David Joosten

Harvard College 2011

Introduction

“You didn’t want to come. The average man don’t like trouble and danger. You don’t like trouble and danger. But if only half a man – like Buck Harkness, there – shouts ‘Lynch him! Lynch him!’ you’re afraid to back down – afraid you’ll be found out to be what you are – cowards – and so you raise a yell, and hang yourselves onto that half-a-man’s coat-tail, and come raging up here, swearing what big things you’re going to do. The pitifulest thing out is a mob; that’s what an army is – a mob; they don’t fight with courage that’s born in them, but with courage that’s borrowed from their mass.”

– Colonel Sherburn, The Adventures of Huckleberry Finn by Mark Twain[1]

The term scapegoat originated from a Jewish practice described in Leviticus XVI in which a townspeople would confess their transgressions over a sacrificial goat on Yom Kippur and subsequently cast the goat out into the dessert to die, thereby purifying the town of its sins.[2] Today, the term is applied freely to a variety of situations in which a collective fault or social stress is blamed on a particular minority.[3] Modern historians have used the term to describe political developments, from protectionist tax policies to the Jewish Holocaust itself.[4] In economics, the term has been applied to a variety of situations, such as to describe those affected by labor policies or the focus of investors’ attention in the currency markets.[5] Psychologists, particular social psychologists, have conducted experiments and described the dynamic features of scapegoatism.[6] Although the original, ritual meaning of scapegoat is no longer practiced today, the term has come to describe a dynamic social process witnessed in a variety of fields.

This paper analyzes scapegoatism from the perspective of the individual members of a social network, their social utilities, and the decisions that result. Using basic psychological descriptions of the effects of a scapegoat event[7] on the members of a social group, this paper formalizes an economic model to describe this dynamic social process. Furthermore, the model’s results lead to several general conclusions about the factors that increase the likelihood of scapegoat events.

Scapegoat events largely occur because a particular stress damages a group’s solidarity or the strength of its social connections. To alleviate some of the social repercussions of this stress, the group members can choose to blame an individual within the group, thereby sacrificing that individual for the good of the remaining group members’ social connections. In other words, scapegoating relieves the social impact of the stress, or the social stress, and enables the group as a whole to regain solidarity.[8]

The decision to pursue scapegoatism or not is an individual decision on the part of each group member that depends on the relative values of various factors. Generally, the social utility each member could regain by scapegoating must be compared to the social utility lost if a particular member were excluded from the group due to the occurrence of a scapegoat event. Since different members of the group are more or less valuable to the group as a whole, the comparison between the relative social utilities of scapegoating or not may be different for each group member. Therefore, the decision each group member makes depends on his particular circumstances within the group and the resulting group decision is dependent on group composition as well as the social stress inhibiting solidarity.

However, although group members’ individual decisions may be different, they are subject to many of the same factors and so are significantly correlated. The social stress discounts all of the links between the members in a group universally, so that a larger social stress will compel every member to increase the opportunity cost of not scapegoating in his decision on whether to scapegoat or not. Additionally, the value of the weakest member of the group, the would-be target of a scapegoat event, factors into every member’s decision through the cost incurred if he chooses to scapegoat.

Overall, the group as a whole is more likely to scapegoat its weakest member when the social stress inhibiting all group connections is high relative to the value of the weakest member. This result helps explain the prevalence of scapegoat events in the following situations:

  • When a group is large and the weakest member’s value comprises only a small fraction of the group members’ values
  • When a group experiences a high level of variation in social stress
  • When group member values are right-skewed
  • When group leaders support a scapegoat event

Previous studies of historical scapegoat events confirm these driving factors. In the most extreme cases of historical scapegoat events, all of the above factors are present at the time of the scapegoat event. Whether one considers the post-WWI Red Scare, the scapegoat Charles Mitchell at the time of the 1929 Stock Market Crash, or the rise of anti-Semitism during the Third Reich in Germany, a great social stress coupled with a belief that the minority held weak social values is present in all of them.[9]

Although there has been a great focus on scapegoatism in historical literature and in the field of social psychology (particularly in organizational behavior), economic literature has not explored the topic in-depth.[10] Bandiera, Barankay, and Rasul (2007) discuss the effects of manager favoritism and subsequently the incentive systems that can remove favoritism in the workplace.[11] However, their paper does not focus on the opposite of favoritism – scapegoatism, in which a member in the workplace is isolated from his peers and deliberately excluded socially. Additionally, Chwe (2000) focuses on the integration of social network theory and game theory by exploring social coordination and the requirements necessary for coordination.[12] In essence, his paper helps fuel the concepts of link variation and social values found in this paper, and specifically the barriers to achieving a scapegoat event. While Chwe discusses these dynamics generally, this paper focuses on the specific characteristics of coordination as they relate solely to the occurrence of scapegoat events.

The rest of the paper is structured as follows: the first section sets up the model of the social group, including a few stochastic variables and underlying assumptions. The second section analyzes the results of various simulations. The last section analyzes some examples from two papers on organizational behavior within the framework of model. The conclusion discusses the implications of these results and potential areas of further research in the area of scapegoatism.

Scapegoat Model

Network structure

The social group is comprised of k members, or nodes, that are connected to all other members of the group. The complete inter-connection of the group serves as the most socially cohesive configuration of the group’s social network, and so it acts as an effective baseline from which to draw conclusions about the prevalence of scapegoatism. Furthermore, a completely inter-connected network accurately describes many real-world social groups such as those that are found in corporations, on athletic teams, and in families.

Connection structure

As a result of the complete inter-connection of the group, there is the following composition of network connections:

  • total connections (of which k–1 connect to the would-be scapegoat)

Each member of the group (excluding the would-be scapegoat) faces the following:

  • k–2 non-scapegoat connections
  • 1 scapegoat connection

Social values

Each of the k group members is assigned a social value (denoted by Vi) drawn from a random, normal distribution centered so that 5% of the social values are negative. This social value is exogenous to the model and is meant to describe the value of each member of the group to the group as a whole. One could imagine a particular team working on a project requiring physical strength and certain team members being inherently stronger than others. In this model, the stronger team members are denoted as having higher social values than the rest of their team. Furthermore, one could imagine that some team members are so weak that they actually detract from the group’s efforts, which would result in a negative social value. Note that these social values are different from the link values that are discussed subsequently.

Links and social stress

The social stress (denoted by δ) is the discount factor applied universally to all links within the social network of the group. All links are assumed to have a value of 1 that is subsequently multiplied by (1–δ) to arrive at the current value of the social link. The assumption that links have a base value of 1 is made to simplify the model – the social values discussed above have been chosen instead to represent the diversity of group members. One could also potentially vary the link values in this model to differentiate group member’s individual links with one another in addition to their social values, but the conclusions of this paper are unaffected by assuming their base value of 1.

The social stress is perhaps the key ingredient into the model, and so it deserves particular attention. The social stress is considered exogenous to the model – it represents the combined effect of all external factors on the social network and the links therein. This model targets the following characteristics for the social stress:

  • It is centered around zero so that it has a 50% probability of inhibiting link values
  • It is derived from a distribution which makes extreme outcomes unlikely
  • It is bounded
  • It cannot increase the link values beyond their base value of 1

Overall, to achieve these characteristics, the social stress is drawn at random from a normal distribution, its cumulative probability is calculated, and then centered at zero (by subtracting 0.5 from it). Additionally, any negative values are set to zero to ensure that link values are never greater than 1.[13] These modifications ensure that all the targeted characteristics listed above are satisfied in the model.

Voting

When a social stress is imposed on the social network, each group member must decide whether he will attempt to scapegoat the stress or not. This is a personal decision that may vary from member to member depending on group composition. In comparing the opportunity to regain social utility by scapegoating versus the cost of excluding the weakest group member, the model applies the following condition[14] for a particular member (member X) of the group choosing to vote for a scapegoat event:

After each member evaluates his situation and votes whether to scapegoat or not, there is a scapegoat event if and only if all members but one (the weakest member) vote in favor of scapegoating.[15] In this model, the weakest member will never vote in favor of scapegoating because he would never benefit from the solidarity a scapegoat event would bring about, but would rather lose all social utility by his exclusion from the group.

Trials[16]

Each trial represents the introduction of a particular social stress on the social network of the group, each group member’s evaluation of the comparison discussed previously and vote, and finally the aggregate result of the individual group members’ votes. Each trial is independent of all other trials. The procedure of each trial is detailed as follows:

  1. For each member of the group (not including weakest):
    1. Calculate the social utility lost due to the social stress.
    2. Calculate the social utility of the weakest member.
    3. Vote in favor of scapegoating if L > W, against scapegoating otherwise.
  2. Tally the votes and perform a scapegoat event if the votes in favor of scapegoating sum to k – 1 (i.e. unanimous decision of all members not including the vote of the weakest member).
  3. Repeat, drawing new social values and a new social stress.[17]

Simulation Results and Analysis

Group size

To gauge the effects of varying group size, this paper presents the results of a simulation with a group size of 3 and compares it to a simulation with a group size of 10 each run for 1,000 trials. The sample proportion of the frequency of scapegoat events for each simulation is shown in the following table:

Table 1

Running a statistical test to compare the proportion means yields a highly statistically significant result at the 5% significance level[18] in which the frequency of scapegoat events for the group of size 10 is greater than that for the group of size 3. The simulation results confirm the reasoning that the greater the number of members in the group, the greater the opportunity cost of not scapegoating is for each member relative to the value of the member with the weakest social value.

Figure 1 Figure 2

If the situation from the perspective of member X in Figure 1 and Figure 2 above is compared, the increase in opportunity cost for larger groups is made apparent. While member X in Figure 1 must sacrifice 50% of his links to gain a proportion δ on 50% of his links, member X in Figure 2 must sacrifice only 25% of his links to gain a proportion δ on 75% of his links. Although this need not always be the case[19], member X in Figure 2 on expectation would be more likely to pursue a scapegoat event than member X in Figure 1 because less of a sacrifice is required proportionally to the expected gain.

Variance of social stress

In analyzing the effect of the social stress on the frequency of scapegoat events, this paper presents the results of a simulation in which the social stress is that which is described in the original model specifications and compares it to the results of a simulation in which the social stress’s variance is subsequently quadrupled, each run for 1,000 trials. The sample proportion of the frequency of scapegoat events for each simulation is shown in the following table:

Table 2

Running a statistical test to compare the proportion means yields a statistically significant result at the 5% significance level[20] in which the frequency of scapegoat events for the adjusted variance is greater than that for the original variance. The simulation results support the idea that the more variant the social stress is, the greater the likelihood is of a scapegoat event.

A greater social stress leads to a greater probability of a scapegoat event, since the social stress increases the opportunity cost of not choosing to scapegoat and decreases the cost of choosing to scapegoat[21]. As shown in Figure 3, since the Modified Social Stress (social stress with greater variance) is greater than the Original Social Stress for all values greater than zero, the probability of a scapegoat event for the Modified Social Stress is greater than that for the Original Social Stress.

Social value dispersion

To understand the effects of varying the dispersion of social values, this paper presents the results of a simulation in which the social value distribution is that which is described in Section I (normal distribution) and compares it to the results of a simulation in which the social value distribution is right-skewed[22], each run for 1,000 trials. The sample proportion of the frequency of scapegoat events for each simulation is shown in the following table:

Table 3

Running a statistical test to compare the proportion means yields a statistically significant result at the 5% significance level[23] in which the frequency of scapegoat events for the right-skewed distribution of social values is greater than that for the original, normal distribution.

Figure 3

These results support the reasoning that as the distribution of social values is skewed to the right, the probability that Vweakest is low enough relative to the other members’ social values to set off a scapegoat event increases[24]. In other words, the likelihood of having a member weak enough to scapegoat increases under a right-skewed distribution.

Leadership

In determining the effect of leadership on the probability of scapegoat events, this paper presents the results of a simulation in which the social values distribution is the same as that which is described in the original model description and compares it to a simulation in which the kth group member’s social value is the sum of all other members’ social values. The results of running these simulations each for 1,000 trials is found below:

Table 4

Running a statistical test to compare the proportion means does not yield a statistically significant result at the 5% significance level[25]. However, a deeper analysis of the data reveals that the voting dynamics of the two simulations are very distinct. A leader event is defined as a trial in which there is not a scapegoat event due to the single vote against scapegoating[26] by the member with the highest social value. The proportion of trials in which there is no scapegoat event due to a leader event is shown in the following table:

Table 5

Running a statistical test to compare the proportion means yields a statistically significant result at the 5% significance level[27] in which the frequency of leader events for the Leader Model is greater than that for the Original Model. In fact, in all cases, the strongest member of the group is the least dependent on the social network for social utility, and is therefore always the least likely to vote for a scapegoat event.

The effect of a leader in the social group[28]

Figure 4 Figure 5

Figure 4 above presents a possible social group in the Original Model whose strongest member has a social value of 4. Figure 5 presents the same social group in the Leader Model. In either Figure 4 or 5, the social utility the strongest member receives from his social network is the same. Therefore, the decision of the strongest member is left unaffected by his own social value. However, the same is not true for the other members of the group. While the members whose social values are 2, 2 and 3 in Figure 4 lose 4δ as a result of the social stress imposed on the social network, those members in Figure 5 lose 8δ. These members from Figure 5 have a higher opportunity cost for choosing not to scapegoat relative to their counterparts in Figure 4, and subsequently are more likely to choose to scapegoat. As a result, it is the strongest member’s vote that is both the limiting factor and the deciding factor to achieving a scapegoat event, and this result is borne out in the data under the Leadership Model.

Examples

Mobbing

According to Westhues (2003), the term mobbing is defined as a “collective campaign by co-workers to exclude, punish, and humiliate a targeted worker.”[29] Mobbing is a specific example of the scapegoatism, and there are two characteristics of mobbing as described by Westhues that relate to the conclusions of the model developed in this paper. Firstly, Westhues characterizes mobbing as an act that is “initiated most often by a person in a position of power or influence.”[30] In most cases of documented mobbing, workplace tensions are only released through the form of mobbing when it is legitimized by a manager. This feature of mobbing can be explained in the model by the critical importance of the strongest member in determining whether a scapegoat event is successful or not (as shown through the Leadership Model in the simulation results). Since the strongest member of a group has the least to gain by scapegoating in terms of social utility, it is this member who acts as the barrier to a successful scapegoat event in borderline situations.

Secondly, Westhues describes scapegoating as “an effective if temporary means of achieving group solidarity, when it cannot be achieved in a more constructive way.”  In terms of the scapegoat model, this gain in solidarity is captured by the opportunity cost of choosing not to scapegoat, or . Although a scapegoat event may decrease social value of the group as a whole, each individual member gains in terms of social utility, and it is this that drives a group to perform a scapegoat event even in situations when the weakest member still has a positive social value.

Social role and scapegoatism

Zurcher and Wilson (1981) find that one’s ability to fulfill a particular role in a group setting is highly correlated with group satisfaction and individual performance through a Marine field exercise done with Naval Reservists.[31] Based on a previous field exercise, subjects were told to choose whether they had more satisfaction with a “Naval role,” a “civilian occupational role,” or anywhere in between on a gradient scale. All subjects were then put in groups to complete assignments that strongly favored one role and then the other. Zurcher and Wilson find that those subjects who identified with neither role rated the assignments the most negatively, followed by those subjects who participated in an assignment contrary to their chosen role. This result can be explained through the framework of the scapegoat model developed in this paper in the following manner: Those who participated in an assignment contrary to their chosen role gained from their social network the most since they were able to rely on their fellow members whose self-described role related to the assignment. Those members who identified with neither role did not gain as much from their social network since they were more like their fellow members whose chosen field related to the assignment.

In fact, the study finds that those who identified with neither the “Naval role” nor the “civilian occupational role” were actually “likely to scapegoat someone within the setting”[32].  Since these subjects were neither differentiated from the “Naval role” group members nor the “civilian occupational role” group members, they stood to gain the least from their social network, and therefore would have had the lowest overall social utility. As a result, these subjects’ dissatisfaction with the assignment reached the critical level required to choose a scapegoat event.

Conclusion

This paper develops a model for scapegoatism and examines the factors that lead to higher probabilities of scapegoat events through controlled simulations. First, the paper finds that larger group sizes (or more specifically, group sizes in which the minority is small) lead to higher incidence rates of scapegoatism on expectation. This occurs as a result of the low marginal social utility the weakest group member provides the rest of the group members relative to their total social utility. Second, environments in which a social network experiences highly variant levels of social stress (δ) tend to have higher rates of scapegoatism. As the probability that a social stress is greater than the critical point required for a scapegoat event increases, the probability that a scapegoat event occurs also increases. Third, certain types of social value distributions, namely right-skewed distributions, are more likely to lead to higher rates of scapegoatism. This occurs as a result of the greater probability that a given group has a member whose social value is low enough to merit a scapegoat event. Lastly, leaders emerge as the deciding vote in thwarting scapegoat events as a result of their low reliance on the social network relative to the rest of the group members. This conclusion results from the unanimous voting structure the model utilizes as its framework for determining when scapegoat events occur and the independence a group leader’s vote has from his own social value.

These scapegoat factors have implications that reach a variety of fields: sociology, history, economics, and particularly organizational behavior. The model recommends that to achieve solidarity, groups should be relatively small, should avoid having critically high levels of social stress imposed upon them, should have members whose social values are not skewed-right, and should have clearly defined group leaders. These group characteristics lead to the highest levels of social utility for each of the group members, and can help deter group dynamics from negatively impacting group objectives.

References

Bacchetta, P. and Wincoop, E. (2004) “A Scapegoat Model of Exchange-Rate Fluctuations”, The American Economic Review 94: 2-114.

Bandiera, O., Barankay, I., and Rasul, I. (2008) “Social Connections and Incentives in the Workplace: Evidence from Personnel Data”, (revisions requested, Econometrica).

Charmichael, C. (2000) “The Origin of the Scapegoat Ritual”, Vetus Testamentum 50: 2-167.

Chwe, M. S.-Y. (2000) “Communication and Coordination in Social Networks”, Review of Economic Studies 67: 1.

Colburn, D.R. “Governor Alfred E. Smith and the Red Scare, 1919-20”, Political Science Quarterly 88: 3-423.

Davenport, N., Schwartz, R., and Elliott, G. (1999) Mobbing: Emotional Abuse in the American Workplace, Ames, Iowa: Civil Society Publishing.

Foster, C.R. (1980) “Historical Antecedents: Why the Holocaust”, Annals of the American Academy of Political and Social Science 450: July-1.

Huertas, T.F. and Silverman, J.L. (1986) “Charles E. Mitchell: Scapegoat of the Crash?” The Business History Review 60: 1-81.

Spencer, E.W. (1983) “Japan: Stimulus or Scapegoat?”, Foreign Affairs 62: 1-123.

Twain, M. (1912) The Adventures of Huckleberry Finn, New York: Harper and Brother Publishers.

Unknown (1974) “Labour: The Scapegoat”, Economic and Political Weekly 9: 26-995.

Westhues, K. (2002) “At the Mercy of the Mob,” OHS Canada 18: 8-30.

Zurcher, L.A. And Wilson, K.L. (1981) “Role Satisfaction, Situational Assesment, and Scapegoating”, Social Psychology Quarterly 44: 3-264.


[1]Mark Twain. The Adventures of Huckleberry Finn, (New York: Harper and Brother Publishers, 1912), 203.

[2] Calum Carmichael, “The Origin of the Scapegoat Ritual,” Vetus Testamentum, Vol. 50, Fasc. 2 (Apr., 2000), pp. 167-182.

[3] “Labour: The Scapegoat,” Economic and Political Weekly, Vol. 9, No. 26 (June 29, 1974), p. 995.

[4] Claude R. Foster, Jr, “Historical Antecedents: Why the Holocaust,” Annals of the American Academy of Political and Social Science, Vol. 450, (July, 1980), pp. 1-19.

Edson W. Spencer, “Japan: Stimulus or Scapegoat?” Foreign Affairs, Vol. 62, No. 1 (Fall, 1983), pp. 123-137.

[5] “Labour: The Scapegoat,” Economic and Political Weekly, Vol. 9, No. 26 (June 29, 1974), p. 995.

Philippe Bacchetta and Eric van Wincoop, “A Scapegoat Model of Exchange-Rate Fluctuations,” The American Economic Review, Vol. 94, No. 2 (May, 2004), pp. 114-118.

[6] Louis A. Zurcher and Kenneth L. Wilson, “Role Satisfaction, Situational Assesment, and Scapegoating,” Social Psychology Quarterly, Vol. 44, No. 3 (Sep., 1981), pp. 264-271.

[7] The concentrated casting of blame for a collective social stress on a particular individual

[8] Kenneth Westhues, “At the Mercy of the Mob,” OHS Canada, Vol. 18, No. 8 (Dec., 2002), pp. 30-36.

[9] Claude R. Foster, Jr, “Historical Antecedents: Why the Holocaust,” Annals of the American Academy of Political and Social Science, Vol. 450, (July, 1980), pp. 1-19.

David R. Colburn, “Governor Alfred E. Smith and the Red Scare, 1919-20,” Political Science Quarterly, Vol. 88, No. 3 (Sep., 1973),  pp. 423-444. – Political Scientist Colburn characterizes the rise of Gov. Alfred E. Smith and the social tensions that brought about the post-WWI Red Scare in the United States.

Thomas F. Huertas and Joan L. Silverman, “Charles E. Mitchell: Scapegoat of the Crash?” The Business History Review, Vol. 60, No. 1 (Spring, 1986), pp. 81-103. – Historians Thomas Huertas and Joan Silverman discuss Charles Mitchell’s role in the 1929 Stock Market Crash and his subsequent role as scapegoat during the Depression.

[10] Such as in: Zurcher and Wilson, “Role Satisfaction, Situational Assesment, and Scapegoating,” Social Psychology Quarterly, Vol. 44, No. 3 (Sep., 1981), pp. 264-271.

[11] Oriana Bandiera, Iwan Barankay, and Imran Rasul, “Social Connections and Incentives in the Workplace: Evidence from Personnel Data,” (revisions requested, Econometrica).

[12] Michael Suk-Young Chwe, “Communication and Coordination in Social Networks,” Review of Economic Studies, Vol. 67, (2000), pp. 1-16.

[13] This is a simplification made to avoid issues with members whose social values are negative, which when multiplied by a link value greater than 1 (a negative social stress) would actually yield a more negative social utility, an illogical result considering there is a negative social stress, or positive effect on the social network.

[14] Note that if the social stress is equal to 0.0, there is a scapegoat event iff Vweakest < 0.0. In other words, when there is no social stress, only members that detract from the group can be scapegoated.

[15] One could use different voting systems, such as simple majority, but the implications of voting by unanimous decision lead to conclusions supported by models of leadership, discussed in the simulation results under “Leadership.”

[16] For the actual PHP program used to produce the data, refer to Appendix B [editor’s note: published online].

[17] Note that we still have the original total number of members, so that we are essentially running the same simulation but with different random values.

[18] See Appendix A for the full statistical test [editor’s note: published online].

[19] If social values are negative, then member X in Figure 2 would be more likely to want a scapegoat event.

[20] See Appendix B for the full statistical test.

[21]The opportunity cost of not choosing to scapegoat is: and therefore the probability of a scapegoat event is increasing as δ increases, assuming positive social values.

[22] The right-skewed distribution is modeled by using the Χ2 Distribution.

[23] See Appendix B for the full statistical test.

[24] Note that the proportion of members whose social values are negative has been kept at 5%, so that the number of negative social values in the group does play a role in the results presented.

[25] See Appendix B for the full statistical test.

[26] This does not include the vote of the weakest member, who always chooses not to scapegoat. The justification for exactly why the weakest member chooses not to scapegoat is found in Section I, “Voting.”

[27] See Appendix B for the full statistical test.

[28] In the Figures, the numbers within the circles indicate the social value of each node.

[29] Westhues… See also Noa Davenport, Ruth Schwartz, and Gail Elliott, Mobbing: Emotional Abuse in the American Workplace (Ames, Iowa: Civil Society Publishing, 1999)

[30] Westhues, paragraph 9.

[31] Zurcher and Wilson…

[32] Zurcher and Wilson, pg. 270.

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