trivial conditions. Complete compliance means total power ðP ¼ 1Þ concerning group compliance. However, there may be constraints on the agentÕs use of sanctions, which, thus, limits the agentÕs power. Put differently, it is likely that the agentÕs ability to obtain group compliance is a function of constraints on its use of individual and collective sanctions. This leads to the two questions I consider. As Heckathorn (1990) notes, under the assumption of rational actors, that is, the assumption that each actor will choose the behavior that maximizes its expected payoff, the model works identically and produces identical outcomes, whether sanctions are taken to be negative or positive. When sanctions are taken to be positive, the agent confers the individual sanction

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on each group member whom the agent does not detect not complying. The agent confers the collective sanction on each group member if the agent fails to detect non-compliance by any member of the group. When sanctions are taken to be negative, the agent applies the individual sanction to each group member whom the agent detects not complying. The agent applies the collective sanction to each group member if the agent detects non-compliance by any member of the group. However, constraints on use of sanctions are likely to be different, depending on whether they are positive or negative. Thus, we need to analyze these separately. When sanctions are positive, if sanctions are material (rather than symbolic), each sanction used is a cost to the agent. Thus, the most likely constraint on the agent is budgetary, that is, a limit to total cost. The limit may stem from a limit to the agentÕs resources or it may be imposed externally on the agent, for example, by law or the agentÕs boss. It may even be a self-imposed limit due to opportunity costs, that is, payoffs yielded by alternative uses of resources. When sanctions are negative, such as fines or physical punishments, a likelier constraint is a limit to the amount of sanctions an individual group member can bear.1 Such constraints may stem from characteristics of the group member or again they may be imposed externally, for example, by law or agents to the agent. They also may be a function of the group memberÕs situation, such as the memberÕs dependence on the group (Hechter, 1987). Oliver (1980) presents an insightful comparison of positive and negative sanctions, relevant to issues here. She discusses why positive sanctions may be less costly if low levels of cooperation are needed, while negative sanctions may be less costly if virtually complete cooperation is needed. Negative sanctions are frequently cheaper for an agent than positive sanctions. (Moreover, considerable research has shown that actors respond more strongly to negative sanctions than to nominally equivalent positive sanctions (Molm, 1997).) However, negative sanctions have an additional disadvantage in that they may arouse hostility and resistance, which would work against obtaining cooperation (see also Molm, 1997). Finally, in the case of near-universal cooperation, use of positive sanctions by the agent can seem like use of negative sanctions to the actors affected. Since virtually everyone receives the positive sanction, failing to receive it feels like punishment. In this study, to focus on the two questions above, and due to limitations of the simulation model used, I do not address differences between positive and negative sanctions. I also do not allow the agent to combine positive and negative sanctions. I treat use of positive sanctions and use of negative sanctions simply as two different scenarios, which need to be considered

1 Costs, including opportunity costs, of applying negative sanctions may also constrain an agentÕs use of such sanctions. Which constraints are paramount will depend on the situation.

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separately because of the possibility that the interplay between collective and individual sanctions may differ between them. The only comparison I make between use of positive sanctions and use of negative sanctions concerns that possibility. In other words, I look at whether the answer to the first question above, concerning how best to combine individual and collective sanctions, differs between the two scenarios. I therefore set aside other important comparisons between use of positive sanctions and use of negative sanctions. As Oliver (1980) points out, positive and negative sanctions may differ in their cost-effectiveness for agents (see also Molm, 1997). In addition, authorities may restrict especially use of negative sanctions or agents may dislike one or the other on moral grounds, as, for example, when educators think that negative collective sanctions cause negative peer pressure (Kerr and Nelson, 1998). Molm (1997) found that actorsÕ use of sanctions differed depending on whether sanctions were positive or negative. These issues deserve further analysis, but that will require a model considerably different from that used here.

3. The model With one small alteration, I use HeckathornÕs (1990) simulation model of group compliance here. Accordingly, I describe it only briefly, referring readers to a more full description in Heckathorn (1990). The model is a sequential decision model. N group members take turns choosing between six possible behaviors; they choose the behavior that yields the highest expected payoff. The six behaviors (see Table 1) are combinations of complying or not, exercising compliant control (trying to get others to comply) or not, and exercising oppositional control (trying to get others not to exercise compliant control). Of the eight possible combinations, two are not considered because they are internally contradictory— namely, those in which an actor exercises both compliant control and Table 1 Six behavioral choices for each group member Behavior

Comply with agent (level 1)

Exert compliant control (level 2)

Exert oppositional control (level 3)

cc cd co dc dd do

C C C D D D

C D D C D D

D D C D D C

C denotes cooperate (comply or exert control); D denotes defect (do not comply or exert control).

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oppositional control. The only divergence of the model used here from that of Heckathorn (1990) is that my version does not allow a group member to exercise compliant control over itself, which HeckathornÕs (1990, but not 1993 or 1996) does. This alteration affects outcomes only to a small extent and causes no qualitative differences in outcomes. In addition to N, remaining parameters of the model are precisely the factors that go into a group memberÕs decision. These are: Si , the strength of the individual sanction; Sc , the strength of the collective sanction; M, the probability that the agent monitors any particular actorÕs non-compliance; K1 , the cost to an actor of compliance; K2 , the cost to the actor of exercising compliant control; K3 , the cost to an actor of exercising oppositional control; E2 , the efficacy of compliant control; and E3 , the efficacy of oppositional control. Efficacy E, of the final two parameters, is defined as the proportional diminution in a targeted actorÕs ability to perform the action in question. The agent outcome of the sequential decision model is group compliance (number of members complying). Starting from an initial condition of full non-compliance, with group size N ¼ 10, the model reaches equilibrium within 20 decisions, that is, 2 decisions by each actor. Equilibrium is a state where group compliance fluctuates little or not at all. This equilibrium is stable (Heckathorn, 1990). It may be noted that the decision-making process is fairly robust. When HeckathornÕs (1990) original rule of sequential decision-making is changed to one of random assignment of decision-making, equilibrium compliance remains the same more than 99.5% of the time. Specifically, that holds for a 10-member group, varying parameters over their feasible or reasonable ranges. Natural situations undoubtedly do not feature sequential decisionmaking, with group members taking turns deciding what to do. However, since the decision-making process is robust, it makes practical sense to continue with sequential decision-making in the simulation. In particular, sequential decision-making simplifies and shortens the simulation, and makes outcomes more transparent. Again, as Heckathorn (1990) notes, it makes no difference to model outcomes whether sanctions are positive or negative. Differences in effects of positive and negative sanctions (Molm, 1997; Oliver, 1980) would matter only if the model allowed concurrent use of positive and negative sanctions, which it does not. Positive sanctions are rewards for compliance. Thus, Si is what a target actor receives from the agent if the agent fails to detect noncompliance by the actor and Sc is what each group member receives if the agent fails to detect non-compliance by any group member. The agentÕs cost C is then the expected total amount of sanctions the agent pays out C ¼ ½N  MðN  GÞSi þ N ð1  MÞN G Sc ;

ð2Þ

where G is the expected amount of group compliance (number of compliers).

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Let me explain Eq. (2). The first component of C is the cost from paying out individual sanctions. It is the individual sanction (Si ) multiplied by the number of individuals whom the agent does not detect not complying, i.e., whom the agent thinks are complying. There are N  G non-compliers; the agent therefore detects MðN  GÞ non-compliers, so the agent thinks there are N  MðN  GÞ compliers. The second component of C is the cost from paying out collective sanctions. Collective sanctions are paid out only if the agent detects no non-compliance, and in that case, they are paid to each of the N group members. Thus, the expected cost from collective sanctions is the product of the probability that the agent thinks all members are complying, the number of group members (N), and the collective sanction (Sc ). The chance that the agent thinks a non-complier actually is complying is 1  M. The number of non-compliers is N  G. Therefore, the chance that the agent thinks all of the non-compliers actually are complying, and therefore that there is no non-compliance in the group, is the product of the chance for each non-complier or ð1  MÞN G : When sanctions are positive, we are interested in the maximum amount of group compliance the agent can obtain given a limit to the cost C. We are also interested in what combination of individual and collective sanctions enables the agent to obtain a given level of group compliance for minimal cost. Now suppose sanctions are negative, say, fines for non-compliance. Then, Si is what the agent fines a target actor if the agent detects non-compliance by the actor and Sc is what the agent fines each group member if the agent detects non-compliance by any group member. Here, there is a possible scenario under which a limit to C would still be important. Namely, assume that the agent has some uniform maximum amount it can tax group members. Every case of apparent compliance will then result in revenue loss for the agent. Si will be lost for each individual who appears to comply and Sc will be lost if it appears the entire group is complying. Then, cost to the agent C, still given by Eq. (2), can be seen as fines foregone. A fining procedure, thus, amounts to reducing the income the agent can obtain from group members by making some of that income contingent on non-compliance. Such a reduction in income, or cost C, may be constrained by the agentÕs superior or by law. However, as discussed above, it is much more likely that for negative sanctions the important constraint will be a limit to the amount of sanctions imposable on an individual group member. We can denote the maximum amount of sanctions an individual group member may have to bear as Ci , where Ci ¼ Si þ Sc :

ð3Þ

Thus, for negative sanctions, we are interested in the maximum amount of group compliance the agent can obtain given a limit, say Ci , to the

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maximum possible individual cost Ci . We are also interested in what combination of individual and collective sanctions enables the agent to obtain a given level of group compliance for minimal Ci . In analyzing the positive and negative sanction scenarios, it is important to keep in mind that C refers to the expected cost to the agent, while Ci refers to the maximum possible cost for a group member. One key assumption of this model, which Heckathorn relaxed on subsequent uses (Heckathorn, 1993, 1996), is homogeneity of group members among the parameters. I used the simpler, homogeneous model here to provide a relatively uncomplicated baseline analysis. Since the focus is on the agentÕs power, rather than on absolute or critical levels of group compliance, it is not likely that small or moderate deviations from group homogeneity would affect qualitative conclusions reached. As stated earlier, the agent has control over the strength of the individual sanction Si and collective sanction Sc . For remaining parameter values, in most analyses, I used the values commonly used by Heckathorn (1990), which I call the standard setting of the parameters. Group size is taken to be N ¼ 10 and the agentÕs monitoring ability M ¼ 0:1. Efficacies of compliant control and oppositional control are taken to be E2 ¼ E3 ¼ 0:2; costs of compliant control and oppositional control are taken to be K2 ¼ K3 ¼ 3; and cost of compliance itself is taken to be K1 ¼ 100. It should be noted that results are invariant under scaling of sanctions and costs. That is, multiplying costs and sanctions by a constant yields costs (C and Ci ) scaled by the same constant with no effect on the expected group compliance. Power concerning group compliance is simply the expected proportional level of group compliance. This means that the model determines power conditional on sanction levels, which is proportional group compliance given those sanction levels. To see this, refer to the power measure given by Eq. (1). Since the referent phenomenon is group compliance, the denominator for Eq. (1) is the possible change in group compliance. The possible extremes are that all group members comply and that none complies, making the denominator equal to the number of group members. The numerator for Eq. (1) is the change in group compliance the agent could cause. Now according to the model, the agent could bring about zero compliance by setting all sanctions to zero. So the expected maximum change the agent could cause is the expected maximum number of compliers the agent could obtain minus zero, that is, simply the expected maximum number of compliers the agent could obtain. Thus, power concerning group compliance, measured using Eq. (1), becomes proportional group compliance. Because the numerator is a function of sanction levels, power itself is a function of sanction levels. In this study, to make results clearer in fact I do not report the power of the agent but rather the number of compliers (see, e.g., Figs. 1–4). In other words, I report the numerator of power measure given by Eq. (1).

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Fig. 1. Expected number of compliers as a function of the expected cost to agent due to use of positive sanctions, collective and individual. Standard setting of parameters is used: E2 ¼ E3 ¼ 0:2, M ¼ 0:1, N ¼ 10, K1 ¼ 100, K2 ¼ K3 ¼ 3.

However, this measure differs from power only by a scale factor, the size of the group. To obtain the power of the agent concerning group compliance, simply divide the expected number of compliers by the number of group members. To answer the question concerning power as a function of budget (most likely, for positive sanctions), we find the following set of points: for each level of expected group compliance, we find the minimum cost to the agent, sufficient to obtain that level. To answer the question concerning power as a function of maximum imposable cost (for negative sanctions), we find the following set of points: for each level of expected group compliance, we find the maximum imposable cost to individual group members, sufficient to obtain that level. Expected group compliance is the sum of the number of voluntary compliers plus the expected amount of involuntary compliance due to exercise of compliant control. Being the weighted aggregate of discrete behaviors by group members, it rises in steps rather than continuously. Group compliance is a non-negative function of individual sanction. That is, with other factors constant, as individual sanction increases, group compliance increases or holds steady. However, as Heckathorn (1990) found, the relationship between group compliance and collective sanction is not so simple. However, through a simple search algorithm it was possible to identify the points of minimum C and Ci for each level of group compliance.

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Fig. 2. Expected number of compliers as a function of the maximum imposable cost on group member (a constraint on the agent) due to use of negative sanctions, collective and individual. Parameters are as in Fig. 1.

4. Results Figs. 1 and 2 show the maximum expected number of compliers as a function of expected cost to the agent C (for positive sanctions) and maximum imposable cost to a group member Ci (for negative sanctions), respectively. Again, the agentÕs power concerning group compliance is simply the maximum expected number of compliers divided by the group size, 10. Parameters used are the standard parameters used by Heckathorn (1990), namely, group size 10, efficacy of group control 0.2, monitoring efficacy 0.1, individual cost of compliance 100, cost of compliant control 3, and cost of oppositional control 3. Again, note that results are invariant under scaling of sanctions and costs. Thus, only relative not cardinal values of sanctions and costs affect qualitative results. Fig. 1 shows that especially for positive sanctions the agentÕs power concerning group compliance, that is, the degree to which the agent can get the group to comply, is a non-negative, non-linear step function of what we can call the agentÕs budget. Fig. 2 shows that especially for negative sanctions the agentÕs power concerning group compliance is a non-negative, non-linear step function of maximum imposable cost on an individual group

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Fig. 3. Expected number of compliers as a function of the expected cost to agent due to use of positive sanctions, collective and individual. Parameters are as in Fig. 1, except E2 ¼ E3 ¼ 0:5.

Fig. 4. Expected number of compliers as a function of the expected cost to agent due to use of positive sanctions, collective and individual. Parameters are as in Fig. 1, except that group size N ¼ 50.

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member. These results show that in each scenario, compliance up to a certain level may be obtained very cheaply. However, to obtain full or nearly full compliance is much more expensive, either to the agent (in the case of positive sanctions) or potentially to some group members (in the case of negative sanctions). Different values of model parameters produce different results. In general, increasing values for group membersÕ efficacies of control over each other (E2 and E3 ) and for monitoring capacity of the agent (M) has the following results. Number of compliers still is an increasing step function of cost to agent and of maximum imposable cost on a group member, as in Figs. 1 and 2. However, the number of steps decreases. Fig. 3 shows an example for the positive sanction scenario, with E2 ¼ E3 ¼ 0:5, and all other parameters including M remaining standard. When group size N increases, it is logical that the agentÕs monitoring capacity M and group membersÕ efficacies of control over each other E2 and E3 would decrease correspondingly. Under such changes in parameters, relationships between costs and amounts of group compliance remain qualitatively similar. Fig. 4 shows this for the positive sanction scenario, with group size N ¼ 50, monitoring capacity M ¼ 0:02, and efficacies of control E2 ¼ E3 ¼ 2M ¼ 0:04. Under the positive sanction scenario in which we are concerned with cost to agent, one important difference is that the agentÕs costs per complier are much higher with larger N. Specifically, for the situation shown in Fig. 4, agentÕs costs per complier are about 300 each for the first 30 compliers. For the comparable standard situation shown in Fig. 1, agentÕs costs per complier are about 100 each for the first nine compliers. Perhaps, the most interesting result of the analysis concerns the points of minimum cost. To obtain a given level of compliance for a given setting of parameters in the positive sanction scenario, there is always one pair of values for collective and individual sanctions that gives minimum cost to agent ðCÞ. Likewise, to obtain a given level of compliance for a given setting of parameters in the negative sanction scenario, there is always one pair of values for collective and individual sanctions that gives minimum Ci (maximum possible cost for group member). In fact, for all settings of the parameters, these points of minimum cost are identical for C in the positive sanction scenario and Ci in the negative sanction scenario. That is why results using C and Ci such as Figs. 1 and 2, are quite similar. Moreover, at those points of minimum cost (C and Ci ) either collective incentive is zero or individual incentive is zero. In fact, a thorough exploration of the parameter space—possible combinations of values of the different parameters—turned up no setting of the model parameters for which a point of minimum cost involved both non-zero individual sanction and nonzero collective sanction. This suggests that it may never be optimal for an agent to mix collective and individual sanctions. Naturally, this conclusion

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needs further investigation. It was obtained using a model embodying a number of assumptions and it may not be generalizable. In general, the agent may obtain lower levels of group compliance most cheaply by using only collective sanctions. Moreover, some of those ‘‘lower levels’’ may be quite high. Under the parameters of Figs. 1 and 2, over 80% compliance can be obtained with just collective sanctions; under those of Fig. 3, over 90% can be obtained. In many real-world situations, agents might be very happy with such levels of compliance. To obtain higher levels, individual sanctions may be necessary—but then collective sanctions are not necessary and are wasteful. Consider the model with the standard setting of parameters. To get one through eight expected compliers, no individual sanctions should be used. For example, to get at least eight expected compliers with minimum cost (C or Ci ), a collective sanction of 114.15 (with no individual sanction) is necessary, which produces an expected compliance of 8.356. To get more than 8.356 expected compliers, and in fact to get at least nine expected compliers, with minimum cost, an individual sanction of 1000 (with no collective sanction) is necessary, which produces an expected compliance of 10. The analysis yields additional implications concerning power use. Let us focus on the positive sanction scenario and let us assume that budget is not a problem—that the agent can afford to pay for total compliance, if so desired. Since increased group compliance comes only with increased minimum cost to agent C, it follows that whether or not the agent expends that cost will depend on the value of different levels of group compliance to the agent. The two relevant considerations will be cost per complier as a function of the amount of compliance and marginal cost of each additional increment of group compliance. These relationships are shown for the standard setting of the parameters in Figs. 5 and 6. Figs. 5 and 6 can be used to predict what a rational agent will do. In general, this will depend on the value of compliance to the agent as a function of the level of compliance. For example, suppose that the value to the agent of each additional unit of compliance is constant. This may be the case when non-compliance is essentially individual, such as cheating or pilfering. Then, Fig. 5 tells us that the lowest expected cost per complier to the agent is 86.64 (all in collective sanctions), which gets an expected 7.54 compliers. Thus, if the value to the agent of each unit of compliance is worth less than 86.64, the agent should not seek compliance at all! Fig. 6 tells us that to get to the next highest level above 7.54, the marginal cost per complier is 374.39, and to get to the next highest level above that, the marginal cost is 5498.82 per complier. Thus, if the value to the agent of each unit of compliance is at least 86.64 but less than 374.39, the agent should settle for 7.54 compliers. If the value to the agent of each unit of compliance is at least 374.39, but less than 5498.82, the agent should settle for 8.36 compliers.

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Fig. 5. Cost per complier as a function of level of the compliance for positive sanction scenario with standard setting of parameters.

Fig. 6. Marginal cost per complier as a function of the level of compliance for positive sanction scenario with standard setting of parameters.

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Finally, the agent should seek total compliance only when the value to the agent of each unit of compliance is at least 5498.82. Moreover, only then should the agent use individual sanctions and collective sanctions should not be used at all. More generally, this suggests that the agent should not employ individual sanctions unless the value of compliance to the agent is considerably greater than the value of non-compliance to group members (i.e., K1 ). This is true in particular for the standard levels for the agentÕs monitoring capability ðMÞ and the efficacies of control of group members over each other (E2 and E3 ). An increase in M, for example, would mean the agent could use a lower individual sanction. The workplace with employer as agent may provide an example. When compliance means performing the job for which one was hired, compliance may be much more valuable to the employer than non-compliance is to the employee. Thus, individual sanctions (only) for job performance may be optimal. However, for lesser types of non-compliance, such as misuse of resources, collective sanctions (only) are likely to be preferable. Other functions of the value of compliance to the agent will yield different predictions. For example, some types of compliance may be worthless to an agent unless all group members comply. This may be the case when noncompliance consists of an act such as betraying a secret or other catastrophic damage that even one act of non-compliance will bring about. Here, Fig. 5 is relevant. The agent should use individual sanctions of 1000 if and only if the value to the agent of each unit of compliance is at least 1000, or more appropriately, if the value of total group compliance is at least 10,000. Otherwise the agent should not seek compliance. Yet another possibility is that the marginal value of compliance to the agent declines with each additional amount of compliance, or perhaps when compliance has reached a certain threshold. For example, a low level of background talk and commotion (i.e., a small amount of non-compliance) may not bother teachers or supervisors, but when it crosses a certain threshold it may become intolerable. The interplay between the value of compliance to the agent, the marginal value of compliance to the agent, the cost per complier, and the marginal cost per complier will determine the level of compliance the agent will seek and the amount of sanctions the agent will use.

5. Conclusion In this study, I have analyzed the power concerning group compliance of an external agent with control over sanctions for members of a group who also have some control over each otherÕs compliance. For this analysis, I have used HeckathornÕs (1990) sequential decision model of group-mediated social control in which the agent can sanction an individual both according

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to the individualÕs detected non-compliance (individual sanction) and according to detected non-compliance in the group (collective sanction). I have focused on two issues, the effect of cost constraints on the agentÕs power and how much power the agent will use. In the case of positive sanctions, the important cost constraint on the agent is likely to be a limit on the total expected cost to the agent. I showed that the amount of group compliance is an increasing step function of the expected cost. In the case of negative sanctions, the important cost constraint on the agent is likely to be a limit to the maximum possible cost for a group member. Here too, I showed that the amount of group compliance is an increasing step function of the maximum possible cost. Those qualitative characteristics of the functions do not change with variation in parameters such as the efficacy of group membersÕ control over each other, the agentÕs monitoring capacity, and group size, although the actual functions do vary. The most surprising result is that it appears that a rational agent should never mix individual sanctions and collective sanctions. Results of the simulation model suggested that to achieve lower levels of compliance, only collective sanctions should be used, leaving the cost to the agent (in the positive sanction scenario) or maximum possible cost for a group member (in the negative sanction scenario) relatively low. Results suggested that to achieve the highest levels of compliance, it might be necessary to use individual sanctions at a high level, with correspondingly no need for collective sanctions. This will result in high costs to the agent for compliance. Finally, focusing on the positive sanction scenario, I used calculations of cost per complier for different levels of compliance and of marginal cost per unit increase in level of compliance to discuss the agentÕs use of power. If we assume the agent has complete power concerning group compliance (P ¼ 1), the extent to which the agent uses that power will depend on those costs in relation to the value of compliance to the agent. For example, if the value of compliance to the agent is independent of the level of compliance, under the standard setting of the parameters, the agent should not seek compliance if its value to the agent is low, or else settle for a level of 7.54 compliers (out of 10) unless the value of compliance is fairly high. The usefulness of the results of this study depends on their applicability to naturally occurring situations. The results are theoretical; they are logical consequences of the assumptions made, many of which greatly simplify naturally occurring conditions. Thus, while the findings are suggestive, their usefulness in natural situations remains to be demonstrated. One place to begin is in the classroom. Simulation results agree with Jones (1987) that collective sanctions can be a cost-effective way of obtaining compliance. They also suggest, however, that they will be less effective than individual sanctions in obtaining total compliance. That is, collective sanctions will be efficient means of keeping the level of talking—or

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clowning, or using obscenities, or whatever else the problem behavior may be—to low levels. However, they will not be able to eliminate the problem behavior completely. This implication should be straightforward to investigate. A more subtle implication is that using collective sanctions (only) the marginal cost per complier does not rise with the number of compliers until we get to high levels of compliance (see Fig. 6). This suggests that effective users of collective sanctions will not use them just to obtain low or even moderate levels of compliance, but rather will use them to obtain fairly high (though again, not total) compliance. This can again be investigated in classroom settings, perhaps through controlled interventions. Results are also applicable to workplaces. Bosses can use individual or collective sanctions to achieve everything from accomplishment of production goals to prudent use of photocopiers. Results here again suggest that, regardless of the goal, it would be foolish for bosses to mix sanction types. Where it is important for every employee to comply—say, with regard to production—individual sanctions may be preferable. Where some non-compliance is tolerable as long as most comply—say with photocopier use—collective sanctions may be preferable because of being much cheaper. Again, these implications are testable. One way to test them is to examine common practices, on the assumption that bosses tend to be efficient with their use of sanctions. Thus, we would predict that collective sanctions would be used more where some non-compliance is tolerable. Another way to test them is through intervention. Thus, researchers could substitute collective for individual sanctions concerning some behavior, to see if a certain level of compliance could be attained more cheaply. Conversely, individual sanctions could be substituted for collective sanctions to see if total compliance could be achieved thereby. The analysis in this study is mathematical, hence, not falsifiable in itself. Hence, if results from experiments or natural situations do not match results of this study, the source of the problem will be in the failure of assumptions and parameters of the model to match situational conditions closely enough. Ultimately, the usefulness of this analysis will rest in our ability to match the model and its parameters with naturally occurring situations. In addition to application to empirical situations, we can build on the analysis of this study for deeper analysis of an agentÕs power. Note that use of individual and collective sanctions typically does not exhaust an agentÕs means for increasing compliance. The agent may be able to change conditions to improve its monitoring ability M. The agent may also be able to alter the situation to increase the efficacy of control of group members over each other (Hechter, 1987). We can use HeckathornÕs (1990) model and the analysis in this study as a base for analyzing such other means of obtaining group compliance.

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References Coleman, J.S., 1990. Foundations of Social Theory. Harvard University Press, Cambridge, MA. Collins, J.C., Porras, J.I., 1994. Built to Last: Successful Habits of Visionary Companies. HarperCollins, New York. Durkheim, E., 1982 [1907]. The Rules of Sociological Method. Free Press, New York. Gibbs, J.P., 1975. Crime, Punishment, and Deterrence. Elsevier, New York. Gibbs, J.P., 1989. Control: SociologyÕs Central Notion. University of Illinois Press, Urbana, IL. Gibbs, J.P., 1994. A Theory About Control. Westview, Boulder, CO. Hechter, M., 1987. Principles of Group Solidarity. University of California Press, Berkeley. Hechter, M., 1990. The attainment of solidarity in intentional communities. Rationality and Society 2, 142–155. Hechter, M., Kanazawa, S., 1993. Group solidarity and social order in Japan. Journal of Theoretical Politics 5, 455–493. Heckathorn, D.D., 1990. Collective sanctions and compliance norms: a formal theory of groupmediated social control. American Sociological Review 55, 366–384. Heckathorn, D.D., 1993. Collective action and group heterogeneity: voluntary provision versus selective incentives. American Sociological Review 58, 329–350. Heckathorn, D.D., 1996. The dynamics and dilemmas of collective action. American Sociological Review 61, 250–277. Hosking, G., 2001. Russia and the Russians: A History. Harvard University Press, Cambridge, MA. Jones, F.H., 1987. Positive Classroom Discipline. McGraw-Hill, New York. Kanazawa, S., 1997. A Solidaristic theory of social order. In: Markovsky, B., Lovaglia, M., Troyer, L. (Eds.), Advances in Group Processes, vol. 14. JAI Press, Greenwich, CT. Kerr, M.M., Nelson, C.M., 1998. Strategies for Managing Behavior Problems in the Classroom, third ed. Prentice-Hall, Upper Saddle River, NJ. Ludden, D., 1985. Peasant History in South India. Princeton University Press, Princeton. Marriott, M., 1955. Little communities in an indigenous civilization. In: Marriott, M. (Ed.), Village India. University of Chicago Press, Chicago, pp. 171–222. Miller, A.S., Kanazawa, S., 2000. Order by Accident. Westview, Boulder, CO. Molm, L.D., 1997. Coercive Power in Social Exchange. Cambridge University Press, Cambridge, UK. Nader, L., 1990. Harmony Ideology: Justice and Control in a Zapotec Mountain Village. Stanford University Press, Stanford, CA. Oliver, P., 1980. Rewards and punishments as selective incentives for collective action: theoretical investigations. American Journal of Sociology 85, 1356–1375. Petee, T.A., Milner, T.F., Welch, M.R., 1994. Levels of social integration in group contexts and the effects of informal sanction threat on deviance. Criminology 32, 85–106. Portes, A., 1998. Social capital: its origins and applications in modern sociology. Annual Review of Sociology 24, 1–24. Simpson, R.L., 1985. Social control of occupations and work. Annual Review of Sociology 11, 415–436. Stokes, E., 1978. The Peasant and the Raj. Cambridge University Press, Cambridge. Whitmeyer, J.M., 2000. Power through appointment. Social Science Research 29, 535–555. Whitmeyer, J.M., 2001. Measuring power in exchange networks. Sociological Perspectives 44, 141–162. Zhou, M., Bankston, C.L., 1996. Social capital and the adaptation of the second generation: the Case of Vietnamese Youth in New Orleans. In: Fortes, A. (Ed.), The New Second Generation. Russell Sage Foundation, New York, pp. 197–220.