Abstracts 2002 Douglas R. White

Abstract: A field experiment conducted in Central Australia in 1971-72 explored differences between what Aborigines actually did and what they said they did when anthropologists interviewed them. Fieldwork entailed observing behavior and recording it in numerically coded forms; analysis entails extracting patterns computationally that would not appear in traditional ethnographic data. This paper focuses on discrepancies between expected and observed with regard to descent, marriage and kinship. First it examines field methods and the resulting dataset, then it reviews a wide range of analytical methods that have been used to interpret the data. The alternative analytical methods reviewed here serve to test "competing hypotheses" about the nature and operation of Alyawarra descent, marriage and kinship. At the same time, however, the cumulative result of using these diverse methods has been increasingly complex and subtle understandings of previously unknown aspects of Central Australian social organization. The fact that the data continue to repay increasingly sophisticated analyses thirty years after they were recorded attests to the success of the field experiment. Abstract: Abstract: The rich cognitive and network ethnography of the Alyawarra offers a test of and counter-argument to the proposition that for any given culture to operate coherently, only a single logic is possible. First, the Alyawarra strictly adhere to Logic1 in which 'normative' kinship terms conform to a marriage pattern of sidedness composed of binary supersets of named exogamous unilineal descent groups. There are both matri- and patri-sided exogamous bipartite supersets ('sides'), however, and they cross-cut one another to form doubly-sided sections. The four sections are named, but not the exogamous patri-sides, the exogamous matri-sides, and alternating generations that form interleaved endogamous matrimoieties (the latter are not 'sided' because they are not exogamous). As with the neighboring Aranda, marriage occurs only between delimited subset of those in the permitted pairs of sections, so that there are effectively eight subsections (among the Northern Aranda, these are named. Spencer and Gillen 1927:320-322 describe how the various group leaders led meetings to legislate changes from four to eight-section marriage rules, for example). These are consistent with both the 'normative' kinship terms and rules that prohibit MBD marriage but permit MMBDD and FMBSD, as is common with sub-section systems.

Second, because female age at marriage is significantly lower than that of males, the axiom of generational closure - successive sibling-in-law links that close into cycles - does not apply. The age bias yields Logic2 in which recurrent patterns of marriage between patrilineages are highly asymmetric, like classificatory MMBDD marriage, rather than symmetric, as in sister exchange. Marriage practices associated with Logic2 lie within the 'norms' of Logic1, although the conventional 'genealogical' diagram for Aranda-Alyawarra type of kinship terms created by Radclifffe-Brown (1930) shows equivalence classes in which sister exchanges and bilateral second cousin marriages are permitted. His model of the Aranda "system" is one of delayed direct exchange between classificatory patrilines, following the erroneous logic of his diagram. In fact, neither sister exchange nor bilateral second cousin marriages occur among the Aranda or Alyawarra. To remedy this defect - a problem in interpreting equivalence classes in classificatory kinship terminologies - of the conventional Radclifffe-Brown model of Aranda-type section systems, the two previous proposals made by Denham et al. (1979) included an 'open format' model of directed wife-giving relationship in which women's generational time runs 50% faster than that of men. This is the model that that we call Logic2. Secondly, they created a closed double helix version of these same equivalence classes in spiraling generations that close back on themselves (we call this a helical Logic2), cyclically. They found that the open format model and double helix variant could account for both the 'normative' Aranda-Alyawarra kinship terms and the stated preferences in both cases for MMBDD marriage. What they could not explain, however, was why so very many classificatory kinship terms of the Alyawarra (23%) were non-reciprocal and why Omaha terms were often employed as an exceptional pattern outside the 'normative' pattern of kin-term usage.

In this study we use network analysis - and methods for the empirical study of equivalence classes with respect to actual behavioral patterns - to help resolve the problems still unsolved with the double helix model. A network analysis of equivalence sets, conforming to the fact that members of local patrilineages are observed to forget the matrilineal ties of departed ancestors, establishes that Logic2 is one of generations that have time intervals of different length for men and women, and are shallow, open-ended, flexible, and extensible so as to include alliances with neighboring groups. We argue that since patterns of marriage among cohorts that have departed are successively erased, these patterns fail to constrain the emergence of new patterns in cohorts where marriages are taking place more than four generations later. Thus the network pattern does not form a structure that closed on itself with a fixed algebraic kinship structure, like the double helix model, but is a limited and partial realization of that model. This finding is consistent with a dynamic of alternative marriage choices that, as their network locations and frequencies change within the possibilities offered by Logics 1 and 2, alter the very topology of the kinship and marriage network. Wife-giving and wife-taking choices of members of the named patrilineages may be realized as exceptional marriages that inflect behaviors generated by Logic2 into new systemic patterns that lead to lineage remapping of generations. This allows the kinship pattern to evolve dynamically across a class of network models (Tjon Sie Fat 1983) influenced stochastically by age distributions at marriage. This opens up the possibility of a new understanding of the evolution of social organization in Australian societies, where age differences between spouses, and classificatory terminologies consist with section systems, are very common.

The unintended effect of the demography of H>W age differences resulting from a preference dynamic is supplemented by Logic3, the widespread and intended use of an extra-'normative' Omaha terminology. A detailed analysis shows this usage to correspond to an exclusionary device that says "don't marry here," but does so nonreciprocally.

Examining relationships amongst the Logics 13 at the level of practice shows how they form a coherent dynamical system oriented towards demographically and strategically inflected adaptation. A strictly 'normative' approach to modeling Alyawarra kinship would be misleading as a theoretical paradigm. We argue for a broader framework that takes into account the interplay of multiple cultural logics as integral within a networked system of kinship practices.

Abstract: We examine data on and models of small world properties and parameters of social networks. Our focus, on tie-strength, multilevel networks and searchability in strong-tie social networks, allows us to extend some of the questions and findings of recent research and the fit of small world models to sociological and anthropological data on human communities. We offer a ‘navigability of strong ties’ hypothesis about network topologies tested with data from kinship systems, and potentially applicable to corporate cultures and business networks. Abstract: Longitudinal network analysis is coupled in this study to a systematic analysis of the results of long-term ethnography of a nomadic group. Data collection using genealogical, interview and observational methods is complemented by analytic methods using graph theoretic concepts and dynamical as well as structural methods to assess various cross-cutting and hierarchical levels of social cohesion (nuclear and extended families, lineages, clans, tribal groups, and village or nationality affiliations as found within the nomad group) to formulate and test hypotheses about social mobility and political leadership. Predictive hypotheses about the inverse relation between out-mobility and social cohesion versus the direct relation between cultural transmission and marital relinking as a form of cohesion are thought to validate the basic approach. The model of distributed cohesion developed from these data provides a new understanding of processes supporting the emergence of leaders in egalitarian nomadic groups. Abstract. We show how simple rules shared by actors acting somewhat independently and with local rather than complete global information can nonetheless generate coherent global structures. In the case of dual organization, from analysis of actual marriage networks and genealogical linkages, we find many ethnographic instances where two-sided networks and marriage choices go unnoticed by ethnographers because global labels and descent rules for sides are absent. To understand global structures and institutions that may be at play, unnoticed, in social systems, it is simply not sufficient to look for shared labels attached to the parts of global structure: their structure may reside in patterns of relationships, in their instantiation. What patterns residing in relationships instantiate, however, is not necessarily a set of local decision rules that are shared and identically labeled, but rather sets of local outcomes of behavior that contribute - in possibly heterogeneous even if structurally equivalent ways - to a global configuration.

Abstract. A network approach to economic organization, kinship systems and complexity dynamics is used to explore nomadic pastoralism as a socio-natural system. Graph theoretic measures of network cohesion are related to issues of the emergence, transformation and decay of social and economic networks and their sustainability and resilience in relation to the environment and the organization of energy, material, social, and informational flows. Abstract. Following Houseman and White's definition of the core of a marriage network, we identify the core of the elite network of families colonial Guatemala in the period 1680 and 1800 in structural terms, ones related both to the concept of marriage relinking, used in research on the social organization of cognatic societies, and to the concept of wealth consolidation through structural endogamy. To test hypotheses about the relationship between the structural core of relinked marriages and the consolidation of wealth and prominence in a sample of elites in the richly documented dataset assembled by Casasola (1998, 2001), we develop a second measure of the prestige core of a marriage network, and measure the correlations between the two measures. The second measure uses the notion of network redundancy (White, 1998), in this case, redundancy between husband and wife in the accumulation of prestigious family names. This set of definitions is useful describe the structure and dynamics of cognatic descent groups, such as the Spanish kinship system. We find support for the following hypotheses:

Abstract. Under certain conditions, when diverse individuals (e.g., ants, individuals, agents) independently traverse a sequential decision space in reaching objectives (e.g., as modeled by a maze) they acquire synergetic properties of global problem solving (even in the absence of global knowledge about the problem space) by virtue of some form of pooling experience. The laying of pheromones on random paths taken by ants, for example, has been shown to map the set of shortest paths to a food source. This paper shows the conditions under which certain very general classes of mazes have the property of "collective advantage" to finding shortest paths by aggregating ceretain types random individual behavior (individuals have local but no global knowledge of the maze and no perception or reckoning of network distances). Of three factors considered as conditions for collective advantage, two were identified by Johnson (2000, 2001) from simulations: First is the method of traversal of the maze, and second is the method of marking trails towards a collective solution. The third - the structure of the maze - is explored here through graph theoretic concepts. These include precise definitions, theorems and observations, and simulations. They provide a language and a set of results as to the structural factors that affect collective advantage. In general, biconnected maze networks - where every node has independent paths to every other -, with many parallel paths, and many crossover paths between them, assist collective advantage. Rules developed to measure the collective advantage of a maze help to refocus the problem on the coevolution of the learning environments that endow agents with collective intelligence that is distributed across their behaviors and not condensed by selection for individual actors with better forms of global strategies or global knowledge. Results support March's (1991) findings of advantages to exploratory behaviors over selection for exploitation.

Abstracts 1997-2000

Introduction: White et al. (1998-in press, Brudner and White 1997) develop a theory of a very general form of social integration based on multiple connectivity, in which every pair of nodes is connected ("relinked") by multiple independent paths. Elaborating one of the dominant hypotheses in the theory of social class, for example, they argue that multiple connectivity of marriage links between families defines a boundary condition for cohesive social classes. They apply this theory, which recognizes a generalized and potentially large-scale networked basis for cohesive social integration, to explain the basis in network evolution of two different systems of social class. There is a critical density threshold for the transition to a giant multiple-connectivity core of a network, and the kinship network in the two cases studied have passed this threshold. After a network has evolved in density beyond the criticality transition, its nodes partition into a giant core in which every pair of nodes is connected by multiple independent paths; a periphery of nodes connected to the core by a single path, and marginals not connected to the core. In the Tlaxcalan case the principle of equal division of inheritance assimilates part of the periphery - the descendants of the core - into the same class as the core. This contrasts with their study of an Austrian village with an unequal division of inheritance between principal heirs of estates and children who are bypassed as principal heirs, where the class division is more strictly between core and periphery-plus-margins.

This is the first theoretical application of the concept of structural endogamy as identifying an empirical variable or boundary condition within social networks that is linked in causal-explanatory ways to social class formation. Using an ethnographically rich case study of an Austrian village in which oral and (ca. 100) household genealogies provide 150 years of marriage network data, while manorial archives continue the stem-line household genealogies back to the founding of the "house system" in 1517, the hypothesis is formulated that the social class boundary between farmstead owner-operators (including heirs and buyers) and secondary service occupations not linked to farmstead ownership is established and maintained through the mechanism of structural endogamy. Two principles of inheritance are in conflict in this farmstead house-system, that of passing the principal productive property intact to a principal heir (usually a son, or if not is available, a daughter), and that of the intestate rights of children to equal division of parental inheritance. The use of wills or testaments resolves his conflict through "equitable division" which maintains stem-line impartibility of farmsteads along with quitclaims to those who are not principal heirs. Structural endogamy, in this case specifically the marriage of a potential heir to a spouse who brings in divided property from another divided patrimonial stemline, is shown to be (1) a qualification for class membership via principal heirship, (2) a means of reconstituting subdivided estates, and (3) a means of social perpetuation of the two-class system which often even divides siblings within the same nuclear family. The predicted statistical relationship between class-membership, heirship and structural endogamy is confirmed empirically and implications for new approaches to studies of social class formation are discussed.

[[The following two articles represent a second theoretical application of the related concepts of structural endogamy and multiple connectivity as identifying an empirical variable or boundary condition within social networks that is linked in causal-explanatory ways to social class formation. Here, ranked statuses differentiated by wealth are integrated into a single solidary social class by ties of marriage and compadrazgo that avoid homogeneity of rank and actively cross-cut rank differences with greater than random frequency. As hypothesized from a structural endogamy model, structural endogamy integrates a core of 38% of the couples in community to which up to nearly 90% of the entire community are connected by marriage, if not by marital relinking. Unlike the Austrian case, however, those who are not relinked are not descendants of core property- owning ancestors, but rather are immigrants from other villages or the descendants of unrelinked immigrants. Relational analysis shows that the children of core couples may marry outsiders but resist intermarriages with descendants of outsiders that would lead to bringing peripheral lines of outsiders into relationships of relinking or structural endogamy. Moreover, nearly 100% of the structural endogamy is within the village. Eventually, however, as the descendants of outsiders persist in living in the village for several generations, they are gradually absorbed into the relinked core. This fits the predicted model of a one-class social system, but with local solidarity and the gradual absorption of outsiders, or a local core-periphery structure. Further, it is shown that the great majority and most important types of compadrazgo ties are oriented not towards the periphery of the village but towards other neighboring villages, integrating the cores of different villages into a single class system. Relinking also occurs between villages but only for compadrazgo ties.]]

Abstract. This paper develops a concept of social integration based on multiple pathways of connectivity. In a cohesive set of a network, every pair of nodes is connected by multiple independent paths. This measure of cohesion identifies maximal group boundaries independent of density or proximity. It is ideal for the study of cohesion on a large scale. In a network study of the two most important social relations in a Mexican community - kinship and compadrazgo (ritual kinship) -, we confirm theoretical predictions as to effects of social cohesion, such as higher participation in local offices by members of cohesive sets. Both kinship and compadrazgo have passed a critical density threshold in the ratio of network edges to nodes for transition to a network in which the nodes are partitioned into the structural positions of a giant core in which every pair of nodes is connected by multiple independent paths, a periphery of nodes connected to the core by a single path, and marginals not connected to the core. The dimensions of our analysis include the relative density of the independent social relations, the structural positions they define, the relative spatial extensions of their cores, the manner in which these cores cross-cut one another over time (such as the local concentration of the sparser kinship core versus the quicker-to-relink extensions of the compadrazgo core), and the question of how migrants are absorbed from one spatial location to another over time. How separate networks and their institutional forms interrelate on these dimensions give new insights on the dynamics of social cohesion, social class, and large-scale "invisible communities" that relink families within and between the local segments of a regional social system. The present case is one of extended group cohesion associated with egalitarian norms and informally organized resistance to power groups from outside.

Abstract. This article presents a new way to conceptualize social integration based on different modes of connectivity in network components. Within a social network, a multiply connected component is one where every pair of its nodes is connected ("relinked") by multiple independent paths. Social boundaries are derived from multiple connectivity as follows: For any network, there exists a critical density threshold for the transition to a giant multiply connected core. After a network evolves in density beyond the criticality transition, its nodes partition into (1) a giant core in which every pair of nodes is connected by multiple independent paths, (2) a periphery of nodes connected to the core by a single path, and (3) marginals unconnected to the core.

We test three facets of a theory of integration by differential modes of connectivity as it applies to a study of the social networks of a Mexican village. First, we show that the set of boundaries of social groups defined by differential connectivity are correlated in turn with predicted features of social cohesion, such as social participation in the central community institutions. This provides construct validation for the theory and predictions from network structure to emergent social phenomena.

Second, we apply our theory of a generalized and potentially large-scale networked basis for cohesive social integration to explain certain aspects of the network evolution of different systems of social class. Elaborating one of the dominant hypotheses in the theory of social class, we argue and demonstrate that multiple connectivity of links between families defines a boundary condition for cohesive social classes. Social network findings are matched by belief statements of villagers regarding egalitarian social relations among members of Tlaxcalan heartland villages. This provides construct validation for this application of the theory to the present case, where the principle of equal division of inheritance assimilates part of the periphery - the descendants of the core - into the same social class as the core, although the mode of connectivity is weaker.

Third, we apply our theory of cohesion to the differential structures and functions of two social relations that are fundamental to Mexican social organization, examining how multiple connectivity operates first for kinship networks, then for compadrazgo (ritual kinship between parents and godparents), and finally, for both in combination. In the kinship and marriage network, relinking is only locally cohesive as it occurs only within the village. In the compadrazgo network, in contrast, multiple connectivity integrates the village with other villages in the locality into a large-scale local segment of an "invisible community" of the regional egalitarian social class system, in which inter-village migration is facilitated. Combining both social relations under one framework reveals an astonishing synergetic effects both for village and regional integration. On the dyadic and on the broader structural level both networks are almost orthogonal to one another and thereby perfectly complement one another. Compadrazgo simply cross-cuts the limitation of the kinship and marriage network and knits new migrants and other more loosely connected families into the community long before the marriages of their children could do so in further generations.

Review: "Methods and techniques [of kinship analysis] have strong implications on the theoretical side. For that reason, their use pertains to the reexamination of kinship nomenclatures. [In the Godelier et al., edited volume, 1998] One article vigorously distinguishes itself in the domain of precise procedures. In contrast with Tjon Sie Fat, who presents a meticulous algebraic treatment of purely terminological kinship, Michael Houseman and Douglas R. White, using a variety of informatic tools, collaborate to show the emergent properties of a network of marriages that are effective through their dynamic aspect in the pratique -- behavioral practices -- of matrimonial alliances, where they find observed regularities that are not a simple effect of a terminological logic and rules of marriage. These constitute, at the level of practice, a sort of primary behavioral regularity [encodage], of a complex order. This is precisely demonstrated in that the two researchers, in the course of their analysis, are able to detect a structure of sidedness [structure ŕ coté], or bipartite network where a pair of supersets of marriages, connected by agnatic and uterine decent links, operate so as to organize network configurations of marriage alliances across a range of societies in lowland Amazonia. The authors succeed in creating an empirical sociology of high quality that takes the first steps towards a conceptual and theoretical advance towards a sort of grounded theory (Glaser and Strauss 1967) based on facts established methodologically through carefully controlled working hypotheses [and precise analytic definitions]" (translation from review by Jean-Luc Jamard in L'Homme 2000:735-736).

Editors' Summary: "Michael Houseman and Douglas R. White develop a new method of representing Dravidian-like kinship systems that visually renders both empirical cases and ideal-type models -- the "statistical" and "mechanical" models of Lévi-Strauss's well-known discussion (1969:xxvii ff.) -- in the same register, so that they can be directly compared. They introduce into the discussion of Dravidianate systems a rigorous graphic modeling of actual marriage networks that is based on their conception of "sidedness," which occupies a middle ground between the egocentric structures of the kinship terminology and sociocentric structures of social groups, such as moieties and section systems. Their elegant new instrument has a number of promising applications in kinship studies." (Editors, p. 14)

The p-graph approach that has proven an invaluable aid to the study of kinship, marriage and genealogical network analysis here is explicated – in terms of solving five key conceptual problems of network studies, including that of identifying subgroup boundaries -- and combined with a computer package for sparse-network algorithmic analysis and visual representation of large (up to 90,000 node) networks. The results of this new marriage between graph-theoretical analysis, computer science, network anthropology and network-visualized social history are illustrated for a 1600- person social system consisting of an entire Turkish nomad society, with a relinking density of 75%, the highest density of structural endogamy yet recorded. It is shown how the algorithmic, analytic and graph-editing technology of this new concatenation of elements for network analysis leads to striking new understandings of social structure and social processes, and how to prepare visualizations of discoverable emergent properties of structure in such a large and dense network. This article reviews the developments and contributions of the authors to the evolution of these tools and methods for large-scale network analysis, and provides a complete series of guides and illustrations for the reader to utilize the two software packages discussed.

In writing an introduction to this refereed book, in which two articles of the co-editor appeared, we argue for a paradigm that treats social action such as kinship and exchange and decision making as embedded in a specific nexus of social relations that require a dynamic approach to social transactions, taking into account the local variability of resources and of positions within the network of relations, and giving an account of how the actor as agent is both embedded in and productive of choices and links that will perpetuate or dynamically alter social structure and organization. We argue for a network-based reconfiguration of theories of social exchange, the distribution of personal rights, and the biography of material and symbolic goods as they flow through temporal networks intersecting with the biographies of individuals and groups.

This ethnographic and historical study of social networks in Tlaxcala, Mexico, examines a number of hypotheses derived from the idea that the number of independent paths connecting individuals is a source of social cohesion with measurable consequences. "Biconnectivity" is where all individuals in a group have two or more independent paths of connection, and "higher order connectivity" applies where there are more than two such paths. The general hypotheses are:
(a) Biconnectivity is a source of emergent, potentially decentralized social cohesion that can occur (with observable effects) at low density in the bicomponents of relatively stable social networks.
(b) This is especially true for relations that have very high "currency" or life-support salience, such as relations of political influence, property transmission, or kinship and marriage connections.
(c) Hence, social class, elites, wealth-transmission, and marriage systems are especially well-suited for analysis. Here are some further points of clarification for these hypotheses:

(d) Dynamic evolution of 1-connectivity and biconnectivity (and higher order connectivities having both global "giant component" effects and localized interaction effects) can give rise to phase transitions in network configurations that may account for observed changes in social organization and institutions. Abstract: While questions about social cohesion lie at the core of our discipline, no clear definition of cohesion exists. We present a definition of social cohesion based on network connectivity that leads to an operationalization of social embeddedness. We define cohesiveness as the minimum number of actors who, if removed from a group, would disconnect the group. This definition generates hierarchically nested groups, where highly cohesive groups are embedded within less cohesive groups. We discuss the theoretical implications of this definition and demonstrate the empirical applicability of our conception of nestedness by testing the predicted correlates of our cohesion measure within high school friendship and interlocking directorate networks.

Keywords: Graph theory, social networks, algorithmic detection, cohesive groups, social boundaries

Other reviews

Using Galois Lattices to Represent Network Data Freeman L C, White D R Sociological Methodology 1993, Vol 23 Sociological Methodology 23: 127-146 1993

Betweeness Centrality Measures for Directed-Graphs White D R, Borgatti S P Social Networks 16 (4): 335-346 Oct 1994

Structure and Dynamics of the Global Economy - Network Analysis of International-Trade 1965-1980 Smith D A, White D R Social Forces 70 (4): 857-893 Jun 1992

Statistical Entailments and the Galois Lattice White D R Social Networks 18 (3): 201-215 Aug 1996

Network structures of marriage practice Houseman M, White D R L'Homme 36 (139): 59-85 Jul-Sep 1996

Kinship networks and discrete structure theory: Applications and implications White D R, Jorion P Social Networks 18 (3): 267-314 Aug 1996

Anthropology - Analyzing large kinship and marriage networks with Pgraph and Pajek White D R, Batagelj V, Mrvar A Social Science Computer Review 17 (3): 245-274 Fall 1999

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