This paper was inspired by Piero De Giacomo's book Finite Systems and Infinite Interactions:  The Logic of Human Interaction and its Application to Psychotherapy.  I met Piero at the WPA meeting in Madrid in the summer of '96, and we subsequently exchanged books.  After brief perusal, I laid his aside to await a thorough reading during my winter sojourn in India.  And it certainly repaid the wait.  It is not an easy book to read, but I strongly recommend it, both for its logical approach to human interaction, and for the originality of some of his therapeutic interventions.     For instance, he has an intervention which derives from the interactive style of "moving into the world of the other".  He uses this with anorectic girls, and will so manipulate the family that the girl, together with her distant father, evade the intrusive mother, and spend a month together during which they are in each other's company 24 hours a day, and during which the father learns about his daughter.  This was effective in a high proportion of cases.  I have used it myself (slightly modified) in one case, to good effect.  I got the impression that it tackled what is probably a widespread alienation of daughters from their fathers, caused by modern working and family practices, fear of incest, adolescent rebellion, etc., and as a result of which the daughters have low self-esteem and are at risk of various types of psychopathology.

   Piero has been Professor of Psychiatry in Bari in southern Italy since a very young age, and, like the Milan group, moved from psychoanalysis into Batesonian/Palo Alto type family therapy in order to deal with the situation which followed the sudden closure of Italian psychiatric hospitals.  His book is a remarkable application of logic to human interaction and so to styles of intervention.



Defining animal relationships


Most animals form relationships which are asymmetrical in terms of power;  that is to say, one becomes dominant and the other subordinate.  No species apart from man seems able to form a close, equal relationship with a member of the same sex.  Probably the nearest is the female chimpanzee, but their relationships tend not to be close in the wild. 

   The procedure of forming a relationship was described for the first time in English by Schjelderup-Ebbe in 1935, when he described the confrontation between two strange hens.  Three things could happen.  Both hens could claim dominance, in which case they fought, and the winner became dominant.  Or one hen could claim dominance, and the other not contest the issue, and automatically adopt a subordinate role.  Or both could behave like subordinates, in which case one or the other would eventually realise that the dominant role was vacant, and adopt it.  Once formed, the asymmetry in the relationship was stable, and a reversal of asymmetry was associated with behaviour disturbance (Price and Sloman, 1987;  Price, 1988).  The vast majority of animals develop relationships with strange conspecifics in the same way.

   It is useful to think of the operation as occurring in two stages:  a stage of assessment and a stage of engagement.  The stage of assessment may end, as described above, with an amicable distribution of roles.  One animal can see clearly that the other is bigger, stronger, and with more powerful allies, and so makes a signal of deference and/or submission.  It is only if they are equally matched that a serious fight occurs, leading to the victory of one and the defeat of the other.  So an animal can reach subordinate status either by backing off in the assessment stage or being defeated in the engagement phase.



Defining human relationships


A human relationship may be defined in the above way, but it is likely to be complicated by two factors that do not apply to animals.  One is the possibility of symmetrical closeness already referred to;  the other is the influence of outsiders and outside forces (cultural expectations).

   I am using the term "definition of a relationship" in the sense of Bateson (1972) and Sluzki and Beavin (1965).  Relationships may be either symmetrical or complementary in terms of power.  The ultimate source of power lies in the person who defines the relationship (or,in a symmetrical relationship, the definition is shared as the result of negotiation).  Thus every dyad either contains two "joint definers" or a "definer" and an "acceptor" (of the definition provided by the other).  Every communication within the dyad has an informational component and a definitional component (which acknowledges the current definition of the relationship).  Most definitional components are redundant, and when they are redundant, the relationship may be said to be in the hedonic mode.  When the definitional components of communications are not redundant (that is, when they offer a new definition of the relationship, not yet mutually accepted) the relationship may be said to be in the agonic mode (Price, 1992).

   In order to depict the various possibilities, I will follow the example of De Giacomo (1993) and use Venn diagrams.  In a Venn diagram, two people are represented by overlapping circles situated within a rectangle.  The intersection, or overlap of the circles, represents what they have in common;  the remainder of the circles represent what they each have but do not share;  and the area of the rectangle outside the circles represents what they do not have, but other people have.  An element can be taken from any of four areas - from the space of one or other person, from the shared space, or from the space occupied by neither person.  De Giacomo considers the case of the interaction of George and Mary, and the way it affects George.  George enters the interaction and exits from it, having had the chance to select an element from any of the four spaces:  from his own space, from Mary's space, from their shared space, and from the space outside them.  There are 2 times 2 times 2 times 2 = 16 interactive styles, which result from George's repetitive tendency to take elements from one or other space.

   I would like to make two modifications to this scheme.  One

is to make the relationship the protagonist, rather than George.  We are concerned with defining the relationship, and we can say that the final definition can select an element from the definition proposed by George, and from the definition proposed by Mary, from proposals that they both put forward, and from outside people and forces.  We insert George and Mary into the system, and come out with (let us say) the Smiths.  In doing this we lose some detail (the difference in interactive style between Mary and George) but we gain by moving from the linear concept of interactive style into the systemic concept of the relationship.  In the psychology of differences, we are concerned, not with the differences between individuals, but with the differences between pairs of individuals.

   The other change is to acknowledge that outside forces may or may not affect the symmetry of the relationship.  Instead of two options, there are four, as follows:


     0  Outside forces do not affect the relationship

     1  Outside forces require George to be dominant

     2  Outside forces require Mary to be dominant

     3  Outside forces require George and Mary to be equal


Therefore, with this new model, instead of having 16 Venn diagrams depicting 16 interactive styles, we have 32 diagrams depicting 32 different ways a relationship can be defined.  Of course, not all of the 32 diagrams are of equal interest, and I shall only deal with some of them.

   I shall start with those relationships in which outside forces have no influence, and I shall take first the diagrams which represent symmetrical relationships.






                   George    Mary







(the shaded area represents the source of the definition of the relationship)


f1:  a relationship based only on agreed defining elements.  A marriage of convenience.  Or two people who come together to play golf once a week, but do not meet in the intervening time.









f6:  a relationship in which shared elements are rejected, and the final definition is a compromise between opposing definitions.  This is the classical family therapy meaning of "symmetrical relationship", implying hostility between two evenly matched parties.  It is likely to be unstable, tending either to disintegrate in what Bateson called "symmetrical schismogenesis" (Bateson, 1972) or to lead to the defeat of one party.  The usual example given is the marital relationship depicted in Edward Albee's play Who's Afraid of Virginia Wolf?  Another example is the antagonistic relationship between Struan and Brock in James Clavell's novels Taipan and The Noble House.








f7:  an equal relationship between two relatively independent people who are nevertheless willing to share what they have in common.  The equivalent "interactive style" is that of "maintaining one's own world, accepting the world of the other and sharing".  An early classical example is that of Theseus and Pirithous.  In John Birtchnell's two dimensional scheme it is represented by "neutral closeness" (Birtchnell, 1993).  f7 is probably the peak of human relating.  It includes a joy in similarities and a respect for differences.  Of course, it is in danger of becoming unstable if any differences of opinion become salient and irreconcilable, as occurred in Rosamund Pilcher's novel September. 

   If we can agree that being close and sharing with another person is a situation of trust which, if the trust is broken, may give the other person power or at least some advantage over us, then two people in f7 are formally in a Prisoner's Dilemma situation.  Each benefits from co-operation over many iterations, but in the short term there is a temptation to make a sudden bid for the definer role, and whoever defects in this way scores an advantage, whatever the other does.








f0:  a relationship in which no definitions are offered.  This type of relationship was found in the families of schizophrenics by Palazzoli et al. (1978).  No decisions were ever made, and no initiatives taken.  Any statement that seemed likely to offer a tentative definition was immediately invalidated either by the speaker or by another family member.


That completes the symmetrical relationships (apart from those including outside influence).  In dealing with asymmetrical relationships, it will be convenient to make use of the fact that each relationship has a mirror image, and to include the variable of "initiative in creating asymmetry".  Those in which George on the left is dominant I will assume are so because of his assertiveness, while those in which Mary is dominant I will assume are so because George idolises Mary.









f3:  George is assertive, and only accepts those of Mary's definitions with which he agrees.  This kind of relationship is typical of the husband-dominated marriage.

   The process of forming this type of relationship (and also f2) is best described by game theory (hawks and doves or game of attrition - Maynard Smith, 1982).








f2:  George is again assertive, but this time he rejects those elements of the definition which he shares with Mary.  In doing this he denies himself in order to reduce Mary's power.  He is the typical tyrant husband, who does not enjoy his wife and will not let anyone else enjoy her (or let her enjoy herself).








f4:  George idolises Mary, and puts her on a pedestal, so that she is on a different level from him and they cannot share.








f5:  George loves and respects Mary, seeing her as a superior being, but not so superior that they cannot share.  Perhaps this is the best definition for a happy marriage.  It also applies to mentor/protege relationships of various sorts.



Outside influences


Then we come to those cases in which the outside world affects the definition.  There are 24 of these, and it would be tedious to detail them all.  In fact, they are only of interest when the definition demanded by the outside world clashes with the definition arrived at by the interacting couple. 














f12 and f13:  The world expects George to be dominant to Mary, but in fact Mary is dominant to George.  This common situation was called "marital skew" by Lidz et al. (1957), who related it to pathology in the offspring.  It can certainly cause suffering in the subordinate spouse, who has not only the pain of being dominated, but also the ridicule of the outside world at his pathetic situation.  Bishop Proudie in Anthony Trollope's The Last Chronicle of Barset is the prototype here, and it is probably no coincidence that Trollope makes the Bishop undergo a recognisable episode of clinical depression.

   It causes trouble in the work situation too, when a subordinate feels more competent than his boss, and both suffer.  The problem was tackled in the past by psychologists under the heading of "status incongruence".








f11:  The boss treats his subordinate as an equal.  This is a delicate situation which might reflect excellent working practice, or it might confuse the subordinate as to his exact role.  Not to be recommended for the "authoritarian personality".



Limits of the model


All theories are oversimplifications, and one hopes that the information left out justifies the simplicity of the model.  One variable I have left out is John Birtchnell's axis of closeness/ distance.  This is not because the axis is unimportant, but that it is less important for the kinds of negotiation represented here.  I have also left out that component of Birtchnell's axis of upperness/lowerness which includes the sort of lowerness that people want to have (like being looked after), because I think that lowerness of that sort is different from the sort of lowerness that Bateson and others talk about, and with which I am concerned here.  Birtchnell's lowerness is to do with nurturance and parent/child relationships, whereas the sort of subordination I am talking about is a property of relationships between adults, and is unrelated to the question of who nurtures whom.  To some extent, closeness/distance must be related to whether any of the definition of the relationship is shared (i.e., to the difference between f2 and f3, f4 and f5, and f6 and f7).

   Also left out is the question of whether the equal relationships are co-operative or competitive, and whether the unequal relationships are protective or exploitative.  In my view this depends on whether the definitions are accepted fully by both parties, in which case the relationships are co-operative and protective, and interaction can be said to take place in the hedonic mode (Price, 1992).  If the definitions are not accepted (in the case of symmetrical relationships) or if they are only accepted with reluctance and resentment (in the case of asymmetrical relationships) the interaction of the relationship can be said to take place in the agonic mode.  To reflect the agonic/hedonic variable, we would need each of the Venn diagrams to be repeated in agonic and hedonic forms, giving us 64 diagrams altogether.  That, of course, is the number of hexagrams in the I Ching, so perhaps at that stage we are approaching some natural limit.

   John Birtchnell (1993) distinguishes between positive and negative relating, and some of this difference is subsumed under the agonic/hedonic distinction.  Other aspects of the positive/negative axis such as whether the parties feel secure in their relating, and whether they treat each other with respect, are not included in the present scheme.

   A final comment on the situation in which outside forces prescribe symmetry.  In this case, they may also prescribe the mode.  An example of outside forces prescribing the hedonic mode is provided by the Athenians sending both Nikias and Alcibiades as equal joint generals to command the expedition to Sicily.  The message is "We want you to co-operate for the common good."  The fact that in the event they did not co-operate and the expedition failed is another matter, reflecting the limited influence of outside forces, at least at a distance.  Contrasted with the Alcibiades/Nikias relationship is the relationship between two boxers before a fight, or two parliamentary candidates before an election.  Here the message from neutral observers is, "Be equal but competitive, until the ritual event proves one of you the better man" (in addition, each competitor is getting messages of his superiority from his supporters, but, of course, these cancel each other out from the point of view of the diagram).





I have tried to extend to relationships the logical approach which Piero De Giacomo applied to the interactive styles of individuals.  With 64 Venn diagrams we can portray the diversity of power relationships between same-sexed adults (and, with less confidence, to opposite-sexed adults).  Each of the 64 can vary continuously on the axis of closeness/distance, giving a multiplicity and complexity which is likely to defy analysis, and to leave the art and mystery in human relationships safe from the probes of science.









Bateson, G. (1972) Steps to an Ecology of Mind. New York: Ballantine Books.


Birtchnell, J. (1993)  How Humans relate:  A New Interpersonal Theory.  Hove:  Erlbaum.


De Giacomo, P. (1993) Finite Systems and Infinite Interactions:  The Logic of Human Interaction and its Application to Psychotherapy.  Norfolk CT:  Bramble Books.


Lidz, T., Cornelison, A.R., Terry, D., & Fleck, S. (1957) The intrafamilial environment of schizophrenic patients. 2.Marital schism and marital skew. American Journal of Psychiatry, 114,241-248.


Maynard Smith, J. Evolution and the Theory of Games. Cambridge:  University Press, 1982.


Palazzoli S, Cecchin G, Prata G, Boscolo L. (1978)  Paradox and  Counterparadox. New York: Aronson.


Price, J.S. (1988) Alternative channels for negotiating asymmetry in social  relationships. In Social Fabrics of the Mind (ed. M.R.A.Chance) Hove:  Lawrence Erlbaum. Pp. 157-195.


Price, J.S. (1992) The agonic and hedonic modes: definition, usage, and the promotion of mental health. World Futures, 35, 87-115.


Price, J.S. & Sloman, L. (1987) Depression as yielding behavior:  an animal model based on Schjelderup-Ebbe's pecking order. Ethology and Sociobiology, 8, 85S-98S.


Schjelderup-Ebbe, T., 1935, Social behaviour of birds. In Handbook of  Social Psychology. C. Murchison (Ed.). Worcester, Mass.:  Clarke  University Press, pp. 947-972.


Sluzki, C.E. and Beavin, J. (1965) Symmetry and complementarity: an operational definition and a typology of dyads. Acta psichiatrica y  psicologica de America Latina, 11, 321-330. Reprinted in Watzlawick, P. &  Weakland, J.H. (Eds) The Interactional View. New York: W.W.Norton, 1977. Pp. 71-87.





Goa, March, 1997                           John Price