Expanded Contents | Figures | Tables 1. Perspective And Summary 15A. Phasing Propositions and Their Evidence on International Conflict Vol. 1: The Dynamic Psychological Field
Democratic Peace page |
Policies and distances are clearly interrelated.
---- Wright, 1942: 1255 |
In the previous discussion and Volumes, I have tried to make clear that distance vectors between actors empirically reflect their relative, latent attitudes and capabilities, and that attitudes are transformed into interests through the stimulation of associated needs. Attitudes are therefore inactive interests. And by themselves, distances only define potentiality. All this will be discussed further in Section 10.2 regarding the structure of conflict.
However, here and in Figure 8.1, I am concerned with distances in a situation in relation to behavior. A perceived situation stimulates needs; it transforms attitudes into interests, potential capability into actual capability. Therefore, the distances linked to an actor's behavior in a situation will reflect his living interests and relevant capabilities. Of course, not all interests will be weighted in a situation--not all interests will be active. It is the situational weights that measure the transformation of attitudes into interests and the relative weight these interests will have. But between the activation of an actor's interests and the utilization of his relevant capabilities is the his will. The will is an actor's power to actually choose and try to gratify his interests--to bring himself to behave.^{2} But not all behavior requires the will. Some behavior is routine, habitual, automatic, reflexive. The will, however, is engaged in interrelating actions and acts, in intentional behavior. Behavior that comprises practices are routine, and habitual, norm and rule following behavior, and therefore due to reasons; behavior that comprises reflexes is automatic, due to causes. Thus, Figure 8.1 shows the variation in an actor's behavior as divisible into that brought intentionally about by the will, and that due to reasons and causes. Note also that some unique practices may be also a matter of will; they may be individualistic, against the common grain, and thus require the will to maintain.
With this crucial understanding that an actor's will is engaged in common acts and actions, I can now deal more precisely with the equation of interests, capabilities, and wills. In a situation, the variation in behavioral dispositions of an actor towards others will be a function of his common interests and capabilities regarding them and his unique interests and capabilities. In vector terms,
Equation 8.1:
- W_{gi} = _{}_{gi}d_{i} + Q_{gi},
- where
- W_{gi} = variation in (vector of) i's behavioral dispositions towards others in situation g;
- _{gi} = the perceived salience in situation g of i's interests and capabilities reflected in the distances along the ^{th} common component of international space-time;
- d_{i} = i's variation in (vector of) distance vectors^{3} from other actors;
- Q_{gi} = i's (vector of) unique interests, capabilities, and will in situation g.
Thus, distances and situation tell only part of the behavioral story. As actor's in international relations, we are also individualistic. We have our particular interests and capabilities and our independent, free will. Note that Q measures the unpredictable part of an actor's behavioral disposition, the part not reducible to a function of his situation and distances from others. Thus Equation 8.1 embodies the belief that an actor's behavior is partly patterned, partly unique; partly due to his will influenced by common social forces, partly to his will acting independently of such influences.^{4}
Equation 8.1 is the vector equation interrelating the various sources of variation in an actor's common behavior that are shown in Figure 8.1. The specific behavioral disposition of an actor towards a specific other is then,
Equation 8.2:
- w_{g,i j} = _{}_{gi}d_{,i-j} + Q_{g,ij},
- where
- w_{g,i j} = the behavioral disposition of i towards j in situation g;
- d_{,i-j} = i's distance vector from j on the ^{th} component of international space-time;
- Q_{g,ij} = i's unique interests and capabilities regarding j in situation g.
In words, the specific behavior of an actor towards another is a function of an actor's situational expectations and dispositions, where these dispositions themselves are a function of situational perception and distances. More precisely, for common behavior h, from Equations 6.3 and 8.2,
Equation 8.3:
- _{h,ij} = _{g}_{hig}w_{g,ij},
- = _{g}_{hig}(_{}_{gi}d_{,i-j} + Q_{g,ij}).
The vector counterpart of this equation is shown at the bottom of Figure 8.1 [note that the subscript i was accidently omitted from the d term, which is corrected below]. It is
Equation 8.4:
- _{hi} = _{g}_{hig}(_{}_{gi}d_{i} + Q_{gi}).
Equation 8.3 is the basic equation of field theory.^{5} To be sure it is understood, Figure 8.2 conceptually defines its elements.
Now to consider again the international sociocultural space-time. Figure 8.3 pictures this space-time, and the inner, common space-time spanned by the components of Table 7.1, such as wealth and power. As shown, the common behavior of an actor related to his distance vectors is a subspace of this common space-time. In other words, that common behavior of an actor associated with his common interests and relative capabilities is imbedded in sociocultural space-time. From Figure 6.3 and Section 6.4,
Equation 8.5:
- _{i} = W_{i}_{i},
- where
- _{i} = matrix of i's dyadic behavior towards others;
- W_{i} = matrix of i's situational, dyadic dispositions;
- _{i} = matrix of i's expectations of the outcome of behavior in different situations.
This defines i's region of common behavior space-time, as shown in Figure 6.3. Then for the matrix of i's dispositions,
Equation 8.6:
- W_{i} = D_{i}_{i} + Q_{i},
- where
- D_{i} = the matrix of i's distance vectors from other actors on the common components of sociocultural space;
- _{i} = the matrix of i's situational perceptions;
- Q_{i} = the matrix of i's unique dyadic interests, capabilities, and will regarding others in various situations.
And from Equations 8.5 and 8.6.
Equation 8.7:
- _{i} = W_{i}_{i}
- = (D_{i}_{i} + Q_{i})_{i}
- = D_{i}_{i}_{i} + Q_{i}_{i}
- _{i} - Q_{i}_{i} = D_{i}_{i}_{i}.
Thus, as with the expectation and disposition equations of Chapters 5 and 6, there are also matrix, vector and scalar versions of the behavioral equations of interests, capabilities, and situation. These are shown in Table 8.1.
Of course, in day-to-day reality, interests, capabilities, wills, and situational expectations and perceptions interact in complex and multifold ways. International behavior in its rich daily variation is neither simple, linear, nor wholly reducible to mathematical functions. Historians have tried to capture this flow of events and activities, this interaction of personalities and situations, and often have become convinced thereby that international relations are idiosyncratic, unique, and irreducible to general forces, principles, or laws. At a more abstract level, many who have tried to analyze international relations statistically or mathematically have also become convinced that simple linear equations cannot fit the complex, interdependencies between national behaviors, forces, and conditions.
Here I do not wish to again join this issue.^{6} The equations of situational expectations, perception, and distances are meant to represent latent interwoven interests, perceptions, and so on, at the most general, manifest level. Distances and situations are latent functions^{7} reflecting patterns in this complex, in the same way the historian or statesman reduces the complex reality of potentials, dispositions, powers, and manifestations to abstract concepts like the "balance of power" or "national interest."
The behavioral equations express relationships, interactions, dependencies. But they are not linked into the process of developing international orders, of conflict. The question is central: how do these equations reflect the conflict helix? Answering this is the burden of the following Chapters, and will require far more discussion and specificity about the elements of the behavioral equations than yet given.
* Scanned from Chapter 8 in R.J. Rummel, War, Power, Peace, 1979. For full reference to the book and the list of its contents in hypertext, click book. Typographical errors have been corrected, clarifications added, and style updated.1. This Figure is no "taxonomy gone wild." I am trying to reduce distinctions to only those necessary to understand the equations, which have also been kept to a minimum number. And I am also introducing the distinctions in the Sections where they serve a role in clarifying the empirical analysis. Thus, the three important variance charts, Figures 5.3, 6.1, and 8.1 have been introduced in this book rather than Vol. 1: The Dynamic Psychological Field or Vol. 2: The Conflict Helix, because only here is manifest dyadic behavior empirically analyzed.
2. The nature of the will in relation to the self and the question of free will was analyzed in Part VI of Vol. 1: The Dynamic Psychological Field.
3. The distance is the difference between the location of i and the other on a component. This difference can be plus or minus and is a single element vector. The vector of differences is therefore of vectors. Admittedly, this is clumsy. But the wording is necessary to avoid the ambiguity between distance as magnitude and distance as vector. Throughout I argue that the direction of difference is crucial, as for example whether an actor is the dominant or subordinate power to another. Distance magnitudes ignore direction. Vectors take this direction into account. See the Distance Vector Proposition 16.6 for supporting evidence.
4. As shown in Figure 8.1 unique interests and capabilities explain both some common behavior, Q_{gi}, and unique behavior, Q^{*}_{gi}. Because the empirical concern is with variation in common behavior, only Q_{gi} is dealt with here.
5. In my development of Model II of field theory published in Field Theory Evolving (1977) I had defined the basic equation as (in the notation used here)
- w_{g,ij} = _{}_{gi}d_{,i-j},
- where
- w_{g,ij} = the location of the dyad i-j in behavior space on a component W_{g}
This is the same as Equation 8.2, except for the definition of Q and the subscript g. The addition of Q marks my change in philosophy from determinism to a belief in free will--see my "Roots of Faith" (1976b) [and "Roots of Faith II, " 1988]. The addition of subscript g to was left undefined in my previous work to avoid introducing another layer of notation, even though it was necessary to define the coefficients of the different canonical equations emerging from canonical analysis.
Here I have now conceptually and substantively defined the terms and subscripts in the basic equations to bring out g as situation, and to relate this basic equation explicitly to specific, common behavior, as in Equation 8.3.
Admittedly, discussion of w _{ij} in Field Theory Evolving is sometimes inconsistent with its treatment here as disposition w_{g,ij} in situation g. Nor am I striving to maintain consistency. The previous theoretical-empirical work antedates by many years that of these Volumes. Then I had only a partial conception of the conflict helix. (see particularly 1977: Chapter 9, Section 4), and only a hazy view of the dynamic psychological field.
6. I have tried to cover this central issue in various ways, including from the perspective of the major method (1970: Section 2.2; 1972, Section 2.3.2), from philosophy (Chapters 9 and 10 in Vol. 1: The Dynamic Psychological Field), and from a probabilistic perspective (Chapter 2 of Vol. 2: The Conflict Helix). See also 1977: Chapter 16.
Each age and each discipline has its mindless slogans. One of these particularly dominating quantitative social science work is: "But that is linear." It is not realized that linearity is a concept covering many different types of equations, including those critics ordinarily propose to replace "linear" ones. In my work, a linear equation is of a linear space; it is linear only in the function--the separate terms can be complex. For example, distance d, could reflect some interconnected complex of forces, such as d_{1} = xy^{2}(1- z), or a differential term dx/dt.
7. Situation is a latent function, operationally, in being defined by the canonical variates. Each canonical variate is, mathematically, an eigenvector and interpretable as a component. On latent functions see Chapter 10 of Vol. 1: The Dynamic Psychological Field.