Download On the Complementarity of Expectations: Coupling

yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Document related concepts

Bioecological model wikipedia , lookup

Background music wikipedia , lookup

Cyberpsychology wikipedia , lookup

Culture and positive psychology wikipedia , lookup

Cognitive development wikipedia , lookup

Double negative wikipedia , lookup

Enactivism wikipedia , lookup

Negative mass wikipedia , lookup

Negative affectivity wikipedia , lookup

Negative number wikipedia , lookup

Play (activity) wikipedia , lookup

On the Complementarity of Expectations:
Coupling Parsons with Balance Theory
Kazuto Misumi
Graduate School of Social and Cultural Studies, Kyushu University
4-2-1 Ropponmatsu, Chuo-ku, Fukuoka 810-8560 Japan
[email protected]
When we are to introduce the interpretative dynamic role process against 'homo sociologicus,' we
are confronted with the problem how to capture the various reality systematically.
By coupling
the 'complementarity of expectations' with balance theory, we formally propose a cognitive
framework to analyze the double contingency role relationship.
Through conceptual discussions,
we introduce two basic signed graphs: the unit graph T that presents the in-personal role
regulation and the double contingency graph G in which two unit graphs are connected by the two
inter-unit lines.
While the signs of inter-unit lines, that inter-personally connect role-
expectations, determine the complementarity in G, the signs of G's cycles determine the balance of
G. With regard to G's balance, two theorems are derived. The first states that T's imbalance is
the sufficient condition of G's imbalance, and the second states that one positive cycle in G larger
than 3-cycle is the sufficient condition of the balance of G that is composed of balanced T. Utilizing
these theorems, we systematically classify the role relationship represented by G, and discuss
about the substantial meaning that some paradoxical cases imply.
Key words and phrases:
Complementarity of expectations, Balance theory, Role
1. Introduction
Parsons and Shils (1951:15) proposed the concept of complementarity of expectations
"not in the sense that the expectations of the two actors with regard to each other's action are
identical, but in the sense that the action of each is oriented to the expectations of the other."
In addition, "in an integrated system, this orientation to the expectations of the other is
reciprocal or complementary" (Parsons and Shils 1951:105).
In the framework of social
system, a key concept that mediates between individual and society is role- expectation.
The logic is fundamentally parallel.
Following Parsons and Shils (1951:19- 20) again, "once
an organized system of interaction between ego and alter becomes stabilized, they build up
reciprocal expectations of each other's action and attitudes which are the nucleus of what
may be called role-expectations. .... The pattern of expectations of many alters .... constitutes
in a social system the institutionalized definition of ego's roles in specified interactive
These descriptions evoke a paradox discussed by Dahrendorf (1968:25): "At this point
where individual and society intersect stands homo sociologicus, man as the bearer of
socially predetermined roles.
To a sociologist the individual is his social roles, but these
roles, for their part, are the vexatious fact of society."
In other words, by constructing 'homo
sociologicus,' sociology might develop a rational understanding of society; however, it has
excluded as a result individuality and freedom of the human being.
Against homo sociologicus, some researchers see the dialectical possibility of liberation
from the viewpoint of real actions (Tenburuck 1961, Berger and Pullberg 1965, Yamaguchi
1975, Kurioka 1980, Tanaka 1984, Nomura 1987).
strong assumptions of homo sociologicus.
Others point out unrealistic and too
For example, Habermas (1973; also see Nomura
1982: 240-245) asserts that homo sociologicus shall satisfy following three theorems:
1) Integration theorem (high degree of the complementarity of expectations)
2) Identity theorem (coincidence between role definition and role interpretation)
3) Conformity theorem (realization of normative contents into actions)
Analogously, Levinson (1959) and Morris (1971) assert that homo sociologicus requires
unrealistic high level coincidence among three aspects; role-expectations, role-conception,
and role-behavior.
These assertions imply that the complementarity never be rigid and
stable in the real world; rather, it shall be inherently flexible and unstable, being founded on
interpretative processes.
Although temporary stable interaction may appear through ritual
actions and role-playing (Goffman 1959,1967), the complementarity is no longer a sufficient
(even a necessary) condition for the stability.
Our standpoint is between the extremes. As Parsonians assert, the institutionalization
shall be a basic general process and, resulting in the complementarity to some extent, it
conditions the stability of interaction. However, in the real world, not only the process, but
also the other interpretative processes condition the stability as anti-Parsonians assert.
Among those that are mostly irregular, we focus on a relatively general process, the cognitive
As we will see later, the balance theoretical perspective has primitively presented
in role theory, but the tradition has stopped before formalization.1) The purpose of this
paper is to develop a graphical model that takes in the viewpoint of complementarity and
balance at the same time, and through it, to examine conditions for the stability of role
relationship from multiple angles.
2. Conceptual Framework
Before going forward formal analysis, we introduce our conceptual framework of role. As
already cited, some role theorists developed three concepts (Levinson 1959, Morris 1971,
Funatsu 1976:187-188, Watanabe 1981):
・Role-expectations .... Normative expectations from alter with regard to ego's action. (Its
referent point is functional requirements of a social system.)
・Role-conception .... Ego's normative expectation with regard to action of him/herself. (Its
referent point is functional requirements of a personality system.)
・Role-behavior .... Ego's action actually taken in interaction.
Following Watanabe (1981: 114), we can consider the relationship among the three.
・Role-consensus (⇔role-disensus) .... Compatibility between role-expectations and role-
conception in regard to normative contents.
・Role-adaptation (⇔role-deviation) .... Compatibility between normative contents of roleexpectations and role-behavior.
・Role-identification (⇔role-distance) .... Compatibility between normative contents of
role-conception and role-behavior.
Morris (1971) represented the relationship as a triple graph, and Watanabe
(1981)discussed the substantial meaning of each compatibility pattern.
compatible and " - " be incompatible.
adjustment process.
Let "+" be
Suppose that the sign indicates the result of
As three graphs that have only one negative line carry logical
problems, the following five are valid (Figure 1).
Figure 1.
Triple Graphs in Morris=Watanabe Framework
This graphic presentation is of great help to classify the results of actor's internal role
regulation, although some questions arise. Suppose that an actor whose state is a) and
another whose state is ß) encounter.
Then, certain inter-personal adjustment should occur
between them; however, in this framework, we can neither describe the process, nor judge
whether the complementarity is satisfied or not between them.
Moreover, the state of a)
could represent 'complementarity,' but only when the same role-expectations are shared by
In order to take these interactive viewpoints into the framework, two triple graphs
shall be linked.
Kobayashi (1983), after defining 'role-knowledge' as the typification knowledge based on
social expectations with regard to actions, insists that it exists not only as 'stock,' but also as
The knowledge as flow means messages of expectations that are exchanged between
actors through role-behavior.
In the sense, role-behavior is an output from ego's
role-regulation and, at the same time, an input to alter ego's role-regulation.
As role-
interaction concerns plural roles that make a pair, the input is interpreted by alter as a
message with regard to the role on the alter ego's side.
When ego decides role-behavior to be
taken, he/she anticipates what expectation it should reciprocally indicate toward the role of
In other words, ego anticipates how his/her role-behavior will be interpreted and, as a
result, what reaction will be taken by alter. This is the point when Parsons says, "the
action of each is oriented to the expectations of the other." 2)
Focusing on this aspect of role-behavior, we refine the triple graphs as in Figure 2.
replace 'role-behavior' with 'role-expectation toward the other,' and designate actor i's roleexpectation toward the other actor j as Eij.
We also replace original 'role-expectation' with
'role-expectation toward self,' and designate actor i's role-expectation toward self as Eii.
'Role-conception' is the same; however, as it is strictly 'role-conception of own role,' we
designate actor i's role-conception as Cii.
This refinement makes the graph to describe
consistently the cognitive relationships.
More importantly, it clarifies that the role
regulation is not only on one role, but also on (at least) two roles that make a pair.
the point of the former is the compatibility between Eii and Cii in the sense of coincidence of
normative contents, that of the latter is the anticipated reciprocity between Eii and Eij, as
well as between Cii and Eij.
Figure 2.
Triple Graphs in Our Framework
With regard to a'), 'conformity' is better than 'complementarity' because it describes only
in-personal harmonious state.
as Figure 1.
The meaning of the other types can be interpreted as same
Suppose that there are two normative contents, 'working' and 'keeping house,'
that are not compatible with each other, but are reciprocal. For a husband (actor 1), if both
E11 and C11 are 'working' in regard to the role of 'husband,' the line E11-C11 is positive
(compatible). Moreover, if his E12 toward his wife (actor 2) is 'keeping house' in regard to
the role of 'wife,' both E11-E12 and C11-E12 are positive (reciprocal). We can judge that this
cognitive state is a') in Figure 2.
However, if his C11 is 'keeping house,' not only the
compatibility between E11 and C11, but also the reciprocity between C11 and E12, is broken.
Then, both E11-C11 and C11-E12 turn negative, so that we can judge the state as d'), and so
Notice that our purpose at present is not to describe and predict what role-behavior will
be actually taken by ego and whether or not alter ego will react against it reciprocally.
Rather, given a series of concrete interaction, we are interested in finding a cognitive state
that could give guidance to it, and therefore explains the observation consistently.
that we observed a husband to work till late and his wife to welcome him preparing dinner
everyday, moreover, we could know they had felt no difficulty in the situation.
the relationship among Eii, Cii, and Eij shall be, that is our question.
Then, how
More generally, it is
our purpose to examine under what cognitive states, interaction shall be complementary and
stable, whatever the actual behavioral contents.
Figure 2 will answer it, but only partially.
In order to get a complete answer, as we
already suggested, two triple graphs shall be linked together.
It is plausible to assume that
they are linked by two lines between Eii and Eji (i,j=1,2 and i ≠ j), and that the
'complementarity of expectations' directly depends on the compatibility between the
expectations, that is, whether both Eii-Eji lines are positive or not. 3)
According to the
extended framework, a wife (actor 2) is assumed to receive E12 reciprocally through her
husband's (actor 1's) role-behavior and to check it with E22.
for her husband (actor 1).
The reverse process is assumed
Notice again that, at present, the complementarity is judged
from a third party's viewpoint.
In the previous example, it is neither the wife nor her
husband, but a third party (a researcher), to judge the sign of E12-E22, even though the
former themselves might be in fact able to do it. 4)
Figure 3 summarizes the conceptual framework that we have finally proposed, and
Figure 4 is its simplified graphical representation.
This framework represents the general
cognitive relationship between two actors, but only with regard to a focused aspect of a
Generally, not only that plural role-relations (e.g. husband-wife and doctor-
nurse) sometimes overlap, but also that each relation contains plural pairs of normative
contents that are essentially incompatible with each other, but reciprocal (e.g. 'working''keeping house,' 'working'-'bringing up children,' and 'representing family'-'acting behind,' in
husband-wife relation).
In a real process of role-interaction, such relations and contents
might change one after another, so that a graph in Figure 4 shall be connected to another in
succession, making an infinite chain graph as a whole.
However, if we focus only on one
pair of contents in one role-relation, the process circles on a graph in Figure 4, as far as each
actor never change his/her role-expectations and role-conception.
The framework, as well as
the graph, only captures a limited unchangeable aspect as such.
Figure 3.
Conceptual Framework of the Cognitive Role Relationship
Figure 4.
Graph of the Cognitive Role Relationship
We might have to draw one more line between E11 and E22 to check the reciprocity
between them (i.e. institutionalization).
However, logically thinking, we can judge that the
institutionalization is successful only if all lines are positive in either of Eii-Eij-Ejj (i,j=1,2
and i≠j).
3. Formalization by Balance Theory
Figure 2 and Figure 4 call up the discussions of cognitive organization by Heider (1946)
and its extended formalization by Cartwright and Harary (1956), that is, balance theory.
By introducing the concept of balance, we can have another analytical viewpoint that is
different from the complementarity itself in order to examine the stability (or instability) of
role relationship.
The following assumptions and definitions are required for graphical
formalization of our framework developed in the preceding section.
Assumption 1.
The in-personal role regulation of actor i is represented by the triple
relationship among three aspects: role-expectation toward self (Eii), role-conception (Cii),
and role-expectation toward the other actor j (Eij).
(i,j=1,2 and i≠j.)
Each relation
between them is either positive or negative.
Assumption 2.
Actor i who received Eji from the other checks it with his/her own Eii.
relation between them is either positive or negative.
Definition 1.
'Unit graph,' T, is an undirected signed triple graph that connects three nodes:
Eii, Cii, and Eij. (See Figure 2). Actor i's unit graph is designated by Ti.
Definition 2.
'Double contingency graph,' G, is an undirected signed graph in which two
unit graphs are connected by two lines between Eij and Ejj.
(See Figure 4).
We call the
lines 'inter-unit lines.'
Definition 3.
If both signs of the inter-unit lines are positive, the complementarity of
expectations is satisfied.
Additionally, we confirm some graphical terminologies and an assumption with regard to the
stability/instability of G.
Definition 4.
A cycle is a path (sequence of lines) that returns to its node of origin without
passing the same node or line twice.
The sign of a cycle equals the product of the signs of
the lines it contains.
Definition 5.
G (or its sub-graph, T) is balanced if all cycles in G (or T) are positive, and is
imbalanced, otherwise.
Assumption 3.
When G is imbalanced, there occurs some pressure toward a balanced state.
In that sense, imbalanced G is unstable, although balanced G is stable.
By coupling logically the complementarity with balance, we get a typification of the role
Our next task is to examine balance of G in each type.
(Ⅰ) Perfect complementarity: The signs of all lines in G are positive.
It is always stable.
(Ⅱ) Temporary complementarity: Both of the inter-unit lines are positive, but Ti contains at
least one negative line.
(Ⅱ-1) Stable -: G is balanced.
(Ⅱ-2) Unstable -: G is imbalanced.
(Ⅲ) Half broken complementarity: Only either of the inter-unit lines is negative.
(Ⅲ-1) Stable -: G is balanced.
(Ⅲ-2) Unstable -: G is imbalanced.
(Ⅳ) Broken complementarity: Both of the inter-unit lines are negative.
(Ⅳ-1) Stable -: G is balanced.
(Ⅳ-2) Unstable -: G is imbalanced.
4. Theorems for the Balance of G
At first, it is noticed that imbalance of G is determined by imbalance of T, regardless of
the role relationship type.
This is almost self-evident through Definition 5; however, we
confirm it as a theorem.
Theorem 1. In G, if both or at least either of Ti is imbalanced, G is imbalanced.
◇Proof: A unit graph T has only a 3-cycle (call it c), and as T is a sub-graph of G, c is also a
cycle of G. If one of Ti is imbalanced, then c must be negative through Definition 5; so that, G
necessarily has one negative 3-cycle and therefore is imbalanced. ◇
In Figure 2, imbalanced T is only e), a dissolved case where all three lines are negative,
although Theorem 1 holds even for cases in which only one line is negative. Anyway, if
either of the in-personal state of actors (represented by Ti) is dissolved, the dyadic role
relationship (represented by G) is imbalanced and unstable.
This is true, not only for types
(Ⅲ-2) and (Ⅳ-2) where the complementarity is broken, but also for type (Ⅱ-2)where it is
satisfied temporarily.
When both of Ti are balanced, balance judgment of G seems not so simple.
practically examine G that are possible in each role relationship type.
Let us
It is apparent that G
is balanced if both actors have a), 'conformity' (i.e. for type [Ⅰ]), because all lines (therefore
all cycles) in G are positive. Graphically, this is a special case of the 'positive symmetry'
where both inter-unit lines are positive. In Figure 2, balanced T is exhaustively covered by
the first four, a) through d).
As both inter-unit lines are fixed as positive under the positive
symmetry condition, possible G is given by 16 combinations between Ti as in Table 1.
a positive line is indicated by a solid line, and a negative one by a broken line.
balanced G is marked by ○, and imbalanced G by ×.
Table 1 shows that 8 out of 16 are
These are type (Ⅱ-1), and its special case for type (Ⅰ) (upper-left corner of
Table 1).
Table 2 is for type (Ⅳ), broken complementarity.
Type (Ⅳ) is understood as the
opposite of type (Ⅰ) and (Ⅱ); however, graphically, it is also symmetric in a sense that
Table 1.
Balance of G Composed of Balanced Ti : Positive Symmetry Condition
*) Figures are case number. ○ is balanced, and × is imbalanced. A solid line is positive, and
a broken line is negative. (And so on for the following tables.)
'Positive symmetry' means that
both inter-unit lines are positive.
Table 2.
Balance of G Composed of Balanced Ti : Negative Symmetry Condition
*) 'Negative symmetry' means that both inter-unit lines are negative.
Table 3.
Balance of G Composed of Balanced Ti : Asymmetry Condition
*) 'Asymmetry' means that the signs of inter-unit lines are opposite to each other. The cases in
which positive inter-unit line is lower are omitted, as the balance judgment is the same.
both inter-unit lines are negative. In fact, in Table 2, balanced cases (type [Ⅳ-1]) show the
same combination pattern as Table 1 even under this 'negative symmetry' condition.
(Needless to say, this does not mean that the graphs are identical in the corresponding
From the viewpoint of balance, the opposite of type (Ⅰ) and (Ⅱ), as well as of (Ⅳ), is
type (Ⅲ), half broken complementarity.
Type (Ⅲ) is a unique case of 'asymmetry' where
the signs of inter-unit lines are different from each other.
It is easy to confirm that, in Table
3, balanced combinations (type [Ⅲ-1]) reveals the reversed pattern.
Thus, the 'symmetry' seems critical for balance of G that is composed of balanced unit
Balance of G depends on the signs of its cycles, and the signs depend on the number
of negative lines.
Here, as the number is fixed as even in T, G' s balance depends on the
signs of larger cycles, which depend on the number of negative inter-unit lines.
Of course,
the symmetry means that the number of negative inter-unit lines is 0 or 2 (even), and the
asymmetry means it is 1 (odd).
The idea of symmetry/asymmetry is of help to regulate the relationship between the
Especially, it is suggestive that the types which are substantially located oppositely
have the same pattern of balanced combinations, formally.
However, as balance of G is not
determined only by the signs of inter-unit lines, this idea is not enough to discriminate
balanced cases in each of the combination tables.
More careful examination of the tables
leads next theorem that makes balance judgment very easy.
Theorem 2. In G where both of Ti are balanced, all cycles other than T's 3-cycle have the
same sign.
Which means that the existence of only one positive cycle larger than or equal
to 4-cycle is the necessary and sufficient condition for the balance of G.
Proof:Generally, in G, there are following four cycles other than T.
Let us examine these graphs under the symmetry condition where the signs of two inter-unit
lines, E12-E22 and E21-E11, are identical. Suppose that cycle a) is positive, being based on the
identical sign between C11-E11 and C11-E12. This implies as a rule that E21-E22 as well as E12-E11
must be positive, and that E21-C22 and C22-E22 must have the identical sign. Thus, the sign of
each line in G is automatically almost determined as graph e) below. In this graph, apparently,
cycles b)~d) are all positive, that is, they have the same sign as cycle a). Next, suppose that
cycle a) is positive, but either of C11-E11 or C11-E12 is negative. This implies that E21-E22 as well
as E12-E11 must be negative, and that either E21-C22 or C22-E22 must be negative, which results in
graph f). Again, cycles b)~d) have the same positive sign as cycle a).
Such logic comes from a fact that one of the three lines in each T cannot take the sign freely
because T is fixed as balanced, here. Therefore, when cycle a) is negative, through the same
logic, all the four cycles must have the same negative sign, too. Moreover, even when we start
from another cycle other than a), and even under the asymmetry condition, the same logic is
applicable as long as T is fixed as balanced.◇
It is apparent that, through Definition 5, finding only one negative cycle is enough for
the judgment of G's imbalance.
Similarly, Theorem 2 guarantees that finding only one
positive cycle (larger than 3-cycle) is enough for the judgment of G's balance.
together result that the sign of only one cycle (larger than 3-cycle) is critical for the
judgment of balance/imbalance of G.
5. Implications
The substantial implication of Theorem 1 is relatively clear.
As is already mentioned,
we can say that if either of the actors' in-personal states is dissolved, the dyadic role
relationship is imbalanced and unstable regardless of the complementarity.
speaking, it is not possible that dyadic role relationship is stable although either or both of
the actors are unstable in-personally, even if the relationship is complementary.
On the other hand, Theorem 2 covers the cases where both actors are in-personally
Some of them are paradoxical in the sense that G is complementary but unstable, or
inversely, G is not complementary but stable. Theorem 2 implies that all the paradoxical
cases (as well as all the other cases) can be consistently explained based on just one cycle in
G. As we already saw in the proof of Theorem 2, there are possibly four such cycles. If we
pull out one out of them through certain reasonable assumption, we could consistently and
generally explain the double contingency situations based on just two cycles in G, that is, T
and the extracted one.
We have noticed that our framework stands on a viewpoint of the third party.
It is
apparent that, for a researcher who observes role-interaction and plans to analyze it through
our framework, the minimum cycle is the best as far as it guarantees the same balance
judgment as larger ones.
Needless to say, a cycle that satisfies the condition is c)in the
proof of Theorem 2. We call this cycle the 'minimum contingency cycle' (MCC) and we
confirm its validity as the balance standard in the following corollary.
Corollary of Theorem 2. In G, the minimum contingency cycle (MCC) is a cycle, by the sign
of which balance/imbalance of G (composed of balanced Ti) is determined.
- 10 -
The sign of MCC depends on two components: the signs of inter-unit lines, Eij-Ejj, and
the signs of Eii-Eij (for i,j=1,2 and i≠j).
Coupling the two components with each other, as in
Table 4, we can compactly regulate all the combinations in Table 1 through Table 3, keeping
correspondence to the typification of role relationship.
Now, we go back to the paradoxical cases previously mentioned.
where G is complementary but unstable.
Table 4.
The first is type (Ⅱ-2)
In this type, the signs of Eii-E ij must be
Complementarity and Stability of G Composed of Balanced Ti
different from each other, therefore the MCC takes a form:
This MCC presents that, while the complementarity is kept, role-expectations toward self
and toward the other are not reciprocal on either side.
It is also noticed that E11 and E22
are reciprocal because all lines are positive in either E11-E12-E22 or E22-E21-E11 (This is an
institutionalized situation, in that sense.)
Suppose again two normative contents, 'working' and 'keeping house,' that are not
compatible with each other, but reciprocal. It is impossible in the MCC above to arrange
them with no logical contradiction.
For example, under the condition of negative E11-E12
and positive E22-E21, if E11 is 'working,' E12 and then E22 shall be 'working,' however, as E21
shall be also 'working,' E22 and E21 never be reciprocal (E22-E21 never be positive).
It is
probable that this case is actually observed with no contradiction, only if it is possible to
devise a kind of 'quasi-category' that satisfies the compatibility and reciprocity at the same
time, between either of original categories.
For example, 'part-time working' and '(full-
time) working' can be understood as compatible with each other and reciprocal, at the same
Similarly 'keeping house' could be replaced by 'part-time housework.'
Another point of this case is that role-expectation toward the other never be realized
either in half or at all, even if contradictions could be avoided by utilizing a quasi-category.
Suppose that actor 1 (husband) is 'rebellion' (see Figure 2), therefore E11-E12 is negative.
- 11 -
He rejects '(full-time) working' (E11) and rebelliously expects his wife to perform it (E12).
Actor 2 (wife) interprets the expectation as 'part-time working' in a compatible range of
'working.' Here, E12 will be realized, but only in half, because the wife will not actually
engage in full-time work.
On the contrary, the wife reciprocally expects her husband to
perform 'full-time working' (E21), but her expectation will not be realized at all because her
husband rejects it.
Thus, instability of this case implies mutual dissatisfaction. We can understand this
paradoxical case as the unsatisfied complementarity kept by quasi-categories.
The next paradoxical case is type (Ⅳ-1) where G is not complementary but stable.
this type, the signs of Eii-Eij must be identical, and the MCC takes a form:
When both Eii-Eij are positive, this MCC presents that role-expectation toward self and
toward the other are reciprocal in each in-personal state, even though the complementarity
is broken.
This reciprocity may come from 'conformity,' or may be just role-playing founded
on 'suppression.'
Anyway, as E11 and E22 are not reciprocal (a negative line is included both
in E11-E12-E22 and E22-E21-E11), the actors are conformable, but only in-personally.
probable situation is that both actor 1 (husband) and actor 2 (wife) have 'working' for Eii,
and, obeying it, expect to perform 'keeping house' each other.
exactly founded on the separated relationship.
The stability of this case is
Their expectations completely keep missing
each other; however, they keep their social identities, respectively. Thus, we can call this
case, which is probable in multi-cultural situations, the stable separation founded on social
When both Eii-Eij are negative, all relations in the MCC are broken, and E11 and E22 are
neither reciprocal (one and more negative lines are included in both E11-E12-E22 and
E22-E21-E11). If both actors are 'rebellion,' a probable situation is that actor 1 (husband),
rejecting 'working' (E11), rebelliously expects his wife to perform it; on the contrary, actor 2
(wife), rejecting 'keeping house' (E22), rebelliously expects her husband to perform it.
(Though E11 and E22 are apparently reciprocal, it is not a result of institutionalization, but
an accidental result through the role regulation.)
As same as the previous case, the
separated relationship brings about the stability; however, in this more disordered case, the
separation is founded on personal identity rather than social identity.
In fact, each actor
keeps his/her isolated but unshakable internal world irrespective of expectations from the
society and his/her partner.
In the sense, this case is the stable separation founded on
personal identities.
On the other hand, if both actors are 'impracticability,' the situation implies the
existence of external obstacles to role performance.
For example, both E11 and C11 are
'working' for actor 1 (husband), but some obstacle (e.g. unemployment) not only prevents
- 12 -
him from performing it, but also makes his E12 'working' unwillingly.
Similarly his wife
neither be able to perform 'keeping house' following E22 and C22, and she inevitably shows
'keeping house' for E21.
The stability of this case clings to the internal consistency between
Eii and Cii in each actor. We can call the case the stable but inevitable separation caused by
external obstacles.
Likewise, the other situations are also able to be explained thoroughly based on T and
the MCC. Having this compact analytical framework, we could systematically find not only
the graphical regularity among various G, but also the comprehensive meaning underlying
identical cases from the viewpoint of complementarity and balance.
6. Concluding Remarks
The discussions of social system and homo sociologicus make sense to understand the
mechanism of stabilization of a society.
On the other hand, the criticism against them also
makes sense to understand the dynamic reality which is going on even under the stability.
An important theoretical problem is that, as soon as we introduce the latter standpoint and
say that the complementarity of expectations shall be seen as inherently flexible and
unstable, we are confronted with the infinitely various world.
We believe that the previous
analysis could suggest a possibility to grasp such world systematically and to link the two
theoretical streams that have confronted each other.
We have considered the role relationship as a cognitive framework in which actual role
interaction is explained from a viewpoint of the third party.
In order that we stand on a
viewpoint of the actor and follow actual interaction under the framework, some specific
problems must be resolved (see also note 4]).
The cognitive instability of G due to its
imbalance probably reduces an actor's utility, therefore influences interaction. On the other
hand, irrational interaction will not be interrupted, but will be continued through the
revision of role relationship toward balance.
It is open to further discussion whether we see
the aspect in a unified utility formation process or in a dual framework of action.
Additionally, we will be confronted with the problem how to compare objective payoff with
mental comfort and distress.
With regard to the cognitive revision, the dynamic process of G's change is also our
further subject.
From a formal point of view, we will be able to utilize the 'line index' of
balance to examine which G is easier to be transformed into which. Perhaps, it is also
required to investigate the relationship between our model and 'expectation states theory'
(Berger et al. 1974,1977; Fararo and Skvoretz 1986; also see note 1]). 5)
Our graphical formulation can easily be extended to triad and, possibly, to a general
interaction system that is composed of plural actors.
Based on the extended G, as
exemplified in Figure 5, we will be able to re-examine Simmel's discussion, the concept of
role-set, and empirical findings in sociology of family as well as in ethnomethodology and
symbolic interactionism.
- 13 -
Figure 5.
Examples of Extended Triad Graph
There have been so many graphical approaches to role theory (especially in social
network researches); however, most of the discussions have been concentrated on the
'structural equivalence' and on objective role-relations. We hope that this paper stimulates
another graphical approach that incorporates the process of in-personal role regulation into
the inter-personal double contingency relations.
An earlier version of this paper was presented at European Japanese Conference on Rational Choice and
Formalization (Leipzig, Oct. 2001) and 102nd Conference of Japan Sociological Association for Social
Analysis (Tokuyama, Dec. 2001). I appreciate all the productive comments.
1) 'Expectation states theory' developed by Berger et al. (1974,1977) should be seen as a formal extension of
this tradition.
It is directly concerned with organization of status characteristics through task
performance and evaluation in a task-oriented group; however, 'task' may be analogously replaced by
The theory also includes balance theoretical formulation.
It is expected that our formulation,
that focuses on dyad and actors' internal states as well, can be linked together.
2) According to Kobayashi, the process consists of two aspects: 1) ego refers to role knowledge as an
interpretative code in expecting alter ego's reaction, and 2) ego refers to it as a code switch between social
role-expectations and role-conception of him/herself. (Also see the discussion on 'relevance' by Schutz
[1970], and the distinction between 'logic-in-use' and 'reconstructed logic' by Fukazawa [1990, 1994]).
In the conceptual framework of Watanabe (1981:111), on which we developed our framework in Figure 2,
the latter aspect was incorporated as 'role negotiation process'; however, the former was neglected.
refinement is capturing the aspect.
3) In this paper, the term 'complementarity' is limited to this inter-personal aspect, and is distinguished
from the 'anticipated reciprocity' in the individual recognition previously mentioned.
be synonymous with the anticipated 'complementarity.'
The latter should
However, through this conceptual distinction, we
can clearly describe those unsuccessfully institutionalized cases as the broken complementarity, in which
Eii-Eij is positive, but Eij-Ejj is negative.
4) If we stand on the actors' viewpoint, we have to consider even judgment discrepancies between them.
Such more complex situations where directed graphs are differently defined for the same role relationship
is within our scope of analysis, but in the future.
5) Also see Misumi (1991) for a graphical analysis of in-personal change of the role knowledge.
- 14 -
process of cognitive revision should be consistently related to the mechanism that determines
compatibility (or reciprocity) between the nodes in G. A Boolean role model developed by Misumi (2001,
2002) is suggestive on that point.
Berger, Peter and Stanley. Pullberg 1965. "Reification and the sociological critique of consciousness." History
and Theory 9(2): 196-211.
Berger, Joseph, M. Hamit Fisek, Robert Z. Norman, and Morris Zelditch,Jr. 1977. Status Characteristics
and Social Interaction: An Expectation-States Approach. New York: Elsevier.
Berger, Joseph, Thomas L. Conner, and M. Hamit Fisek (eds.) 1974. Expectation States Theory: A
Theoretical Research Program. Washinton,D.C.: Winthrop Publishers.
Cartwright, Dorwin and Frank Harary 1956. " Structural balance: A generalization of Heider's theory."
Psychological Review 63(5): 277-293.
Dahrendolf, Ralf. 1968. " Homo sociologicus: On the history, significance, and limits on the category of social
role." In R. Dahrendolf, Essays in the Theory of Society. Stanford: Stanford University Press: 19-87.
Fararo, Thomas J. and John Skvoretz 1986. " E-state structuralism: A theoretical method." American
Sociological Review 51: 591-602.
Fukazawa, Kenji 1994. "Structural role and interactive role." Saitama Daigaku Kiyo 30: 57-68. (深澤健次「構
造的役割と相互行為的役割-役割知識における両者の関係について」『埼玉大学紀要 (教養部)』.)
Fukazawa, Kenji 1990. "The structure and the character of role knowledge." Saitama Daigaku Kiyo 26:
51-63. (深澤健次「役割知識についての基本的考察-役割論の統合をめざして」『埼玉大学紀要 (教養部)』.)
Funatsu, Mamoru 1976. Symbolic Interactionism. Tokyo: Koseisha Koseikaku. (船津衛『シンボリック相互作
Goffman, Erving 1967. Interaction Ritual: Essays on Face-to-face Behavior. New York: Doubleday.
Goffman, Erving 1959. The Presentation of Self in Everyday Life. New York: Doubleday.
Habermas, J rgen. 1973a. "Stichworte zu einer theorie der Sozialisation." In J. Habermas, Kultur und
Kritik. Suhrkamp Verlag: 118-194.
Heider, Fritz 1946. "Attitudes and cognitive organization." Journal of Psychology 21: 107-112.
Kobayashi, Shu-ichi 1983. "Role relevance and visibility." Hosei Daigaku Kyoyo-bu Kiyo 47: 45-59. (小林修一
Kurioka, Mikiei 1980. "A trend in role-theory." Soshioroji 25(1): 37-53. (栗岡幹英「役割概念の一傾向-現象
Levinson, Daniel J. 1959. "Role, personality, and social structure in the organizational setting." Journal of
Abnormal and Social Psychology 58: 170-180.
Misumi, Kazuto 2002. "A Boolean model of role discrimination." Journal of Mathematical Sociology 26: 1-11.
Misumi, Kazuto 2001. "Two levels of dyscommunication: An analysis by Boolean role model." Riron to Hoho
16(2): 229-243. (三隅一人 [in English]『理論と方法』.)
Misumi, Kazuto 1991. "A model of the role by digraphs." Riron to Hoho 6(2): 3-19. (三隅一人「ダイグラフによ
Morris, Brian 1971. "Reflections on role theory." British Journal of Sociology 22: 395-409.
Nomura, Kazuo 1987. "Simmel on role theory." Shakaigakushi Kenkyu 9: 64-82. (野村一夫「ジンメルと役割理
Nomura, Kazuo 1982. "Theoretical structure of normative concept of role." Soka Daigaku Daigakuin Kiyo 4:
233-251. (野村一夫「規範的役割概念の理論構造-<個人と社会>の虚偽的媒介」『創価大学大学院紀要』.)
Parsons, Talcott and Edward A. Shils 1951(=2001). Toward a General Theory of Action: Theoretical
Foundations for the Social Sciences. Harvard University Press (Reprinted by Transaction Publishers,
New Brunswick.)
- 15 -
Schutz, Alfred 1970 (H.R.Wagner [ed.]). On Phenomenology and Social Relation. Chicago: University of
Chicago Press.
Tanaka, Shigeru 1984. "A logical structure of 'the other'." Shakaigaku Hyoron 35(3): 103-119. (田中滋「『他
Tenbruck, Friedrich H. 1961. "Zur deutschen rezeption der rollentheorie." Kölner Zeitschrift für Soziologie
und Sozialpsychologie 13: 1-40.
Watanabe, Hideki 1981. "Individuals, roles, and societies." Shiso 686(Aug.): 98-121. (渡辺秀樹「個人・役割・
Yamaguchi, Setsuo 1975. "Sociology and role theory." Episteme 1975 Nov.: 136-147. (山口節郎「社会学と役割
- 16 -