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Social Influence Network Theory: Toward a Science of Strategic Modification of Interpersonal Influence Systems Noah E. One& Depar~nent of Sociology University of California, Santa Barbara Abstract Social influence network theory is a mathematical formalization of He process of interpersonal influence that occurs In groups, affects persons' attitudes and options on issues, arid produces mte~persona] agreements, including group consensus, from an initial state of disagreement. The theory also may be employed to predict the consequences of particular modifications of a social influence system. A Ascription of social influence network theory is presented. Using network data from a field study of a policy group, simulated modifications of an influence system and Me consequences of these modifications are described The illusion introduces a large subject: Be development of a scientific basis for constructing and modifying Be social structures of groups so Cat Be expected outcomes of Be influence system of a group will be close to desirable Open al outcomes for tile group win some pre- specified degree of reliability. Toward Be development of such a science and within the framework of social influence network theory, some key lines of research are outlined Cat are related to Be operation and s~uc~al dynamics of ~nte~person~ influence networks and ~at, In my view, would advance Be development of a science concerned wad Be strategic modification of interpersonal influence systems. ' Direct all correspondence to Professor Noah E. Friedkin, Depar ment of Sociology, University of California, Santa Barbara, CA 93106. Emma: frie~king~soc.ucsb.edu. URL: .httF':.'flvlY~& .soc.ucsb.ed~ffacu.ItY..'6iedl;.irr ' DYNAAIC SOCIAL NT:TWORKAlODE~WG ED ISIS 89

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go 2 1.1 INTRODUCTION In this paper I briefly describe a Atonal theory of the Connation of attitudes and options, including the production of consensus, in a network of interpersonal influences. Lois theory has been advanced in successive generalizations Tom the 1950s to Me present by social psychologists and mathematicians concerned win developing a formal mode! of how consensus is produced in groups through nterperson~ interactions (se Groot 1974; French 1956; Fnedkin and Johnsen 1990; 1999, Haraly ~ 959~. The theory incorporates an assumption on which Were ho been a remarkable convergence of independent theoretical work: that persons integrate conflicting attitudes and opinions as if they were upping a "cognitive algebra" of weighted averaging (Anderson 1981~. The integration is triggered by Me display of differences of opinion and Me susceptibiii~r of persons to Persona influences (in essence, a social comparison tugger) in which the pursuit of "correct" or "satisfic~ng:' positions on an issue takes into account the current positions of others on Me issue. Persons' efforts to integrate discrepant influences arid to form socially validated positions on issues often occur in a s~uct~al context, mat is, in a more or less complexly configured network of impersonal influences. This network` has profound effects on Me course of the opinion change process and the revised positions Mat persons may settle on. The content of pemons' equilibnum positions on an issue, Me efficiency wad which tills content is produced, and Me relative net influence of each group member on others depend on Me structure of the influence network in Me group. Social influence network theory describes how a network of inte~person~ influence enters into He process of inte~person~ influence on attitudes and opinions in a group, and it allows an analysis of He way in which He structure of He influence network of He group has shaped individual and group-level outcomes. Social influence network theory offers a dis~ncHy sociological perspective on the attitude and opinion change process; it is a realization of a structural social psychology Hat was at the core of social psychological work in psychology in the 1950s and 1960s, during He flowering of He group dynamics field, but Hat currently is not being addressed by the more cogn~nvely-onented generation of psychologists. Festinger, French, Newcomb, and Cartwright, among other founding members of modern social psychology, were social network analysts who sought to build a theoretical foundation for social psychology in which network structures figured prominently; these social psychologists underwood the potential importance of social networks in He development of a science of group dynamics but their agenda was derailed by He cognitive revolution in psychology. Social network analysis has grown rapidly since He 1970s, especially in sociology and anthropology and, most recendy, in schools of business. The line of work on social influence network theory Hat is the focus of He present paper is a contnuat~on of He classical agenda of He group dynamics field to understand He mechanisms aIld Euchres entailed in He process of attitude and opinion change and consensus ~ . . proc auction in Soups. The present paper is a first effort to bring social influence network theory to bear on the development of a scientific basis for conseucung aIld modifying He social structures of groups so Hat He expected outcomes of He influence system of a group can be made close to desirable optimal outcomes for He group win some pre-specified degree of reliability. My treatment is schematic and introductory. Fit ~ briefly describe social influence networl: Peony. Second, using network data Dom a field study of a policy grow, ~ describe several simulated modifications of an influence system arid He DYNAMIC SOCIAL NETWORK MODELING ED THESIS

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3 consequences of these modifications. Third, within the framework of social influence network Peony, lines of research are outlined Cat are related to He operation and structural dynamics of interpersonal influence networks and that, In my view, would advance He development of a science concerned wad He strategic modification of inte~person~ influence systems. 1.2 SOCIAL INli[UENCE NE1~VORK THEORY There are several lines of work in social psychology on so-called "combinatorial" theories of consensus fommation and group decision-making that focus on how agreements are formed in groups when there is an initial state of disagreement on an issue (Davis 1973; Fne& and Johnsen 1990; 1999; Latane PHI; ~996; Laughlin ~980; Stasser, weir, and Davis ~989; Witte and Davis ~996~. My colleague, Eugene Johnsen, and ~ have developed one of these comb~natonal thrones social influence network theory (Fnedkin 1991; 1998; 1999; Friedkin and Johnsen 1990; 1997, 1999~. Social influence network theory includes as special cases French's formal theory of social power (French 1956; Harary 1959) and DeGroot's consensus formation model (Berger 1981; Chatterjee and Seneta 1977; DeGroot 1974). The theory has close formal relationships with the rational choice model of group decision making proposed by Lehrer and Wagner (Lehrer and Wagner 1981; Wagner 1982; 1978), the social decision scheme model for quantitative judgments proposed by Davis (1996), and the infonnation integration model of group decision making proposed by Graesser (1991). The theory is formally consistent with Ande~on's weighted averaging model of information integration (Anderson 1981; Anderson 1991; Anderson and Graesser 1976). It also has a close formal relationship wad an interdisciplinary tradition in statistics that includes work in geography, political science, and sociology on models of He interdependence of persons and spatial units (Anselin 1988; Doreian 1981; Duncan and Duncan 1978; Duncan, Hailer, and Fortes 1968; Erbnng and Young 1979; Fne& 1990; Marsden arid Fne& 1994; Ord 1975~. Social influence network theory describes an influence process ~ a group of N persons in which He members' attitudes and options on an issue change as they revise they positions by taking weighted averages of the influential positrons other members: y,f'+O = a'Twi,y(') + Wj2y2 )+...+Wj~vyt it+ (1 -aj)y; (1) for ~ = 1,2,. and each of the N persons in the group, i = 1,2,. , N . The opinions of persons at hme are ye') ,Y2'),.~.,Y(') and their initial opinions are' ,Y20,.. SYNC The set of influences of the group members on person i is {w;,, W,2,. ~ W;N}, where 0 < wy < 1, and ~,j wjj = ~ . The susceptibility of person i to the influence of others is a;, where 0 < a; ~ 1 and al = 1- wit . Thus, a person's susceptibility is equated to the aggregate weight of He interpersonal influences on him or her (i.e., a; = Hi, wjj ). Social influence network theory rests on a model of how individuals cognitively integrate hi confllichng opinions, EM (1), but the outcome of this process depends on the social structure in which the process occurs. This social structure consists of He set of members' initial positions, interpersonal influences, arid susceptibilities to influence. In a group of ~ persons, the system of equations described by Eqn. (1) can be represented as ye'+ ~ = AWy ~ ~ + (I - A)y (2, DYNAMIC SOCIAL NETWORK MODELING AND ANALYSIS 91

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4 for t = 1,2,. . ., where y`" is a N x 1 vector of persons' opinions on an issue at time t, W = [w;,] is a N x N matrix of interpersonal influences, and A = diag(a, ,a2, ,a,; ) is a Nx if diagonal matrix of persons' suscepubilides to interpersonal influence on Be issue. Under suitable conditions, this process transforms persons' ~ Cal opinions into a set of equilibrium . Opmlons: yams = Vy(l) (3) where V = [vij] is a matrix of red7lced-form coefficients, describing the total or net interpersonal effects that transform the initial opinions into equilibrium opinions. The coefficients in V are nonnegative (O S vjj S 1) and each row of V sums to unity (2,j vij = 1) . Hence, vij gives the relative weight of the ha] opinion of person j in determining the fine] opinion of person i for all i andj. If I-AW is nonsingular' Den Tom EM (2) V = (I - AW)-I (I - A) . More generally' since V(') = (AW )' + [ah, (AW )' ](! - A), for t = I,2,. . ., V can be estimated numerically for a sufficiently large ~ when lim V(') exists. taco Ah equilibrium opinions will be in range of the group members' initial opinions. Equilibm~m opinions may settle on He mean of group members' Weal opmons; Hey may settle on a compromise opinion Mat hem from the mean of initial opinions; Hey may serge on an initial opinion of a group member; or they may settle on altered opinions that do not form a consensus. When a consensus is fanned in a group, V win commonly have He fonn of a sea~aficabon of individual conmbubons~ V= v, ~ v22 van Vi ~ V22 VAN V] ~ \'22 VNN _ In WhlCn each person s 1nlual opinion makes ~ particular relative contnbuhon to dle emergent consensus. The production of consensus is a special case of a larger domain of group outcomes encompassed by social influence network theory, in which stable patterns of disagreements may be formed. Thus, the theory satisfies Horow~tz's criterion Hat "any serious theory of agreements and decisions must at the same time be a theory of disagreements and the conditions under which decisions cannot be reached" (1962, p. 182~. Abelson (1964) was frustrated to find that consents was an inevitable outcome In He broad class of mathematical models Hat he examined, and he touted to simulation models in order to account for equilibrium disagreements. Similarly, the most prominent combinatorial theories in psychology today either do not deal win an account of disagreement (Davis 1996) ornery rely on simulation models (Gigone and Hastie 1996; Latane 1996; Stasser 1988). I believe that it is one of the more useful prejudices of the scientific community that simulation models should be maintained as a last resort after analytical approaches have been exhausted or appear to be intractable. Thus, I abandoned work on a simulation model of attitude and opinion change when it became apparent that a simpler mathematical mode} would suffice. In this light, an Important conmbunor~ of social influence network theory is in 92 DYNAMIC SOCIAL NETWORK MODELING AND ANALYSIS

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demonstration that both consensus and disagreement are consistent wad an analyhcaIly tractable mathematical model. 1.3 ILLUSTRATIVE MODIFICATIONS OF TORI INFLUENCE SYSTEM OF A POLICY GROUP I now briefly ~pOIt some findings from a study of school board policy groups Hat will illustrate one way in which influence systems may be modified to change Be systems' outcomes (Friedkin Forthcoming). In this application, tile fonnal model described by Eqn. (1) was adapted for an account of a binary op~n~or~he preferences of school board policy group members for a flat or compensatory allocation of a school dismct's resources to schools that diner in Me average academic achievement of Me students. The flat preference stipulates Cat schools should receive resources proportionate to Me number of students In a school regardless of their average academic performance. The compensatory preference stipulates Mat schools with low average academic perfonnance should receive more resources than some schools with a higher average performance. Relational, attitudinal and demographic data were collected on five policy groups. In each group, the membership was defined on the basis of a snowball sampling procedure Mat included all persons (school board members, school dismct personnel, and community members) who were reported to be influential in school board decisions during Me year preceding om inquiry. Among He 267 policy group members who were surveyed, He sample was roughly evenly split between persons who preferred a compensatory or a flat allocation pattem; Here was Cal consensus Hat high performance schools should not be over-rewarded at He expense of low performance schools. With data on social network relations (discussion, advice, fiiendship ties) occumng among the policy group members, ~ employed a technique described in Frie& (1998) to obtain a measure of He influence network W. Given a measure of the influence network and equilibnum options, Ye), 'backward" estimates were obtained for the unobserved initial resource allocation preferences of the group members, YE . More precisely, estimates of the unobserved preferences were obtained for the small subgroup of memben whose opinions were influential] in detem~ng equilibrium preferences. The preferences of non-influenhal members cannot be estimated wad this approach and, in any case, are irrelevant to an understanding of group outcomes. The core subgroup of influentials in each of the policy groups was comprised mainly of key central office staff members in He school distnct (the superintendent and other high-level school district administrators), and among these administrators there was disagreement on the preferred resource allocation pattern for He district. Ike interpersonal influences of the core members were projected throughout the network to the other members, including most of the school board members' and He cross-pressures Tom He disagreement among He influentials produced, in each group, a distribution of resource allocation preferences that was roughly evenly split between a flat and compensatory preference. I was able to show wad a s~mulahon Hat He equiiiDn~n dis~buton of allocation preferences is susceptible to substantial modification; i.e., that a change in the initial preference of a core influential could produce a substantial shift in He equilibrium distribution of group members' resource allocation preferences; see Table I. The sulfated modifications were of two sorts: (a) a neutralization of a person's preference in which the person became indifferent rather than positive or negative about a flat or compensatory pattern, and (b) a reversal of preference In which a person switched positions Tom DYNAMIC SOCKS NETWO~MODE~G ED CYSTS 5 93

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6 positive to negative, or vice versa. Of course, reversals of positions had stronger impacts Can neu~ali=tons, but it is s~pns~ng how much of an impact neu~im~aon some~nes had on He equi inn dis~bu~o~ Table 1. Effects of a Simulated Change in He Estimated Initial Position of Each Core Member on the Expected Proportion of the Group Favoring the Flat (F) versus Co mpensato~y (C) Allocation at Equilibrium | Core Member's Estimated Observed Effect ofa Effect ofa ID ~ & Role Initial Equilibrium Neutralization of Switch of Position Position ID's Position on Be ID's Position on the Distribution of Issue Distribution of Issue Positions Positions % Flat Group A (61% Flat) 4 School Board -7.28 C 76 85 15 Central Office -5.76 C 82 92 29 Central Office -3.60 C 75 84 21 Central Office 5.82 F 39 21 34 Central Office 10.25 F 21 6 40Cornmunuty 7.10 F 53 44 Group B (46% Flat) 4 Central Office -2.00 C 52 58 15 Central Office -2.66 C 57 67 41 Central Office -2.22 C 55 63 46 Central Office -1.92 C 54 61 49 Central Office -2.32 C 52 58 60 Principal -11.39 C 57 67 17 Cenual Office 12.98 F 10 2 Group C (54% Flat) 32 Cenual Office -132.28 C 93 95 36 Cenual Office -5.78 C 78 90 50 School Board -7.21 C 69 80 51 Central Office -23.04 C 93 95 39 Cen=1 Office 45.10 F 1 0 43 Principal 8.55 F 42 31 Group D (67% Flat) 25 Cen=1 Office -3.79 C 86 95 49 Cenual Office -267.44 C 98 98 8CenumlOBice 1.18 F 66 64 26 Cen=1 Office 10.35 F 24 8 58 School Board 26.95 F 3 2 Group E (49% Flat) 9 School Board -~.97 C 58 65 20 Cenmal Office -3.67 C 62 73 22 Cen=1 Office -23.91 C 92 95 51 Cenual Office -2.50 C 59 68 66 Principal -3.51 C 60 69 19 Central Office 3.00 F 40 31 65 Community 44.51 F 3 2 - 94 DYNAMIC SOCIAL NETWORK MODELING AND ANALYSIS

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7 1.4 TOWARD A SCIENCE OF STRATEGIC MODIFICATION OF INTERPERSONAL INFLUENCE SYSTEMS A science of sac modifications of influence systems requires Claris on desirable goals, a technology for p~c~ng structural modifications, an undemanding of He possible multiple unintended effects of a modification on Be relevant structure of Me situation, and a confident grasp on the ~eoreucal underpinrungs of Me dynamic features of Me influence system. I now On to a discussion of various outcomes of it fluency systems Cat might be optimized, the modifications of influence systems Mat might be feasible, key problems Cat need to be addressed, and lines of research Cat might be developed on these key problems. 1.4. ~ Manipulatable Outcomes Some influence networks are not consistent wad He production of consensus, or even with He production of a degree of agreement (e.g., a majority opinion) that is sufficient to allow a collective decision. Strategic modifications of an impotence system can be designed Cat will produce a consensus across a variety of issues, or at least a sufficient amount of agreement to allow decisions to be made. Some influence systems win produce consensus with great difficulty over a range of issues Cat anse. Holding constant He initial relative positions of grow membem on issues, He efficiency of consensus production in a group depends on He structure of He influence network. Strategic modifications of an influence structure can be designed that wiD produce consensus more efficiently across a variety of issues, or at least with a sufficient degree of efficiency as the circums ances warrant Some groups reach consents too quickly, short~ircuiting a careful consideration of alternative positions on an issue. The overly-rapid convergence to agreement has been referred to as groupthink plants 1982), and it appears to be associated wad cen - Sized influence networks and homogeneous distnbu~aons of What positions on an issue. Social influence network theory pumice Cat equilibrium opinions are always in the range of the distribution of initial opinions; hence, some heterogeneity of initial positions is crucial to a thorough vetting of an issue. In groups that regularly deal with judgmental issues, for which proper deliberation is important, strategic modifications of a group's influence system can be designed to slow down the process of convergence to consensus and to maximize the degree of initial diversity of opinion, consistent with a sufficient Resee of efficiency. ~ some groups, issues of control by a person or subgroup are crucial. Control loss in organizational hierarchies is a ubiquitous phenomenon that occurs whenever influence is transmitted indirectly from a single authoritative source to a large number of persons via a series of subordinate au~ontes. We have recently analyzed this phenomenon from the perspective of social influence network theory and shown how control loss may be mitigated by the addition of lateral lines of influence among subordinates (Friedkin and Johnsen 2002). The general point is that strategic modifications of an influence structure can be designed Hat will produce a consensus that is more closely representative of the initial preferences of au~ontative sources. The influence system of a group may be made more robust in the sense Hat its outcomes are less sensitive to minor changes in He influence structure or initial opinions. For ~nstar~ce, if the goad were to develop a robust influence system that is insensitive to a switch or neutralization of the position of any one person, Len He strategic problem would be to find a feasible change in He influence sure of DYNAMIC SOCIAL NETWORK MODELING ED ^4YSIS 95

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the group that would make its influence system less sensitive to such idiosyncratic opinion changes. For a fixed pauem of interpersonal influence among He initial positions of group members, Be influence network can be made more robust so that net relative effects of initial positrons are less sensitive or vulnerable to Moor perturbations of Orphan opinion or ~nte~person~ influence. The foregoing outcomes are illustrative of goals that might be viewed as desirable under particular circumstances. In this brief treatment, I do not believe that I have come close to exhausting the potential number of manipulatable outcomes. ].4.2 Feasible Modifications Modifications of an influence system can be made in different ways. The initial attitudes and opinions, Y('), of one or more members may be modified. The direct interpersonal influences, W. including susceptibilities, A, may be modified, holding the structure of nonzero weights in W constant; that is, this type of modification would not alter who influences whom, but orgy the relative weight of some of these influences. Feasible structural modifications also include changes in the persons who are involved in the influence network: Me addition of one or more new members who have particular configurations of interpersonal influences or the loss of one or members. Structural modifications also include changes in the pattern of nonzero interpersonal influences: the addition of new lines of influence, or the loss of extant lines. In some influence systems, slight changes may have large effects; in other systems, obtaining a different outcome from the system might require gross restructuring. Any single set of modifications may affect outcomes over than We particular outcome Bat is being optimized. 1.4.3 Key Problems Sets of applied and theoretical problems need to be addressed in order to develop a scientific basis for modifying influence systems. I describe three problems. First, there is Be practical problem of developing a technology for generating particular modifications of persons' initial aides or options and their susceptibilities and interpersonal influences. Some of the structural components of influence systems may be more feasible to manupulate than others. Second, there is the problem of ascertaining the precision and reliability of the mode! and measures that are employed to predict attitude and opinion changes in interpersonal influence networks. Models and measures need not be precisely accurate, but they should not be seriously misleading; hence we must have a priori estimates of the reliability and precision of the predictions that the model and measures allow. Third, there is the problem of building a mode] of structural interdependency that can be dovetailed wad social influence network theory. The social shuctuTa] components of a group may be interdependent, so that making a change in one component (e.g., an initial position, a susceptibility, an interpersonal influence) may generate changes in other parts of the structure. If ceteris paribus is not a feasible assumption, Men we must have a reliable prediction of Be consequences of making changes In a structure for Be over relevant parts of Be structure. 96 8 DYNAMIC SOCIAL [JETWORKAJODELING ARID ANALYSIS

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9 1.4.4 Lines of Research Certain lines of research are suggested by We problems that ~ have just sketched. ~ do not intend to make a global assessment about what lines of work are most important In the field of social network analysis. The lines of work that ~ describe are important only In Me context of an application of social influence network theory to the development of a science of strategic modification of influence systems. First, there should be filament work on the mathematical fra~nework of social influence network theory mat would test and refine its assumptions about Me influence process. My colleague, Eugene Johnsen, and ~ have published some work on this problem Dine& 1999; FneUkin and Johnsen 1999), and we are hoping to continue to do more work on it. Second, methodological work needs to be done on Me measurement of persons' susceptibilities and interpersonal influences. March and S~mon's work (March 1955; 1956; Sunon 1953) once measurement of ~nte~person~ influence has not been pursued, and my can for more work by social psychologists on Me measurement of influence networks (FneUkin 1990) has not had much of an effect either. ~ regard the stn~c~ral measures of susceptibility and interpersonal influence Mat ~ have developed (Fne~n 1998) as Me beginning of what should be a concerted effort to fill an a~bitarily large Nx N mat w~thv~id and reliable measures of persons' susceptibilities and interpersonal influences. Third' ~eoreucal and empirical work on structural interdependencies also is important, because such work shows how a change in one component of a social structure generates changes in other components. There are extant research programs that deal with interdependency but interdependency is a vague concept that can be defined In different ways, not all of which bean on Me application of social influence network~eo~y. In teens of We application of social influence network Peony, Me relevant interdependencies are defined by two constructs Y(') and W and concern the effects of a change In any part of these constructs on We over parts of either arbor of these constructs. My collaborator and I have recently completed a project (Friedkin and Johnsen Forthcoming) in which the evolution of an influence network is described in terms of persons' Steal set of sentiments about one another as attitudinal objects. Hence, changes In the initial sentiment structure, Y('), may affect the entire structure of W. A research program on an applied science of influence networks cannot be pursued without a broad appreciation of Me various types of work that are unport~t In its development. The program includes applied wow on Me technology of making modifications, me~odolog~cal work on Me development of measures of Bedsores' susceptibilities and interpersonal influences, mathematical work on mode} development and refinement, experimental wow Cat probes Me meets of basic assumptions, and field studies that allow an assessment of the reliability and precision of He model's predictions. 1.5 CONCLUSIONS The broad line of research Hat is represented by social influence theory, involving, the formal modeling of interpersonal influence processes as they are played out in a social network, is In the classical tradition of Coup dynamics that was initiated by Festinger, French, Newcomb, and Carhvright, among others. It was a Madison, ~ might add, that was veIy strongly supported at one time by He Office of Navel Research (Guetzkow 1951), one of the sponsor's of the present symposium on social networks. Thus, an applied science of influence of networks is not a new or odd proposal In any sense; it is an DYNAMIC SOCIAL NETWORK MODELING AND ANALYSIS 97

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10 attempt to revisit and revitalize a line of work on influence networks in social psychology Mat has been sidetracked by the cognitive revolution in psychology and by the "cultural tom" in sociology. My hope is that the present paper will serve as a useful platform for the future development of an applied science of influence networks Mat is based on a formal theory of how influence networks operate to shape persons' attitudes and opinions. Although the mathematical structure of social influence network theory is simple, Me specified process is consistent wad a number of previous independent efforts to model the process of interpersonal influence. Indeed, Me ~eoreuca1 convergence on roughly Me same mechanism is a remarkable development in the social sciences. For this reason, it is important to find out whether or not this basic mechanism is correct and, if not, whether it can be refined or should be replaced. The potential domain of application of social influence network theory is large. My collaborator and I are presently engaged in developing We ~eoIy~s applications to the literature on group dynamics in psychology and sociology. Some of this work has already appeared (Fnedkin 1999; 2001; Fnedkin and Johnsen 1999). The present paper outlines a largely undeveloped potential application in which the theory would be employed' in an Operations Research mode Plier and LieberInan 1995), to analyze and control extant social structures. ~ Me practical world, theoretical tools are rarely entirely correct, but they may be applied with the understanding that the friction and stress generated by unexpected results provide an opportunity for learning new things about fundamental mechanisms, and that trial d- e~ror is usually implicated In He development of any good Meow. 1.6 REFERENCES Abelson, RP. 1964. "Ma~emauca] Models of He Dis~mbudon of Attitudes under Controversy." Pp. 142-160 in Contributions to Mathematical Psychology, edited by N. Frederiksen and H. GuDiksen. New York: Holt, Rinehart & Winston. Anderson, Norman H. 1981. Foundations of Information Integration Theory. New York: Academic Press. . 1991. "Conmbu~aons to lnfoImation Integration TheoIy." Hillsdale, NJ: Lawrence Eribaum Anderson, Norman H. and Cheryl C. Graesser. 1976. "An Formation Integration Analysis of Attitude Change in Group Discussion." Journal of Personality and Social Psychology 34:210-222. Anselin, Luc. 1988. Spatial Econometrics: Methods and Models. Dordrecht: Kluwer Academic. Berger, ILL. 1981. ttA Necessary and Sufficient Condition for Reaching a Consensus Using DeGroot's Method." Journal of the American Statistical Association 76:41 5418. ChaHegee, S. and E. Seneta. 1977. "Towards Consensus: Some Convergence Theorems on Repeated Averaging.'' Journal of Applied Probability 14:89-97. Davis, James H. 1973. "Group Decision and Social Interaction: A Theory of Social Decision Schemes." Psychological Review 80:97-125. . 1996. "Group Decision Making arid Quantitative Judgments: A Consensus Model." Pp. 35-59 In Understanding Group Behavior: Consensual Action by Small Groups, edited by E. H. Witte and J. H. Davis. Mahwah, NJ: Lawrence EtIbaum. 98 DYNAMIC SOCIAL NETWO=~IODELI?JG ARID ANALYSIS

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