Social Balance Theory

3. The Balance of Social System

3.1 The Model

The model we develop here is inspired and become alternative with the one
previously developed by Hummon & Doreian (2003) and Wang & Thorngate (2003).
Hummon and Doreian (2003) developed an agent-based model whose agents change
their relation sign to reach balanced state in their triads based on some certain partitions;
meanwhile Wang and Thorngate (2003) tried to view how a network is divided into two
sub-groups (mitosis) by randomly balancing the triads.

In the paper, we investigate how sentiment relation change at the dyadic level
affects the global (collective) balance index in the whole interpersonal network.
Concerning the assumption that every interpersonal network tends toward higher
balance (Heider, 1946), we also investigate how the states of sentiment relation flows
through trajectory to reach global balance state. The global balanced index ( β) can be
written as:

∑^T

balanced

J≤I

∑^T

tot

I

where, Tbalanced denotes the number of balanced triads, T denotes the total number of
triads in the whole interpersonal network, J is the number of balanced triads and I is the
number of the whole triad.

By the presence of the balance index we can create feedback over the network
balance, so that the system can decide whether accept or not the change of sign of
sentiment relation. The assumption that a network tends toward higher balance brings
the mechanism of accept or not of the change. In other words, a change of sentiment
relation sign will be accepted if the balance index resulted is higher.

Individuals in a large group are connected by specific sentiment relation, be it
positive (+), negative (-), or no-relation (0). In a group consists of N individuals, the
number of dyads (possible sentiment relations), denoted by D, equals to

D = N
(N-2)!2!

If the possible types of dyadic relations formed are 3 (whether positive, negative, or no-
relation), then the possible relation patterns (p)

Whereas the number of individuals combination which formed triads in the group
consists of N individuals are

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