from Kent McClelland (2013.04.29.1130 CDT)]
Mike Acree (2013.04.26.2050 PDT)
Rick Marken (2013.04.27.1812)
Rick Marken (2013.4.26.1820)
Thank you to Mike and Rick for your comments on my paper models of conflict. You are making excellent points.
MA: The paper speaks about conflict as though it were a concept relevant to sociology; the Discussion speaks, for example, about political controversies and family feuds as applications. Yet what is being modeled is only a physical tug-of-war, in a single dimension. The restriction to a single level means that there are no strategies except brute force: to pull harder, or to pile more people on your end of the rope. And I think that induces some distortion in the operations of polarization or solidarity.
The very simplest, and still feasible, accommodation to a more complex reality would be to allow the tug-of-war to take place in a two-dimensional rather than a one-dimensional space. . . .
Any model adequate to actual conflict in humans (or even other animals) would not only have to be multilevel, to account for phenomena like the value of conflict itself (at what point does the tugging cease to be worth it?) . . .
RM: In all the simulations described in your paper you assume that systems are
controlling the exact same aspect of the environment relative to
different references. But suppose they are controlling "similar"
perceptions but not the same. The similarity of perceptions that are
linear functions of environmental variables can be measured in terms
of their orthogonality of the vectors that define the perceptions. For
example, if p1 = x + y and p2 = x-y, where x and y are two
environmental variables, the p1 and p2 are completely orthogonal; p1
and p2 can be controlled by two different control systems w/o any
conflict. If p1 = x+ y and p2 = x+ y then p1 and p2 are completely
non-orthogonal -- they are the same perception and they cannot be
controlled by two different systems without conflict. Intermediate
levels of orthogonality (dissimilarity) of perceptions can be defined
by using different coefficients (other than 1 and -1) for x and y.
KM: As Mike comments, by restricting myself to one-dimensional models, I've portrayed conflict in a drastically simplistic way, and it would require multi-dimension models to provide a more sociologically satisfactory account of the dynamics of conflict. Some of Rick's comments, too, pertain to the dimensionality of conflict, when he talks about the correlation between the aspects of the environment being perceived by two control systems in conflict.
As it happens, I played around years ago with models of two-dimensional conflicts, in which the perceptions controlled by two agents are linear functions in an X-Y plane. Each agent is modeled as having two outputs, one working in the X direction, and the other in the Y.
Just as Rick suggests, I tried to see what happens when you vary the correlation between the two lines that represent the references for the two simulated agents. At the time, I wasn't sure how to relate this modeling work to empirical situations, but your comments have suggested to me some ways these models could be applied. Here's what I found:
Situation A: When the two preference lines are parallel to each other (do not intersect), you get conflict dynamics similar to the one-dimensional situation, with unlimited escalation of output in opposite directions (perpendicular to the preference lines).
B: When the two preference lines are orthogonal to each other, and the initial position of the environmental variable is at a point different from the intersection of the two lines, the combined outputs of the two agents quickly bring the environmental variable to the point of intersection of the lines of preference, and then the agents hold it at that compromise point (approximately) against any random disturbances in the X-Y plane.
C: When the two preference lines meet at an acute angle and thus are somewhat correlated, the outputs of the two agents bring the environmental variable quickly to some point along a center line that splits the difference between the two preference lines, but not immediately to the point of intersection of the preference lines. Then, more slowly, their combined outputs pull the environmental variable along that compromise line till it gradually reaches the point of intersection of the two preference lines. When the environmental variable has finally reached this compromise point, the two systems hold it approximately there against disturbances.
In situation A, the preferences of the two agents are truly incompatible, continuing conflict is inevitable, and the environmental outcome is a set of compromise positions that are fixed with regard to the direction orthogonal to the two preference lines but unstable and free to vary in directions parallel to the preference lines.
In situation B, in which the preferences of the two agents are orthogonal to each other, compromise is easily reached, and the two agents stabilize the environmental variable around their compromise point.
In situation C, in which the preferences are similar, but not exactly the same, we see some initial conflict that diminishes as the environmental variable moves along the line between the two preference lines toward the compromise position at the intersection of the preferences.
A lot of real-life interactions, as Mike suggests, must be some variant of situation C, where people start with similar but not identical preferences, and the initial conflicts diminish as people find solutions that are OK with everyone involved� a degree of solidarity, if not complete agreement. One person may want more of Y when X is low and less of Y when X is high than the other does, but there's some X-Y combination that both can live with. It's only when their preference lines don't intersect at all (within the region over which they both can exert control) that conflict becomes inevitable.
You made some other good points, as well, but this seems like enough from me for the moment.
My best,
Kent
···
On Apr 26, 2013, at 8:19 PM, Richard Marken wrote:
[From Rick Marken (2013.4.26.1820)]
Kent McClelland (2013.4.22.13:25 CDT)
KM: Subscribers to CSGnet may perhaps be interested in a draft article that I've recently written on models of conflict escalation. The paper is to be presented at a sociological convention this summer, and it's aimed at an audience of sociologists, but it uses PCT models and conflict is a topic of some interest in a lot of disciplines.
RM: I asked Kent to send the paper to CSGNet to see if it could
generate some discussion.It looked like it wasn't until Bill chimed in
with his nice post. But I told Kent that I had a couple comments on
the paper so here they are. These comments are not criticisms because
they are not really relevant to the main point of the paper (the
temporal course of a conflict) but I bring them up because they might
be relevant to future studies of conflict.
First, on p. 12 you say: "Conflict is expected to occur whenever two
control systems operating in
the same environment have incompatible goals,..." After goals I would
just add either "for the same perceptual variable" or, possibly
better, "for the same aspect of the environment". I think this is
really the essence of conflict: conflict exists when two (or more)
control systems with incompatible (different) goals for the same
aspect of the environment. This point is kind of nit picky in the
context of your paper but I think it might be something interesting to
look into in future studies of conflict. For example, one thing I have
wanted to study about conflict was how similar the aspects of the
environment are controlled by different control systems have to be for
there to be conflict between the systems. This question comes up
because conflict can occur when systems control very similar aspects
of the environment which are not actually the same. In all the
simulations described in your paper you assume that systems are
controlling the exact same aspect of the environment relative to
different references. But suppose they are controlling "similar"
perceptions but not the same. The similarity of perceptions that are
linear functions of environmental variables can be measured in terms
of their orthogonality of the vectors that define the perceptions. For
example, if p1 = x + y and p2 = x-y, where x and y are two
environmental variables, the p1 and p2 are completely orthogonal; p1
and p2 can be controlled by two different control systems w/o any
conflict. If p1 = x+ y and p2 = x+ y then p1 and p2 are completely
non-orthogonal -- they are the same perception and they cannot be
controlled by two different systems without conflict. Intermediate
levels of orthogonality (dissimilarity) of perceptions can be defined
by using different coefficients (other than 1 and -1) for x and y.
Second, on p. 14 you say "Whenever the organism�s perceptions are
reasonably accurate, successful control of perceptual variables
results in a corresponding stabilization of environmental variables".
I think this can make sense from an observer's perspective. If the
person is supposed to control x-y and he is actually controlling a
perception that is p=x-y then when he successfully controls p he will
be successfully controlling x-y. But from the controller's
perspective, all they are controlling is p, whatever p is a function
of in the environment. So in this case, successful control means p is
kept = to r, which stabilizes whatever it is in the environment that p
corresponds to. The success of control -- the ability to keep p = r,
depends on the design of the control system, which means the
appropriate output function that "takes into account" the type of
perception being controlled and the characteristics of the
environmental connection between efferent neural signal and afferent
perceptual signal. Considering charateristics of the output function
is related to Bill's suggestion that you " might want to consider the
relationship between loop gain and leakage, in which steady-state loop
gain is expressed as the multiplier of the integration term divided by
the fraction of output leaked away on each iteration...". But I agree
with Bill that "the paper will not be diminished by leaving that for
another time".
Best regards
Rick
--
Richard S. Marken PhD
rsmarken@gmail.com
www.mindreadings.com