Goals: A Self-Limiting Proposition

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I will apologize in advance for overloading you with the detail that follows as sufficient information about Causal Loop Diagrams and Stock & Flow Diagrams has not yet been provided. The problem is that the following description is considered critical to the appropriate definition of the desired alternative state.

The establishment of a goal is generally based on some place, or some state, one wants to be at in the future, as compared to where one is currently in the present. The variance, or gap, between the current state and the desired future state, goal, is then used to create motivation for the activity required to transform the current state into the goal. The difficulty here lies in the systemic nature of the structure which is created from the underlying mental model. What happens at the end of a 100 yard dash? The finish line has been reached and the runners stop! This is a general tendency which accompanies goals, and when the activity is dependent on the distance from the goal, the situation is actually even worse than with a 100 yard dash.

Goal

The establishment of a goal essentially represents the creation of a Balancing Loop. In this structure the difference between the goal and the current state creates a gap which promotes activity. The activity tends to move the current state toward the goal. As the current state moves closer and closer to the goal the gap gets smaller and smaller. And as the gap gets smaller and smaller there is less of an inducement for further activity to move the current state toward the goal. Over time progress declines per unit time. It's like trying to walk to a doorway and each step taken is half the remaining distance to the door. Each step takes you a bit closer, yet you never really reach the door.

If we implement Fig. 1 as a Stock & Flow Diagram we can assign values and simulate it to get a much better picture of what's happening within the structure.

Fig. 2 - Goal Simulation [IM-1138]

Stock & Flow Values

• goal = 1
• Current State = 0
• activity factor = 0.2 (to control the activity rate)
• Time Settings
  • Start = 0
  • Length = 10
  • Time Step = 1

Simulating this structure with produces Fig. 3.

As the above graphs shows, as the Current State approaches the goal the activity declines. The activity declines because the gap declines. And the gap declines because the Current State approaches the goal. This all simply boils down to the fact that the result is limited by the establishment of the goal and the management of activity to move the Current State to the goal. So is there a resolution to this situation? Of course, or why would I have started to write this paper in the first place!

Resource Limits

Before moving on to the resolution a bit of an aside might be in order. There is an implication in the above that activity is simply driven by the size of the gap. In most cases this is only partly true. In most situations the gap is sufficiently large that the activity is actually limited by the resources available to produce activity. This is represented by the diagram in Fig. 4 at the right. When the resources available are less than the activity that would result form the influence of the gap then the activity that results is that which the resources have the capacity to produce. As such the activity factor in Fig. 2 is really a representation of resources.

Fig. 5 is the updated Stock & Flow Diagram.

Fig. 5 - Activity & Resources [IM-1139]

Stock & Flow Values (Revised)

• resources = 2
• activity = if (gap>resources,resources,gap)
• Time Step = 0.5

Fig. 6 indicates that the Current State appears to grow in a linear fashion for about 4 weeks. The activity is in fact constant over this period as it is limited by the 2 resources available to produce activity. Once activity moves the current state to where the gap is less than the resources available the activity becomes a function of the gap and there is actually excess capacity going to waste.

Excess Capacity

This is quite evident in the following diagram in which excess capacity has been explicit added to the model. The associated graph depicts the excess capacity as activity declines.

Fig. 8 depicts excess capacity added to the Stock & Flow model.

Fig. 8 - Excess Capacity [IM-1140]

Fig. 9 provides an explicit picture of excess capacity as resources available exceed the size of the gap.

Ever heard the comment, "Activity expands to fill the time available."? Activity also declines to fill the space available!

Reinforcing Progress

At this point it's probably a good idea if I get back to my comment from above about a resolution to the situation of goals being a self-limiting factor of results. Suppose we change the structure so that rather than basing activity on the gap between the goal and the current state we base activity on progress. This structure should then look more like the diagram in Fig. 10 at the right with the Stock & Flow Diagram depicted in Fig. 11. The reference state is the current state at time = 0.
Fig. 11 - Progress [IM-1141]

Stock & Flow Values

• reference state = 1
• Current State = 1
• progress = current state - reference state
• activity = progress

If we now simulate this structure we find it produces the diagrams depicted below.

Ops! What you've just found is that the structure is a lot like your car. It has a lot of potential though you have to start it first. With no difference between the reference state and the Current State the value of progress is zero so there's no activity. This is a lot like a catch-22 in that you don't have progress so there can't be any activity and since there's no activity there can be no progress. Just kick it a little and it will start! Or in this case just a little activity will get it started.

Stock & Flow Values

• IfThenElse([Current State]=[reference state], [reference state], [Current State]-[reference state])

What the graphs indicate is that as activity increases the Current State increases. And as the Current State increases progress increases. And finally as progress increases activity increases. We come full circle and have produced a Reinforcing Loop rather than a structure which is self-limiting and balances as in the initial goals structure. There is very little similarity between Fig. 9 and Fig. 13.

The graph in Fig. 13 above provides a very enticing scenario that just happens to be false. The difficulty lies in the fact that all this activity isn't for free. Activity is the result of available resources applied to producing activity. By modifying the structure to include limited resources we end up with the diagram at the left, Fig. 14.

Fig. 15 provides the Stock & Flow equivalent of Fig. 14. The more realistic situation is that activity is relatively limited for some period due to limited progress. Once progress begins to be produced and sensed activity begins an exponential climb, at least until it runs into a resource limit. At this point activity becomes flat and progress continues at a rather linear rate. This will continue until progress runs into some other limiting factor. There are always limits to growth along the way somewhere, and sometimes they are not always tangible, as will be shown shortly!

[IM-1142]</center>]]

Stock & Flow Values

• reference state = 1
• Current State = 1
• progress = current state - reference state
• activity = if (progress < resouces, progress, resources)

Enough

The potential difficulty with this structure has to do with the influence of a mental model called enough. If the actors hold a belief that a certain amount of progress is sufficient they tend to begin to rest on their laurels. With the belief that they've done good enough so to speak the activity which would have continued to increase begins to decline. The actors think they've progressed enough, or maybe believe that additional progress isn't possible.

Fig. 18 is the Stock & Flow equivalent of Fig. 17.

Fig. 18 - Enough Progress [IM-1144]

Stock & Flow Values

• reference state = 1
• Current State = 1
• resources = 20
• e ref = 15 (reference value for enough)
• e factor = 0.2 (extent to which enough has an impact)

The effects of this are shown in Fig. 19 below. Notice that although progress continues to increase as the activity begins to fall off once enough is reached.

The impact of the mental model of enough has a detrimental affect on progress as compared to the previous model.

The best way to overcome this situation is alter the structure so that rather than continually consider progress based on a single reference state that doesn't change, the reference state is periodically reset to the current state. This results in progress being measured during a period as opposed to the initial reference state. Even this presents a difficulty as progress is likely to become more difficult in time. The methods that were employed to create progress during the previous periods are likely to no longer work. The actors in the system will have to migrate their approach to activities which create progress from incrementally changing, to redesigning, to rethinking their methods.

In conclusion I suppose I should acknowledge that some may contend that this is maybe a bit like driving while looking in the rear-view mirror. In response I would say that using this approach without a vision which provides guidance as to the direction in which one is going would be ludicrous. Vision should be used to continually reassess movement of the Current State to ensure 'progress is in an appropriate direction.

References

• Leadership & Management: A Systemic Perspective

Additional Resources Systems Thinking World Discussions Systems Thinking World Q&A * Gene Bellinger