Influences on the Duration of Wars, Strikes, Riots, and Family Arguments

Influences on the Duration of Wars, Strikes, Riots, and Family ArgumentsAuthor(s): Samuel Vuchinich and Jay TeachmanSource: The Journal of Conflict Resolution, Vol. 37, No. 3 (Sep., 1993), pp. 544-568Published by: Sage Publications, Inc.Stable URL: http://www.jstor.org/stable/174268 .

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Influences on the Duration of Wars, Strikes, Riots, and Family Arguments

SAMUEL VUCHINICH Oregon State University

JAY TEACHMAN University of Maryland

Utility theory has been frequently applied in the analyses of the outbreak of war. The present study extends the application of utility theory to conflict duration. The authors consider how the perceived utility of continuing conflict changes while conflicts are under way, and posit that conflicts end when the utility of continuing is less than the utility of surrender. Predictions developed from the theory are tested, using hazard models, on duration data from actual wars, strikes, riots, and family arguments. Consistent with utility theory, the likelihood of wars and strikes ending is found to decrease while they are under way, exhibiting a tendency for these conflicts to become entrenched. In sharp contrast to this, but consistent with utility theory, riots and family arguments are more likely to end the longer they last. Size of conflict and dispute issue are shown to effect duration in some circumstances. The results offer a way of explaining how conflicts between "rational" organizations become entrenched and resistant to resolution. Implications for efforts to reduce conflict duration are discussed.

The idea that human conflicts are governed by a rational weighing of benefits and costs has been used to understand the nature of wars (Bueno de

Mesquita 1981), strikes (Kennan 1985), riots (Mason 1984) and family arguments (Vuchinich, Teachman, and Crosby 1991). Most work on conflict, from this perspective, has focused on explaining the outbreak of war (Morrow 1985; Bueno de Mesquita 1985; Bueno de Mesquita and Lalman 1986). Patterns of initiation and frequency are important features of human conflicts. But their duration, once they are under way, is of equal significance in

determining how much damage and destruction ultimately occurs. Quickly resolved conflicts do relatively little damage compared to those that continue

AUTHORS' NOTE: Part of this research was supported by a National Institute of Mental Health grant (MH-45073) to Sam Vuchinich and by a grant from the John D. and Catherine T. MacArthur Foundation to E. Mavis Hetherington.

JOURNAL OF CONFLICT RESOLUTION, Vol. 37 No. 3, September 1993 544-568 ? 1993 Sage Publications, Inc.

544



Vuchinich, Teachman /INFLUENCES ONDURATION 545

for a long period of time. The empirical analysis of human conflict duration has been limited largely to studies of strikes (e.g., Lancaster 1972: Kennan 1985; Rubin and Smith 1991). A few diverse investigations have considered war duration (Horvath 1968; Bueno de Mesquita 1978; Wittman 1979; Morrison and Schmittlein 1980), but there has been little accumulation of findings. The purpose of this study is to extend utility theory to the analysis of human conflict durations and test the principles with empirical data on wars, strikes, riots, and family arguments. The overall goal is to advance our understanding of the general processes that determine when human conflicts end.

THEORY

The principle that decisions about human conflicts are influenced by the perceived costs and benefits of direct confrontation has a long, esteemed, and controversial history (Rapoport 1957, 1960; Schelling 1960; Richardson 1960; Bueno de Mesquita 1981, 1985; Majeski and Sylvan 1984; Morrow 1985; McGinnis 1991; Coleman 1991). In this section we (1) draw on

previous work to show that utility theory can be useful for explaining how

long human conflicts last, (2) review important limitations to this theoretical

approach, and (3) develop predictions that can be empirically tested. From the perspective of utility theory, human individuals and groups are

willing to pay the costs associated with conflict because the immediate or

potential benefits of the conflict outweigh the costs. Thus, starting conflicts and continuing them are sometimes considered "rational" due to their rela-

tively high utility (i.e., the benefits are greater than costs). The benefits of conflict include the acquisition of new resources or the protection of ones

already possessed. Resources are valued commodities, which may be physical (e.g., land, water, capital) or social (e.g., rights, laws, freedoms that are based on politics, ethnicity, or religion) in nature. The costs of conflict include resources used to engage in conflict, the losses incurred as a result of attacks from opponents, and what is given up in order to engage in conflict (Bueno de Mesquita 1983; Wittman 1979; Sopher 1990). A well-known principle for conflict initiation is that it begins when the perceived benefits of the conflict are greater than the perceived costs for at least one party (Bueno de Mesquita 1981, 1985; Morrow 1985).

The present analysis extends this principle to what occurs while the conflict is under way. Thus we assume that during a conflict the participants persist in assessing the utility of continuing the struggle.

First, it is difficult to quantify some aspects of the costs and benefits associated with human conflicts. Although some features of resources in-



546 JOURNAL OF CONFLICT RESOLUTION

volved in human conflict have a quantifiable component (i.e., the monetary value of property or the number of human lives lost), others do not (i.e., the value of ethnic identity, national pride, religious rights). And even when resources can be quantified by objective measures, the calculus of benefits and costs must still make untested assumptions about the perceived value placed on them by the individuals or groups involved in the conflict.

One way to address this problem is to focus only on aspects of the theory that can be tested with appropriate measures that are available (Feynman 1967). Some measures are ideal for testing certain theories. For example, a precise, valid, and reliable measure of the perceived benefits of a given war for individuals who have the power to make war would be ideal in an application of utility theory. Such a measure-may not be available for various reasons. Rather than settle for a seriously flawed measure, an alternative approach is to use other aspects of the theory that allow predictions involving concepts for which there are adequate, or at least less flawed, measures (Feynman 1967; McGinnis 1991). Richardson's (1960) model for arms races has serious problems, in part because it involves quantitative estimates of

grievance, fatigue, and threat factors that are difficult to quantify (McGinnis 1991). The present analysis attempts to avoid such difficulties by focusing on predictions from utility theory that do not require measuring the utility of

continuing conflict at any given time. A second limitation is that human conflicts involve some uncertainty

about the outcome of the conflict. When a conflict begins, no one knows who will win. This means that potential outcomes are uncertain and that fighting involves taking risks. This complicates the kind of rationality that is possible (Bueno de Mesquita 1981, 1985). These, and other aspects of the actual context of decisions during conflict, further suggest that individuals and

organizations can only approximate rational behavior (Simon 1982). These considerations are evidence against a model of strictly rational

decisions during conflict. However individuals and organizations may at-

tempt to be rational (Simon 1982; McGinnis 1991). They may not know who will win the conflict, or exactly how much they will gain or lose, but they can and do make estimates about these factors, and such estimates probably change while conflict is under way. We may relax some features of utility theory by positing that they use what information is available to them and assess the utility of continuing conflict on that basis (McGinnis 1991). This

imposes limits on the kinds of predictions that are possible. However, we

suggest that some predictions from utility theory are so general that they hold even for "approximately" rational behavior. Predictions drawn from such an

analysis will be somewhat less specific than those based on strict rationality, but they may be equally useful for understanding the processes involved and




more quantitatively viable because there is less measurement error. A less restrictive approach (McGinnis 1991) is especially applicable in an explor- atory analysis of the duration of different types of human conflicts.

Utility theory focuses on the decisions and behavior of individuals and groups. This analysis proposes that all parties in a conflict apply the same basic principles in evaluating the utility of continuing the conflict. It thus offers a parallel utility perspective on conflict duration. This analysis does not attempt to predict which party will win, but rather only features of conflict duration, regardless of who wins. Focusing on only certain features of conflict is in keeping with efforts to apply less restrictive conflict models. An alternative approach to conflict is game theory, which focuses on patterns of mutual influence between the parties in a conflict and the jointly determined outcomes (e.g., Bueno de Mesquita and Lalman 1992). Although useful in several domains, game theoretic approaches require some stringent assumptions about the conflict process, which may not be necessary in accounting for conflict duration. Other alternative approaches, based on less restrictive, probabilistic or systemic assumptions (e.g., Cioffi-Revilla 1991; Zinnes and Muncaster 1984), have proven to be useful in understanding aspects of conflict.

Following previous work, we suggest that individuals and organizations engaged in conflict assess the utility of continuing the conflict while it is under way. This implies that there are important similarities in the conflict process in wars, strikes, riots, and family arguments. That idea has been a basic tenet of the most influential theoretical work on conflict for many years (Rapoport 1960; Schelling 1960, 1978; Richardson 1960; Coser 1956; Collins 1975; Maynard Smith 1974; Coleman 1991). It further implies that utility theory applies to the behavior of individuals acting for themselves (in the case of family arguments), as well as acting in the context of groups (wars, strikes, and riots). This is in keeping with the scope of utility theory (e.g., Becker 1981) and previous research on these conflicts cited above. However, this does not imply that all aspects of decision processes are the same in nations, unions, corporations, police departments, or individuals. It suggests that conflict is a general form of interaction, which induces some similar

patterns in whatever units engage in the process.

PREDICTIONS

This application of utility theory posits that an organization or individual will continue a conflict as long as the perceived benefits of the conflict outweigh the perceived costs. When this condition is not met for one of the




opponents (in the two-party case), the conflict will end, usually in surrender or compromise (Morrow 1985). Multiparty conflicts continue as long as positive utility is maintained for at least two parties. Pursuing some implications of this general principle and considering some general features of conflict lead to specific predictions about how the likelihood of conflict ending changes during conflict episodes.

First, the costs of conflict increase the longer the conflict lasts. Even if the rate of resource expenditure is constant, the total cost of engaging in the conflict accumulates as conflict duration is extended. Second, benefits to be gained from conflict remain relatively constant throughout the duration of the episode. Opponents usually have objectives to attain. These are the perceived benefits that motivate the conflict in the first place. Although these are subject to some change, it is insignificant compared with the increasing costs.

These two points lead to the conclusion that the utility of continuing conflicts should decrease while they are under way. This is necessarily the case when costs increase while benefits stay relatively constant. These conclusions also hold if the marginal utility of continuing conflict is considered. In that case, previous investments in the conflict are treated as sunken costs. In this view, as conflict continues and resources are depleted, more alternative uses of the resources are foregone. This increases opportunity costs and the overall marginal costs of continuing. In addition, marginal benefits either remain the same, for reasons described above, or decrease due to a general tendency for marginal returns to diminish. Thus a marginal utility approach results in the same conclusion that the utility of continuing conflict decreases while it is under way, because costs increase whereas benefits

usually don't. Finally, we assume that changes in the utility of continuing conflict

influence the probability of continuing it. Specifically, the probability of conflict ending is positively correlated with the utility of continuing the conflict. If the utility of continuing conflict is high, then the probability of conflict ending should be relatively low. But when that utility is low, the

probability of conflict ending is high. Because costs accumulate steadily, a corresponding steady increase in the probability of conflict ending is

predicted. This prediction, derived from utility theory, is general and takes into

account none of the specific characteristics of organizations and individuals that could influence the utility of engaging in conflict. Two factors that could have a large impact on this process are (1) the stockpiling of resources to be used exclusively during conflicts, such as military stockpiles (Bueno de

Mesquita 1981) or union strike funds, and (2) social psychological reactions



Vuchinich, Teachman/INFLUENCES ONDURATION 549

of organizations and their leaders that mobilize for conflicts, such as propaganda (Qualter 1962, Wittman 1979; Herwig 1987; Smith 1989; Altheide 1980). Other factors that could influence conflict duration, such as the number of people involved in the conflict, will be considered later.

If resources (e.g., armaments, capital, trained military organizations, supplies) have been set aside in advance to be used in the event of conflict, then the effects of the costs of conflict on the conflict process must have a somewhat different interpretation (Bueno de Mesquita 1981). Such reserves greatly reduce or eliminate the new costs of continuing conflicts and would thus influence the utility of pursuing conflicts. Specifically, new costs would be relatively small due to the stockpile. Thus, if we assume that perceived benefits are approximately constant, the utility of continuing conflict would tend to be constant as long as the reserves lasted. Because most human conflicts end in surrender or compromise long before resources are depleted (Morrow 1985), stockpiling becomes a key factor in determining how long conflict can be continued.

A second important characteristic of organizations is that the initiation and continuation of conflict are accompanied by social psychological processes that tend to increase the perceived value of the organization to its members. In general, the organization tends to exalt its virtues and values while vilifying and denigrating the opponent. For example, during wars, various forms of propaganda (e.g., slogans, songs, pamphlets, films, books, clubs) appear that serve these functions (Herwig 1987; Smith 1989; Qualter 1962; Lavine and Wechler 1940). The effect of this characteristic is to increase the perceived value of the organization and thus the perceived benefit of continuing a conflict that promotes and defends those ideals. The effects of propaganda accumulate over time. Because perceived benefits increase, this characteristic of organizations tends to increase the utility of continuing conflicts while they are under way.

Taken together, the characteristics of stockpiling and propaganda can have a significant impact on how the perceived utility of continuing conflict changes during the events. With new costs reduced through stockpiling practices and perceived benefits increased due to phenomena such as propaganda, the perceived utility of continuing conflict should increase while it is under way. In other words, the longer a conflict lasts, the less likely it is to be terminated. This corresponds to conflicts becoming "entrenched" (Rubin and Smith 1991) and resistant to resolution.

This application of utility theory thus makes different predictions regarding changes in the likelihood of conflicts ending, depending on the level of institutionalization of the conflict. In conflicts between formal organizations (i.e., wars and strikes), the likelihood of conflicts ending should decrease



550 JOURNAL OF CONFLICTRESOLUTION

while they are under way. In less formally institutionalized conflicts without extensive stockpiling and propaganda (i.e., family arguments and riots), the likelihood of conflicts ending should increase while they are under way. The

prediction that institutionalized conflicts are less likely to end the longer they last provides a theoretical explanation of why so many strikes and wars become bitter, destructive, and extended confrontations.

Previous analyses of the durations of wars (Horvath 1968), strikes (Rubin and Smith 1991; Kennan 1985; Lancaster 1972; Horvath 1968), and family arguments (Vuchinich, Teachman, and Crosby 1991), though focused on other issues, have reported changes in the probability of these conflicts ending that are consistent with predictions derived above. Although these studies are supportive of the theory developed here, they applied such a variety of theoretical and methodological approaches that an integrated analysis is necessary for an adequate test. The use of different data sets for strikes, wars, and family arguments and the addition of an analysis of riot durations provides verification and expansion of the previous empirical work on conflict duration.

Wars, strikes, riots, and family arguments are all direct confrontations in which parties make overt attacks on each other, intending to cause harm or destruction. Such human conflicts are distinct from the negotiations on

disputed issues that precede conflict in all domains. Negotiations involve the airing of grievances, complaints, requests, demands, and so on, carried out

cooperatively with the aim of resolving the problems without resorting to overt conflict. Such negotiations are well known in international relations and labor-management contexts. Analogous, though usually less formal, negotiations also occur in families and in communities where riots might occur. For example, riots in general, and American civil rights riots in

particular, are preceded by years of mounting tensions and efforts by parties to accomplish changes that resolve the tension between groups. Family arguments are preceded by requests, excuses, complaints, and other behaviors that are efforts to accomplish changes in the family situation. In all contexts, after such efforts at negotiation fail, specific events trigger overt conflict. In all types of human conflict, a subset of problems that emerge are not resolved by negotiation and come to be addressed with conflict. This

analysis assumes that the overt conflict process is distinct from the negotiation process.

The primary goal of this article is to test the predictions from utility theory regarding changes in the likelihood of conflicts terminating while they are under way. However, because other characteristics of conflicts may influence their duration, it is important to control for their potentially confounding




impact. Such factors as the number of participants in the conflict, relative resources held by participants, and the issue causing the dispute may influence duration and thus should be taken into account. Several of these factors will be included in this analysis. These are described in the appendix and defined operationally in the Data section.

METHODS

The most accurate method for testing whether specific variables influence the duration of any kind of episode is the use of hazard models, sometimes known as survival models (e.g., Kalbfleisch and Prentice 1980; Lancaster 1990). In this approach, the likelihood of a transition from being in an

on-going state of conflict to a state of nonconflict is treated as a variable

dependent on several other variables in a regression format. Models of this

type have been widely used in previous analyses of conflict duration (Horvath 1968; Lancaster 1972; Kennan 1985; Vuchinich, Teachman, and

Crosby 1991; Rubin and Smith 1991). The likelihood of a transition occur-

ring, the dependent variable in this approach, is the hazard rate. This likelihood is instantaneous in nature due to mathematical convenience and is thus not a probability bounded by 0 and 1. The hazard rate represents the number of transitions that occur in one unit of time.

An important feature of hazard models for this analysis is that they allow

precise detection of changes in the likelihood of transitions occurring while the episodes are under way (e.g., Kalbfleisch and Prentice 1980). This feature

provides a rigorous test of the predictions developed above. Because all four

types of conflict are measured on a time scale (i.e., wars in years, strikes in

days, riots in days, family arguments in seconds), the same type of hazard model can be estimated for each type of conflict. Thus each type of conflict will be analyzed separately, but with the same form of hazard model. This facilitates comparisons across conflict type.

To test our predictions, we examine data on each type of conflict to determine whether the conflict episodes become more likely or less likely to end while they are under way. These models also test for whether this likelihood is constant during all the conflicts. Although a variety of different forms of hazard models could be used, we apply the Weibull specification. The Weibull specification is commonly used in social science research because it can model hazard rates that increase, decrease, or remain constant over time (Blossfeld, Hamerle, and Mayer 1989; Lancaster 1990; Vuchinich, Teachman, and Crosby 1991). Weibull hazard models have been used in




TABLE 1

Means and Standard Deviations for Variables

Variable Mean Standard Deviation

Civil disorders Duration (days) 2.14 1.53 Size of disorder 0.40 0.49 Percentage of Black population 0.19 0.14 City population (x 1,000) 805.82 1,562.05

Family arguments Duration (seconds) 8.04 6.37 Number of participants 2.28 0.66 Relative power .50 0.93 Prior conflicts 3.41 3.55 Wave of observation 0.40 0.53 Family structure 0.45 0.53

Wars Duration (months) 22.24 28.22 Number of nations 2.96 3.22 Population ratio 2.13 9.88 Year 1900.04 48.09

Strikes Duration (days) 33.47 42.45 Number of workers idled 37,090.34 57,338.28 Dispute issue 0.71 0.46 Type of industry 0.18 0.39

previous analyses of conflict duration (e.g., Horvath 1968; Morrison and Schmittlein 1980; Rubin and Smith 1991; Vuchinich, Teachman, and Crosby 1991).

The Weibull model we estimate takes the following form:

h(tlX) = hp(ht)p- leX (1)

where h(t) is the hazard rate at time t, h is a baseline hazard rate, Xis a vector of covariates, P is a vector of coefficients indicating the effects of the covariates on the baseline hazard rate, and p is a scale parameter that determines the speed and direction of change in the baseline hazard rate. For 0 < p < 1, the hazard rate decreases monotonically. For p > 1, the hazard rate increases monotonically. Forp = 1 the Weibull distribution becomes equivalent to an exponential distribution in which the hazard rate is constant across time.

Our predictions are tested by considering estimates of the scale parameter, p. For institutionalized conflict (wars and strikes), we expect the value of p to be less than 1 (e.g., the hazard of ending a conflict decreases over time). For




noninstitutionalized conflict (riots and family arguments), we expect the value ofp to be greater than 1 (e.g., the hazard of ending a conflict increases over time). Figure 1 depicts hazard rate processes with p = 1.5 (Curve A), p = 0.5 (Curve B), andp = 1.0 (Curve C). The regression coefficients in P indicate the tendency for a measured characteristic of a conflict to increase (positive coefficients) or decrease (negative coefficients) the likelihood of the conflict ending at any time during the episode.

Although the Weibull model has been widely used to model duration dependence in hazard rates, it is well known that unobserved characteristics in the sample can artifactually create the appearance of a hazard rate that declines with duration (Heckman and Singer 1985; Petersen and Koput 1991). This occurs when some characteristic of conflict, which is not measured in the analysis, causes those conflicts that have that feature to end more

quickly than other conflicts. When all the conflicts are analyzed without

taking that characteristic into account, it appears that the hazard rate for the whole sample decreases over time because those conflicts with the characteristic terminate sooner than the others. Those that remain end at a slower rate, leaving the statistical impression that the hazard rate declined for the sample as a whole. In fact, the hazard rate was constant for all cases in the sample, but one subgroup had a higher constant hazard rate than another. This circumstance is known as a problem of "unobserved heterogeneity" (Heckman and Singer 1985). Fortunately, such unobserved heterogeneity cannot artifactually produce the

appearance of a hazard rate that increases while conflicts are under way. To a certain extent the problem of unobserved heterogeneity is similar to

the problem of properly specifying any statistical model, especially those

involving regression. A variable that was not included in the analysis might have a large effect if it were included, which would alter the interpretation of the results. Thus this issue is present in any regression analysis, and can never be completely overcome. But, because we posit a decrease over time in the rate at which institutionalized conflicts end, we must be especially sensitive to the possibility that unobserved heterogeneity could generate such a result. Methods are available to address this issue in hazard models. Several

approaches have been developed for taking unobserved heterogeneity into account (e.g., Heckman and Singer 1985; Hannan and Freeman 1989). Though work continues to improve these techniques, the application of a

gamma distribution has been widespread and is used because of its flexibility in diverse applications (Hannan and Freeman 1989; Blossfield, Hamerle, and

Mayer 1989). We take this approach. It adds some statistical complexity to the analysis, but it improves our ability to take into account the considerable

diversity in the data sets being examined and reduces concerns about

artifactually declining hazard rates.




A

/ C /I I I I B I

1 2 3 4

Time

Figure 1: Hazard Functions for the Weibull Distribution

In order to introduce a control for unobserved heterogeneity, first rewrite

equation 1 as follows:

h(tX) = hp(ht)P - 1 l exP, (2)

where Q2 is a nonnegative random variable representing unobserved hetero-

geneity across cases. For convenience, Q2 is assumed to have an expected value of 1. Thus the expected value of equation 2 is h(tlX). It is sometimes useful to consider Q as a "mixing distribution" that accounts for the different

weighting of cases due to unobserved variations in the baseline hazard rate. It is the choice of distribution for Q2 that determines the nature of unob-

served heterogeneity being modeled. For our purposes we choose a gamma distribution because of its flexibility. The gamma distribution can fit a wide

variety of different hazard rates within its parametric restrictions (e.g., from a J-shape to a symmetric unimodal shape). Additional information on the

gamma distribution is provided by Kalbfleisch and Prentice (1980) and Hannan and Freeman (1989).

As indicated by several researchers (Blossfeld, Hamerle, and Mayer 1989; Hannan and Freeman 1989), if the underlying hazard rate follows a Weibull distribution, with unobserved heterogeneity following a gamma distribution, the observed hazard rate will be distributed according to a generalized gamma distribution. The shape of the generalized gamma distribution is determined by three parameters, h, a = p- 1, and k. Assuming a Weibull



Vuchinich, Teachman /INFLUENCES ON DURATION 555

distribution for the underlying hazard rate, values of k not equal to 1 indicate the presence of unobserved heterogeneity (if k = 1 the model is equivalent to a Weibull model) and (-' =p is the scale parameter of the Weibull distribution. In other words, in the presence of unobserved heterogeneity, c'4 indicates whether the underlying hazard rate increases or decreases over time. Hannan and Freeman (1989, 188-91, 252-53) provide an extended discussion of this point. In our analyses we estimate both Weibull and generalized gamma models for the rate at which conflicts end. Following the discussion above, we interpret c-1 taken from the generalized gamma distribution as the scale parameter of a Weibull distribution controlling for unobserved heterogeneity.

The models for strikes, family conflicts, and wars are all estimated using PROC LIFEREG (SAS Institute 1985), which allows both Weibull and generalized gamma distributions to be fit. The estimation procedure for these models must assume that few cases in the data have the same duration of conflict (Kalbfleisch and Prentice 1980). Given the presence of many tied durations for riots (because riot duration was measured only to the nearest

day), we used a grouped-data algorithm available in the SURVREG statistical

program (Preston and Clarkson 1983) for estimating a Weibull model. A similar algorithm is not available for estimation of the generalized gamma distribution. However, the control for unobserved heterogeneity is less

important in this case because we postulate that the rate at which riots end increases over time. Estimates in Tables 2 and 3 are given in terms of the hazard models described above, which are simple transformations from survival model estimates output by SAS LIFEREG (Hannan and Freeman 1989).

DATA

Analysis of conflict episodes requires careful attention to when they begin and end. Previous research has recognized and effectively dealt with this issue for wars (Small and Singer 1982), strikes (Horvath 1968), family arguments (Vuchinich 1987) and, with somewhat less precision, civil disorders (Snyder and Kelly 1977). Most conflict episodes have recognizable beginnings, a period of sustained conflict, followed by cessation of opposi- tion. Coding rules have been developed in each data source to specify what defines a conflict episode and what distinguishes a normal pause in hostilities

(e.g., soldiers sleeping at night during a war) from a conflict ending. Multi-

collinearity considerations limited the variables that were included in the

multiple regression analysis.




TABLE 2

Hazard Model Estimates for Civil Disorders and Family Argumentsa

Variable Weibull Model Generalized Gamma Model

Civil disorders Size of disorder -0.46** (0.09) Percentage of Black population 1.17* (0.38) Total city population 0.00 (0.00) Weibull shape parameter (p) 1.53** (0.15) Baseline parameter (h) 0.17

Log likelihood -208.28 Family arguments

Number of participants -0.73** (0.23) -0.98** (0.28) Relative power 0.11 (0.10) 0.02 (0.12) Prior conflicts 0.01 (0.01) 0.01 (0.02) Age of child 0.20* (0.09) 0.11 (0.10) Family structure 0.23* (0.11) 0.16 (0.11) Weibull shape parameter (p) 1.62** (0.06) 1.68** (3.83) Gamma parameter (k) 9.76** (3.83) Baseline parameter (h) 0.26 0.43

Log likelihood -436.72 -390.85

a. Standard errors are in parentheses beside estimates. *p < .005; **. p < .01.

WARS

Small and Singer (1982) provide a thorough, well-documented compila- tion of information on wars from 1816 to 1980. They define war as "sustained

military hostilities between regular armed forces of two or more states

resulting in 1,000 or more battle fatalities" (p. 35) and coded historical records for war accordingly. Their sample includes 110 wars between different countries, with the duration of each measured to the nearest tenth of a month. They provided only mean durations for the civil wars in their sample, so civil wars will not be included in this analysis. Small and Singer include the following information on each war that will be used as covariates in the

regression for wars: the number of nations involved in the war; population ratio measured by dividing the population of the larger nation in the war by the population of the smaller (if more than two nations were involved the ratio of the populations of the two largest opponents was used); year indicated

by the year the war began minus 1816 to begin the scale at zero. The number of nations will be used as an indicator of how many system participants were involved in the war (using raw population yielded similar results). To ensure consistent coding, only the 110 wars that had ended by January 1980 and




TABLE 3

Hazard Models for Wars and Strikes"

Variable Weibull Model Generalized Gamma Model

Wars Number of nations 0.02 (0.02) 0.02 (0.02) Population ratio 0.01 (0.02) 0.01 (0.01) Year 0.00 (0.01) 0.00 (0.03) Weibull shape parameter (p) 0.74** (0.05) 0.69** (0.07) Gamma parameter (k) -2.48 (1.39) Baseline parameter (h) 0.13 0.17 Log likelihood -219.34 -218.85

Strikes Number of workers idled -0.00 (0.00) 0.00 (0.00) Dispute issue -0.65** (0.19) -0.81** (0.24) Type of industry -0.18 (0.20) -0.20 (0.14) Weibull shape parameter (p) 0.86** (0.04) 0.80** (0.03) Gamma parameter (k) - 19.97 (14.51) Baseline parameter (h) 0.04 0.07 Log likelihood -521.31 -509.89

a. Standard errors are in parentheses beside estimates. *p < 0.05; **p < 0.01.

were coded by Small and Singer will be included. The wars ranged in duration from 0.2 to 122 months.

CIVIL DISORDERS

A civil disorder is defined as an incident involving crowd behavior where damage to person or property occurs. These episodes are usually referred to as riots. These volatile, sometimes chaotic, events may involve conflict between two or more groups within a community, or conflict between groups in the community with police or National Guard. Data on the duration of civil disorders is drawn from two sources. First is a survey on civil disorders obtained from the mayors or chiefs of police in 128 U.S. cities commissioned by the Government Operations Committee of the U.S. Senate (U.S. Senate Hearings 1967). Detailed data was collected on civil disorders that occurred from 1965 through 1967. The published table, "Major Riots, Civil-Criminal Disorders" (U.S. Senate Hearings 1967), includes the duration of each riot to the nearest day and many other details. But it includes only police reports for the cities surveyed and does not include smaller disorders. To obtain a more complete sample, and to cross-check the subcommittee data, the




1965-1967 data in the Civil Disorder Chronology of the Congressional Quarterly (Legislative Reference Service 1967) were used. When there were discrepancies between the two sources, the Congressional Quarterly data were used. These sources used damage to persons or property as the key coding criterion, as well as racial problems as a motivating factor. Damage included death or serious physical injury requiring medical treatment, and substantial property damage. Both of these data sources have been used in previous studies of civil disorders (Spilerman 1976; Wanderer 1969; Snyder and Kelly 1977) and their validity has been verified (Snyder and Kelly 1977). These data sets allowed the following information to be included in this analysis: size of the disorder measured by whether the disorder involved less than 200 participants (coded as 0) or more than 200 participants (coded as 1); the population of the city where the disorder occurred, taken from the 1960 census; percentage of blackpopulation measured by the number of blacks in the city divided by the total city population in the 1960 census. The pooled sample includes the duration of 159 civil disorders that were attributed to racial problems. These ranged from 1 to 9 days in duration.

STRIKES

Strikes are incidents of voluntary work stoppage based on union-

management disputes. The duration of U.S. strikes to the nearest day for strikes involving 10,000 or more workers is reported in the annual Analysis of Work Stoppages (Bureau of Labor Statistics 1967-1980) along with other information on each of these stoppages. Only a few lockouts are included in these data. Detailed data were not available for smaller strikes. These reports from 1967 through 1980 provide information on 309 strikes. For each strike the number of workers idled, the type of industry in which the strike occurred (coded 1 for manufacturing, 0 for others), and the type of dispute (coded 1 for wage disputes, and 0 for others) on which the stoppage was based were included in this analysis. These ranged from 1 to 315 days in duration.

FAMILY CONFLICTS

Several studies have found that the beginning and ending of verbal-conflict

episodes can be reliably located (Patterson 1982; Vuchinich 1987) and timed

(Shantz 1987, 286; Vuchinich, Teachman, and Crosby 1991; Reid 1986). Data on the duration of verbal family conflicts were taken from a previous study of conflict episodes that were videotaped during routine family dinners in the homes of 38 different families (for details, see Vuchinich,



Vuchinich, Teachman / INFLUENCES ON DURATION 559

Hetherington, Vuchinich, and Clingempeel 1991; Hetherington and Clingempeel 1992). Family arguments were defined as a sequence of verbal behaviors, involving at least two family members, in which the parties overtly and directly opposed each other with verbal attacks. These included insults, threats, challenges, disagreements, and so on. The duration of these se- quences in seconds was timed from the videotapes. A longitudinal design was used so that one dinner was taped when the mean age of the children was 10.5 years (coded as 0) and the second dinner was taped one year later (coded as 1).

For the present study, the duration of each conflict episode was timed to the nearest tenth of a second using a microcomputer timing program. The duration of 427 conflict episodes is included in this sample. The following additional information on each family argument was included in the regression analysis: the number of family members who took part in the conflict, the relative power of the participants in the conflict, determined by whether the argument was cross-generational (i.e., between a parent and child, coded 1) or within generations (coded 0); number of prior arguments that took place in that dinner; age of the child coded as younger (mean age 10.5 years) versus older (mean age 11.5 years; parents were also a year older in the second category); and family structure (intact family coded as 0, stepfamily coded as 1). These conflicts ranged from 2 to 55 seconds in duration. Table 1 gives descriptive statistics for all variables used in the analysis.

RESULTS

Tables 2 and 3 give the estimates for the hazard models. In all four types of conflict, Weibull models fit significantly better than exponential models (not shown), indicating that the hazard rate was not constant as the conflicts were under way. The difference between the log-likelihood values for two nested models (e.g., Weibull and generalized gamma) was used as the basis for a likelihood ratio chi-square test for whether one model fits significantly better than another (Hannan and Freeman 1989).

Table 2 gives the estimates for civil disorders and family conflicts. The

log-likelihood statistics for family conflicts indicate that the generalized gamma model provided a significantly better fit than the Weibull model (X2 = 91.74, df= 1). The k parameter indicated that unobserved heterogeneity was

present. With this taken into account, the Weibull shape parameter (p = 1.68, calculated from a = p-~ = 0.59 with standard error 0.021) indicated that the hazard rate for family conflicts increased while they were under way. The




estimate of the shape parameter in the Weibull model for civil disorders was also significantly greater than 1.0 (p = 1.53). Thus the hazard rate for civil disorders and family conflicts increased during these episodes.

The coefficient estimates in Table 2 indicate that the number of participants had a substantial effect on how quickly civil disorders and family arguments ended. For both types of conflict, the involvement of more participants was associated with conflicts of longer duration. Having more than 200 people in a civil disorder decreased the tendency for it to end at any given time by 37%, (e-98 - 1)100. Each additional participant in a family argument decreased by 52% the tendency for the conflict to end. None of the other variables had a consistent significant effect.

Because the same families contributed more than one conflict to the sample, the independence of each episode was in question. To test whether this biased the estimates, a dummy variable for each family was added to the hazard model so that family effects were taken into account. This resulted in only trivial changes in the estimates reported above, and no changes in significance levels.

Table 3 gives the results from the hazard models for wars and for strikes. The chi-square tests showed that the generalized gamma model provided the best fit for strikes (X2 = 22.84, df= 1), as has been found in previous research (Rubin and Smith 1991). However, the generalized gamma was not significantly better for wars than the Weibull model. In both the war and strike models, the Weibull shape parameter was significantly less than 1.0, in sharp contrast to the civil disorder and family argument models. This is evidence that in these conflicts the hazard rate decreased while the conflicts were under way. This supports our thesis that an entrenchment process charac- terizes wars and strikes.

In the models for wars and strikes, the number of participants had no significant effect on conflict duration. The duration of strikes was significantly influenced only by whether the strike was based on wages. Strikes based on wages were 55.6% less likely to end at any given time than were other strikes. This is consistent with previous work on issues that precipitate a strike (Kennan 1985; Rubin and Smith 1991).

To assess overall goodness of fit of these models, we used simple Weibull models without regressors or heterogeneity controls to estimate how many conflicts would be expected to survive until eight points in time. These points were determined by dividing the duration of the longest conflict in each type by eight so that the eight points would be evenly distributed for each conflict type. The above regression results were used to divide the samples according to the variables that had a significant effect on duration. So, for example, wage-based strikes were analyzed separately from other strikes. The number




of observed conflicts that survived to each time point was compared with the number expected from the Weibull survival model in a simple chi-square test (Horvath 1968; Heckman and Walker 1989). This is possible because a Weibull survival model is a simple mathematical transformation of a hazard model. As had been found previously for strikes and wars (Horvath 1968), the Weibull models generated expected values not significantly different from observed values, at the 0.05 level. Probabilities of the chi-square statistic ranged from 0.10 to 0.80.

Figure 2 gives graphs of the specific changes in the hazard rates during the conflicts indicated by the models. These are the changes estimated after the effects of independent variables and unobserved heterogeneity have been taken into account. This figure shows that, during the time spans considered in this study, the hazard rate for riots more than doubled; for family arguments it increased six fold; for wars it decreased by about half; and for strikes it decreased by about 40%. The magnitude of these changes suggests that a more rigid conflict process governs the termination of strikes and wars.

DISCUSSION

This study reviewed previous research and presented new data analysis that found that the likelihood of conflict ending decreases during wars and strikes, but increases during riots and family arguments. We showed how this result is consistent with the principle that conflicts are extended until the

perceived utility of continuing is less than the perceived utility of stopping the conflict. Central to this duration analysis were two key factors that constrain the perceived costs and benefits of continuing conflicts once they are started-stockpiling and propaganda.

The analysis shows that strikes and wars tend to become entrenched, and are less likely to end, the longer they last. From one standpoint this is an

example of the kind of "collective irrationality" often associated with arms races and prisoner's dilemma games (e.g., Fischer 1981; Schelling 1978; McGinnis 1991). Similar to these classic scenarios, extended conflicts seem to waste resources unnecessarily. There is some face validity to the collective

irrationality interpretation from the individual or moral perspective. But

considering the system in which conflicts occur requires attention to ratio-

nality at a different level of analysis (e.g., Bueno de Mesquita 1978, 1981, 1985). Extended conflicts that seriously damage or destroy a given nation, union, corporation, or person do not promote the interests of that unit. But such conflicts may be in the best interests of some part for that unit or a larger system. For example, it may be in the best interests of a nation's economy (a



562 JOURNAL OF CONFLICTRESOLUTION

Civil Disorders

2 3 4 5 6 7

Days

Wars

1 2 3 4 5 6 7 8 9

Years

0 60 120 180 240 300 360

Days

Figure 2: Hazard Rate Graphs

Arguments

0.5

0.4

Hazard Rate 03

0.2

0.1

Seconds

Strikes

0.12

0.1

0.0O

Hazard Rate

0.0O

0.04

0.02

0.03

0.025

0.02

0.015

0.01

0.005

;,???



Vuchinich, Teachman /INFLUENCES ON DURATION 563

larger system) for a weak company to be damaged or destroyed. The systemic benefits of this survival-of-the-fittest logic have been well described and suggest that what may appear to be irrational at a microlevel of analysis may be rational at a different systemic level (e.g., Wilson 1990; Hannan and Freeman 1989).

The competitive nature of most economic and political systems, taken together with the distinctive features of formal organizations that allow them to accumulate resources and execute long term preparations for conflict, may create conditions that require such mechanisms as stockpiling and propaganda for survival in those systems. Because these conditions are not prom- inent in more informal community and family systems, riots and family arguments do not exhibit an entrenchment pattern. This is one plausible explanation that shows how specific features of a systemic unit can determine

aspects of the conflict process, such as duration. This report considered several factors that could influence conflict dura-

tion. The results showed that riots and arguments that involve more people last longer than those with fewer people. But size had no effect on war or strike duration. As found in prior work (Rubin and Smith 1991; Kennan 1985), strikes based on wage disputes last longer than other strikes. Though dispute issue was not included in the analysis of other conflict types, the results for strikes

suggests that such analysis would be informative. Categorizing conflict issues

may not be as straightforward in other conflict types but could reveal important dimensions of what is valued in different social systems. Progress has been made

regarding analysis of the issues involved in wars (Diehl 1992). This analysis expanded the study of conflict duration to four different

types of conflict. Data for three of these (strikes, riots, and family arguments) were drawn from one society (i.e., the United States). It is thus possible that some of the results are culture bound. Data on these conflicts, from other cultures, could be used to test this. Though many other variables not included in the analysis could potentially influence duration, the statistical tests used here implemented controls that reduce this concern. However, a more precise test of the propositions developed here would include direct measures of the extent of stockpiling and propaganda processes in strikes and wars.

Most wars and strikes end before the resources of all parties are depleted. But if conflicts become highly entrenched to the point of depletion, utility theory would predict an increasing hazard rate after a long period of decline. With no resources left, conflict cannot be continued. Evidence for this pattern has been found for strikes (Kennan 1985).

This study suggests that organizations and individuals evaluate the utility of continuing conflict while it is under way. This means that interventions that effectively increase the perceived costs and/or decrease the perceived




benefits of continuing conflict are most likely to be successful in reducing the duration of conflict episodes. This is not news to labor-management and international negotiators, but it does provide a theoretical and empirical basis for conflict resolution efforts in strikes and wars that have this focus. In addition, hazard models of conflict duration can empirically specify what factors tend to make conflicts most resistant to resolution.

This analysis has different practical implications for different types of conflict. Prospects for reducing riot duration are problematic due to the difficulty in predicting exactly when and where riots will occur and the problem of mounting intervention efforts before they are over. Family arguments, on the other hand, recur among the same people over a long period of time, and intervention efforts are feasible. In addition, the duration of family arguments are apparently responsive to both the increasing costs of extended conflict and the number of people involved. They thus might be expected to be less rigid and more open to intervention efforts. Indeed, family therapy can be effective in reducing the amount of family conflict (e.g., Hazelrigg, Cooper, and Borduin 1987).

The effectiveness of interventions in family conflict duration may be due in part to the size of the group involved. The maintenance of larger groups may simply require more rigid structures that present special challenges to

any intervention. Nonetheless, a better understanding of the processes and variables that constrain conflict duration holds some promise for aiding efforts at resolving conflicts involving groups of any size.

APPENDIX

Below is a description of the variables that might be expected to influence conflict duration. These variables are operationally defined in the Data section and included in the statistical analysis.

NUMBER OF PARTICIPANTS

One relevant feature of all types of conflict is the number of participants involved in a conflict episode. This variable can be measured with reasonable accuracy in wars, strikes, civil disorders, and family arguments. In general terms, the involvement of more people in a conflict implies a larger social investment in the conflict. Once mobilized into conflict, larger groups should be more difficult to defeat and more able to extend the duration of conflict. This suggests that more participants in conflict should be associated with longer conflicts.




It is also desirable to consider the possible influence of the relative number of participants on each side of a conflict. This is often an indication of the resources available to each side. When one opponent greatly outnumbers the other, a mismatch occurs and the conflict should be decided quickly, with the larger opponent winning. Available data allow this to be considered for wars and family arguments if we assume that parents usually have more resources than children. But this is not easily concep- tualized in the case of strikes and riots. Another issue is that the number of participants may change while a conflict is under way. Although hazard models allow this to be taken into account (i.e., as time-varying covariates), data on these changes for sufficiently large samples of conflict episodes are not available. Within these limitations, the analysis can provide initial estimates of the effect of size of conflict on how quickly conflicts end.

EFFECTS ON WAR DURATION

Two factors that could influence the likelihood of a war ending are the relative size of the two main opponents and the year it occurred. When the size or resources of opponents are mismatched, earlier termination of the conflict would be expected, as the stronger nation should quickly defeat the weaker. Technological advances have led to weapons of mass destruction. More rapid and extensive destruction in wars could result in shorter wars because the enhanced destruction depletes resources more

quickly. Thus, assuming other factors are equal, more recent wars would be expected to end more quickly due to technological advances.

There is evidence that strike duration is influenced by the industry in which the strike occurs (Lancaster 1972; Rubin and Smith 1991), and the basis (e.g., wages, work conditions) of the strike (Kennan 1985; Rubin and Smith 1991). Strikes in the

manufacturing industries have been found to last longer than those in other industries (Lancaster 1972), although it has not been established whether this is because of the size of the unions or historical factors. The analysis will control for this distinction (i.e., manufacturing industry vs. other industries).

Labor strikes can occur over a range of issues. Wage levels are related to central concerns of both labor and management, such as company profit and worker satisfac- tion. The general importance of the issues involved in conflict in exchange terms has been addressed (Coleman 1991). Strikes involving wage issues may be more difficult to resolve, thus resulting in longer strike durations (Kennan 1985; Rubin and Smith

1991). This analysis will control for conditions of a strike (i.e., wage-based vs. other).

EFFECTS ON RIOT DURATION

There is little previous work on factors that influence riot duration. Since this

analysis focuses on civil disorders based on racial issues, we will include the

percentage of black population in the city where the riot occurred in the models as a control. Presence of more members of the minority group could lead to extended riots because of higher levels of solidarity. Previous research on riots has included such




factors (e.g., Spilerman 1976). Violence is often more prevalent in large urban areas. The larger populations in urban areas may make the expansion and extension of riots more likely, so city population will also be included as a control.

EFFECTS ON THE DURATION OF FAMILY ARGUMENTS

This analysis will control for effects of the age of children, family structure (i.e., intact family with both biological parents vs. stepfamily), and the frequency of prior conflicts during the dinner. More extended conflicts would be expected with adoles- cent children, in stepfamilies, and when there were more frequent prior conflicts that aroused negative feelings (Vuchinich, Hetherington, Vuchinich, and Clingempeel 1991). In addition, the relative power and resources of conflict participants will be considered by indicating whether each conflict was cross generational or within

generations. Assuming that parents generally have more power than their children, cross-generational conflicts have an asymmetrical balance of power between opponents whereas within-generation conflicts are more balanced.

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Documents

Influences on the Duration of Wars, Strikes, Riots, and Family Arguments