Phase 2a

Interactional analysis – Describing internodal relationships

1) Binary properties – does a relationship, x <=> y, exist between nodes?

A relationship in the context of the group is being viewed as transactional. A node having a need of another node irrespective of response signifies the existence of a relationship between those nodes even though it may not be entirely positive. Thus a relationship diagram of the group focuses upon the nodes and depicts levels of neediness along with intensity of demand.

The dynamic in the above map is derived from the recordable need of one node of that perceived to be held by others. It does not suggest whether the need has been met, whether that which is held by a given node, and demanded by others, is available etc. The map simply illustrates whether a node has need of another.

The map provides a holistic view of need/demand from which particulate data can be determined. A useful analytical medium is a matrix to record the number of output/input channels i.e. need/demand relationships respectively. Thus the matrix offers three interpretive views: i) a numerical holistic profile, ii) a distributive needs profile and similarly, iii) a distributive demand profile.

The map does not have ‘self-need’ as a declarative and so might be assumed to be so for all nodes or not so for all nodes. This is likely to be ‘self-determined’, and somewhat subjective??, but certainly not an analytical feature at this primitive level. It will be looked at further in the complex strand (Phase 2b).

For clarity (and to avoid tedious repetition!), subsequent analysis will be illustrated using Ns only – exactly the same principles can be applied to N$.

Each matrix provides for the extraction of column and row summations, need / demand matrices respectively. Transposition of the demand matrix enables a need/demand profile matrix to be derived thus:

Yet another distillation provides ‘resource drain’ (n/d) and ‘contributory’ (d/n) distributions for the group as illustrated above. The bonded pairs thus associated with the group in this context, provides for three potentially useful nodal coefficients:

2) Weightings and scalars – strength and quality of relationships

< requires expansion – note form only at present >

• Set intensity range regarding urgency of need (0 -9?) – define limits

• Consider an ‘anti-need’ (-9 - <0)? Or re apply this as a willingness to supply? Could this be a form of +ve discrimination (Batel)?

• -ve entries within matrix not to be included in row and column summations since an anti-demand or anti-need profile does not reduce the demand or neediness of others

3) Competitive & cooperative behaviours – (Game of Chicken, Stag Hunt Dilemma, Prisoners Dilemma) initially as paired responses

• Interactive paired behaviours of all supplying disputable willingness, all needing disputable declaration

• Standard matrix analysis likely to remain useful

• Revisit ‘Structural Coupling’ (Maturana & Varela)

• Above tied in to game rules and domain demarcation

4) Broader Game Theory – Cellular Automata (including Wolframs classification) – expanding interaction of entities beyond the ‘two-player’

• Interactive multiple behaviours of all supplying disputable willingness, all needing disputable declaration

• Above tied in to game rules and domain demarcation (test with modified Conway rules)

• Matrices moving toward multidimensional arrays

• Descriptive analysis likely to focus upon ‘standard moves’; expected play; end-game format

• Consideration of:

• Above may have solutions in saddle-back diagrams (Flack), catenaries, resolved vectors and vector spaces

• Consider:

o Criticality of need

o Limit / rationing of supply

o Transactional costs

o Transactions via intermediaries (middle man person costs)

• Suggest Nash’s Equilibria? (JWood)

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