Zachary Karate Club
Post date: Nov 29, 2011 7:3:59 PM
Overview
Network Dataset
The dataset name is ZACHARY, and includes the following two 34x34 matrices:
ZACHE symmetric, binary
ZACHC symmetric, valued
Background
These are data collected from the members of a university karate club by Wayne Zachary in 1977. The ZACHE matrix represents the presence or absence of ties among the members of the club. The ZACHC matrix indicates the relative strength of the associations (number of situations in and outside the club in which interactions occurred). Here's how the Zach C matrix was constructed. A finite set of possible contexts, chosen on the basis of observation of the group, will be used as the domain of a scale variable. Then, the relationship between each pair of individuals in the network is examined against this (nominal) scale. A value, equal to the total number of contexts from the scale in which the two individuals interacted, is then assigned to the corresponding entry in C. Eight contexts are included in the domain of the scale applied to the edges in the karate club network. They are: (1) Association in and between academic classes at the university. (2) Membership in Mr. Hi's private karate studio on the east side of the city where Mr. Hi taught nights as a part-time instructor. (3) Membership in Mr. Hi's private karate studio on the east side of the city, where many of his supporters worked out on weekends. (4) Student teaching at the east-side karate studio referred to in (2). This is different from (2) in that student teachers interacted with each other, but were prohibited from interacting with their sutdents. (5) Interaction at the university rathskeller, located in the same basement as the karate club's workout area. (6) Interaction at a student-oriented bar located across the street from the university campus. (7) Attendance at open karate tournaments held through the area at private karate studios. (8) Attendance at intercollegiate karate tournaments held at local universities. Since both open and intercollegiate tournaments were held on Saturdays, attendance at both was impossible. This scale was applied to the relationships between all pairs of individuals in the karate club, using data compiled over the three years of direct observation of interactions in the club. For each existing edge in E (Figure 2), the pair of individuals involved interacted in at least one of the above eight contexts. The quantified matrix of contexts is given in Figure 3, and is the third component in the capacitated network model (V,E,C).
Zachary (1977) used these data and an information flow model of network conflict resolution to explain the split-up of this group following disputes among the members. The karate club was observed for a period of three years, from 1970
to 1972. In addition to direct observation, the history of the club prior to
the period of the study was reconstructed through informants and club
records in the university archives. During the period of observation, the
club maintained between 50 and 100 members, and its activities
included social affairs (parties, dances, banquets, etc.) as well as
regularly scheduled karate lessons. The political organization of the
club was informal, and while there was a constitution and four officers,
most decisions were made by concensus at club meetings. For its classes,
the club employed a part-time karate instructor, who will be referred to
as Mr. Hi.2
At the beginning of the study there was an incipient conflict
between the club president, John A., and Mr. Hi over the price of
karate lessons. Mr. Hi, who wished to raise prices, claimed the authority
to set his own lesson fees, since he was the instructor. John A., who
wished to stabilize prices, claimed the authority to set the lesson fees
since he was the club's chief administrator.
As time passed the entire club became divided over this issue, and
the conflict became translated into ideological terms by most club
members. The supporters of Mr. Hi saw him as a fatherly figure who
was their spiritual and physical mentor, and who was only trying to
meet his own physical needs after seeing to theirs. The supporters of
John A. and the other officers saw Mr. Hi as a paid employee who was
trying to coerce his way into a higher salary. After a series of
increasingly sharp factional confrontations over the price of lessons, the
officers, led by John A., fired Mr. Hi for attempting to raise lesson prices
unilaterally. The supporters of Mr. Hi retaliated by resigning and
forming a new organization headed by Mr. Hi, thus completing the
fission of the club.
During the factional confrontations which preceded the fission, the
club meeting remained the setting for decision making. If, at a given
meeting, one faction held a majority, it would attempt to pass
resolutions and decisions favorable to its ideological position. The other
faction would then retaliate at a future meeting when it held the
majority, by repealing the unfavorable decisions and substituting ones
favorable to itself. Thus, the outcome of any crisis was determined by
which faction was able to "stack" the meetings most successfully.
The factions were merely ideological groupings, however, and were
never organiztionally crystallized. There was an overt sentiment in the
club that there was no political division, and the factions were not
named or even recognized to exist by club members. Rather, they were
merely groups which emerged from the existing network of friendship
among club members at times of political crisis because of ideological
differences. There was no attempt by anyone to organize or direct
political strategies of the groups, and, in general, there was no barrier to
interaction between members of opposing factions. Only at times of
direct political conflict did individuals selectively interact with others
who shared the same ideological position, to the exclusion of those
holding other positions. This selective association during confrontations
is what brought the factions together only at crisis moments.
Political crisis, then, also had the effect of strengthening the
friendship bonds within these ideological groups, and weakening the
bonds between them, by the pattern of selective reinforcement. A series
of political crises, like that which preceded the fission had the effect of
"pulling" apart the network of friendship ties which held the club
together, until the group completely and formally separated.
Hence, row/column 1 in these
matrices designates Mr. Hi, and row/column 34 designates John A.
Person number 9 was a weak
supporter of John but joined Mr. Hi's club after the split. This can be
explained by noting that he was only three weeks away from a test for
black belt (master status) when the split in the club occurred.
Reference
Zachary W. (1977). An information flow model for conflict and fission in small groups. Journal of Anthropological Research, 33, 452-473.