[Martin Taylor 2013.04.30.23.53 PDT]
>From Kent McClelland (2013.04.29.1130 CDT)]
[KM] 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.
Kent,
What you describe is not 2-D conflict, but illustrates what I would call interference between control of two perceptions that ranges from zero (actions that influence one perception do not influence the other) to complete conflict (the two perceptions cannot both arrive at their reference levels at the same time). Interference makes control of at least one of the perceptions more difficult, and complete interference makes control of at least one impossible.
Conflict, true conflict rather than strong mutual interference, occurs when there are more degrees of freedom in the perceptions to be controlled than there are in the means to control them. The 1-D conflict is just a special case.
Imagine, for example, using the X-Y position of a mouse to control perceptions of a grey disc, the perceptions to be controlled being the shade of grey, the diameter of the disc, and the left-right location of the disc in its window. It can't be done. You can control any two, but not the third at the same time. If you add another perception, such as the vertical position of the disc in its window, you can still control any two, but disturbances in the other two must go unopposed. The conflict isn't in any one pair of controlled perceptions that correspond to the same environmental variable. It's intrinsic to the set of them.
In the "standard" conflict, the limiting degrees of freedom are in the environment. In the example above, the limit is in the means of influencing the environment. The effect is the same. Let's modify the example to put the limit into the environment. Assume you have two mice, so you could influence all four of the environmental variables. But now something in the environment links the disc's shade, diameter, and position so that if you think of each as being represented by a number between zero and 100, the four of them always sum to 200. If you control any three to their reference values, you suddenly find that you can't adjust the fourth without altering at least one of the others. The set of four values has only four degrees of freedom, and one of those has been fixed by setting the overall sum, which leaves only three for control, even though you have four degrees of freedom for mouse movement.
Put this into a more general context of competition for limited resources (the limit being analogous to the sum in the previous paragraph), and the conflict becomes manifest in the rich taking resources that are then unavailable to the poor -- in a conflict, the system with the stronger output can overwhelm the weaker system, whether the conflict is 1-D or exists within a high-dimensional set of interactions. In the resource case, money provides power, but so does physical force, and if the conflict is resolved completely one way by the power of money, it might later be resolved in the other by revolution.
I think multidimensional conflict is rather more interesting than one-dimensional, though I do not know whether it involves novel insights or structures beyond what can be seen in a 1-D conflict.
Martin