Web Science • Group Reading MA Digital Humanities and Digital Knowledge, UniBo An Information Flow Model for Conflict and Fission in Small Groups By: Wayne W. Zachary Presenter: Saverio Giallorenzo saverio . giallorenzo @gmail.com 1
Web Science • Group Reading MA Digital Humanities and Digital Knowledge, UniBo Context • General Context Anthropology The scientific study of humanity , concerned with human: • biology • behaviour, societies, and culture • linguistics in both the present and past (archaeology). saverio . giallorenzo @gmail.com 2
Web Science • Group Reading MA Digital Humanities and Digital Knowledge, UniBo Context • Specific Context Social Anthropology Social anthropology is the study of patterns of behaviour in human societies and cultures. Social anthropology is di ff erent from the neighbouring fields of economics and sociology because of its holistic range and methods, based on long-term participant observation. The field is characterised by a commitment to the relevance of micro studies and many social anthropologists use quantitative methods to objectively measure data collected through polls, questionnaires, and surveys, or by manipulating pre- existing statistical data using computational techniques. saverio . giallorenzo @gmail.com 3
Web Science • Group Reading MA Digital Humanities and Digital Knowledge, UniBo Context • Specific Application Zachary studies the problem of Characterising (how) and explaining (why) group scission/fission takes place in small (bounded) groups To do that, he presents data from a university-based karate-club group, in which a concrete political discussion led to an ideological fracture and eventually to a formal separation of the club into two organisations. The political organisation of the club was informal and most decisions were made by consensus at club meetings. The two factors formed around the political rivalry between the club instructor and the manager. saverio . giallorenzo @gmail.com 4
Web Science • Group Reading MA Digital Humanities and Digital Knowledge, UniBo Problem and Motivation Problem : explaining how and why fission takes place in small bounded groups Importance : a (back then) long central issue in social anthropology Contributions of the paper : - Present a new model to explain and characterise group fission, based on a social network approach; - Present a measure, applied to the model, shown to be a good predictor of group membership and able to characterise the phenomenon (who goes where) - second part omitted in this presentation; - Present (network) data on a small group in which a factional division led to a formal separation into two organisations. saverio . giallorenzo @gmail.com 5
Web Science • Group Reading MA Digital Humanities and Digital Knowledge, UniBo Data • Collection Collected from a university-based karate club, in a period of three years. During the collection, the club maintained between 50 and 100 members. The data collected considered activities in which the club members attended both karate lessons and other social events (tournaments, parties, dances, banquets, etc.). The data collected represent a friendship network among the members of the club. The network is a scalar one, where links between nodes are weighted and the weight is quantified by the number of events both nodes attended. saverio . giallorenzo @gmail.com 6
456 JOURNAL OF ANTHROPOLOGICAL RESEARCH Web Science • Group Reading MA Digital Humanities and Digital Knowledge, UniBo FIGURE 1 Social Network Model of Relationships in the Karate Club Data 1 3 34 33 2 Of the (fluctuating) total number of club members who joined and departed the club, only 34 27 8 individuals are considered in the 26 i study. 9 25 10 The reason is that the remaining members did not interact with other club members outside the context of meetings and classes. 19 18 16 17 18 This is the graphic representation of the social relationships among the 34 indi- saverio . giallorenzo @gmail.com 7 in the karate club. viduals A line is drawn between two points when the two individuals interacted in contexts outside those of being represented consistently karate classes, workouts, and club meetings. Each such line drawn is referred to as an edge. two individuals were observed to interact outside the consistently normal activities of the club (karate classes and club meetings). That is, an edge is drawn if the individuals could be said to be friends outside the club activities.This graph is represented as a matrix in Figure 2. All the edges in Figure 1 are nondirectional (they represent interaction in both directions), and the graph is said to be symmetrical. It is also possible to draw edges that are directed (representing one-way relationships); such
Web Science • Group Reading MA Digital Humanities and Digital Knowledge, UniBo Data • Measures As a proxy of group division, Zachary employed the NETFLOW algorithm, which uses the maximum information flow between two given nodes to separate a given network between two groups, either closer to a or a nodes. source sink The premise to use NETFLOW is that Zachary knows that the group could be torn apart by the political tension between two important nodes in the network: on one side the manager of the club and on the other the club instructor . The hypothesis (we omit to present the second hypothesis on group-split determination) of Zachary is that the a ffi liation of a node to either faction can be determined by the NETFLOW algorithm, which implements the maximum flow- minimum cut labelling procedure . saverio . giallorenzo @gmail.com 8
Web Science • Group Reading MA Digital Humanities and Digital Knowledge, UniBo Data • Measures, NETFLOW maxflow ( ) G , i , j NETFLOW uses the Ford-Fulkerson procedure to determine the The residual G ′ ← G maximum information flow between capacity of two nodes in the network. flow ij ← 0 all the pairs of edges in p p ← findAugmentingPath ( G ′ , i , j ) Let be a graph with G = ( V , E , C ) vertices, edges and pairwise V E While ∃ p flow-capacity , the maximum flow C flow ij ← flow ij + min( residual_capacity ( G ′ , p ) ) between two nodes (called i source) and (called sink) j G ′ ← computeResidualGraph ( G ′ , p ) corresponds to the result of the p ← findAugmentingPath ( G ′ algorithm maxflow ( ), , i , j ) G , i , j described by the pseudocode: return flow ij saverio . giallorenzo @gmail.com 9
Web Science • Group Reading MA Digital Humanities and Digital Knowledge, UniBo Data • Measures, NETFLOW NETFLOW uses maxflow to determine the maximum flow-minimum cut labelling, which intuitively corresponds to the capacity (of transmitting information) of the smallest possible “break” in the network separating the source from the sink. j 0 f source , j 0 > f sink , j 0 source f sink , j 1 > f source , j 1 sink j 1 Cut saverio . giallorenzo @gmail.com 10
465 IN SMALL GROUPS CONFLICT AND FISSION Web Science • Group Reading MA Digital Humanities and Digital Knowledge, UniBo TABLE 1 Results OF INITIAL RUN RESULTS NETFLOW SIDE OF CUT FACTION CLUB AFTER INDIVIDUAL FISSION NUMBER 1 Source Mr. Hi's Mr. Hi - Strong Source Mr. Hi - Strong Mr. Hi's 2 Mr. Hi - Strong 3 Source Mr. Hi's 4 Source Mr. Hi's Mr. Hi- Strong Mr. Hi - Strong 5 Source Mr. Hi's 6 Source Mr. Hi - Strong Mr. Hi's Mr. Hi - Strong 7 Source Mr. Hi 's Mr. Hi - Strong 8 Source Mr. Hi's 9 Sink John - Weak Mr. Hi's 10 Sink None Officers' Mr. Hi - Strong 11 Source Mr. Hi's 12 Source Mr. Hi's Mr. Hi- Strong Mr. Hi - Weak 13 Source Mr. Hi's Mr. Hi - Weak 14 Source Mr. Hi's saverio . giallorenzo @gmail.com 11 15 John - Strong Sink Officers' John - Weak 16 Sink Officers' 17 Source None Mr. Hi's Mr. Hi - Weak 18 Source Mr. Hi's 19 Sink None Officers' Mr. Hi - Weak 20 Source Mr. Hi's John - Strong Sink 21 Officers' Mr. Hi - Weak 22 Source Mr. Hi's 23 Sink John - Strong Officers' Sink 24 John - Weak Officers' John - Weak 25 Sink Officers' John - Strong 26 Sink Officers' John - Strong 27 Sink Officers' 28 Sink John - Strong Officers' John - Strong 29 Sink Officers' 30 John - Strong Sink Officers' 31 Sink John - Strong Officers' John - Strong 32 Sink Officers' 33 John - Strong Sink Officers' 34 John - Strong Sink Officers' This table summarizes the results of the first run of NETFLOW, using matrices E and C as input. "Individual Number" identifies the individual with the corresponding row/column in the matrices. "Side of Cut" refers to the subset of V to which the individual was assigned by NETFLOW, either the source side or the sink side. "Fac- tion" gives the factional affiliation of the individual, either with that of John A., that of Mr. Hi, or none. The strong/weak designations in this column indicate whether the individual was a strong or a weak supporter of the faction's ideological position. Finally, "club after fission" indicates which club was joined after the fis- sion, either that formed by Mr. Hi, or that formed by the officers of the original club.
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