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.