Steve Watson

The typical definition of a social group includes some combination of the following characteristics or characteristics that are equivalent to these:

1. Two or more people
2. Direct interaction amongst the members
3. Members are aware of their membership
4. Members share an interest or a cause
5. There is an organizational structure

Insofar as membership of the group is voluntary, the motivation for membership is that membership has the result that the interests of the member are advanced. (Note that these interests may be subjective, immaterial, etc. It is the evaluation of the member that counts in this case.)

Define a Group as a related set of individuals: G = <M, R>

1. The Membership of G is denoted |G|. In this case |G| = M = {m₁, …, m_n}.
2. The nature of a group is determined primarily by the nature of the relationship, R.
1. R stands for various parameters – to be clarified later – that determine the relationships that the group may enter into with other groups, and how the group may act in those relationships, how members interact within and without the group, and so on.
2. R is what distinguishes a group from just a collection of interacting individuals.

Group membership

The group relationship R has to be able to account for at least these characteristics of group membership

1. An individual may be a member of several groups.
• A person may be a male, Christian, labourer, homosexual, …
2. Some groups are mutually exclusive wrt membership. A collection of such groups D = {G₁, …, G_n}, that minimally covers another group, H, is a Division of that group and we write D|H
3. Thus, {G₁, …, G_n} is a division of H iff:
1. |G₁|, …, |G_n| are relatively disjoint, and
2. |H| ⊂ ∪_{i=1, …n} |G_i|, and
3. For i = 1, …, n, |H| ∩ |G_i| ≠ ∅.
• A group defined by religious affiliation might be mutually exclusive, since if one is a Christian one can’t be a Buddhist or a Hindu, and if one is a Hindu then one is not B or C, and, of course, if B then not C or H. Similarly for socio-economically defined groups, or educational, or residential groups, etc.
• An example of a division might be the confessional allegiances in a nation. If the citizens are one only of Buddhist or Hindu – as in Sri Lanka – then {Buddhists, Hindus} is a division of Sri Lanka. Since there are no Christians (we’ll pretend), {Buddhists, Hindus, Christians} is not a division of Sri Lanka, though it contains one.

The group memberships of an individual define its Identity wrt society. Thus for the individual x who is a member of groups G₁, …, G_n, the identity of x is that collection, and we write:

• ID(x) = {G₁, …, G_n} iff x ∈ |G₁| ∩ … ∩ |G_n|.

• The identity wrt society of the person mentioned above is male, Christian, labourer, homosexual, …

Where D is a division of H and x ∈ |H|, ID(x|D) is the member of D to which x belongs. Read it as the identity of x wrt D. Thus: For D = {G₁, …, G_n}, D|H, ID(x|D) = G_n iff x ∈ |G_n|

• Suppose we have H = Sri Lanka, D = {Buddhists, Hindus}, then it might be that ID(Bob|D) = Buddhist (if Bob is a Buddhist.)

Where D₁, …, D_n are divisions of H, we can call A = {D₁, …, D_n} an Analysis of H.

• An analysis of Sri Lanka might include divisions according to religious and racial and linguistic criteria. Thus we might have H = Sri Lanka, D₁ = {Buddhists, Hindus}, D₂ = {monolingual Tamil, monolingual Singhala, bilingual}, D₃ = {Tamil, Singhala}. Then A = {D₁, D₂, D₃} would be an analysis of Sri Lanka.

Let A = {D₁, …, D_n} be an analysis of H. Then the identity of x ∈ |H| wrt that analysis is:

• ID(x|A) = {ID(x|D₁), …, ID(x|D_n)}

In the example above we might have ID(Bob|A) = {Hindu, monolingual Tamil, Tamil}