# Feedback Loop

A **feedback loop** is system structure that causes
output from one node to eventually influence input to that same node.

For example, the *work output* of a population can increase the *goods
and services* available to that population, which can increase
the *average life expectancy*, which can increase the *population*,
which can increase the work output still more, and the loop
starts all over again. Using system
dynamics notation, this feedback loop would look like
the Population Growth loop shown.

## Why feedback loops are an important tool

While the above example may seem simple and obvious, that's because
we drew a simple model with only one loop and 4 variables.
Few real world problems are as simple. For example, The Dueling
Loops of the Political Powerplace model has 43 variables, 3 main
loops, about 5 additional loops, and 4 stocks. It is a simplification
of a larger model that has 123 variables, 11 stocks, and countless
loops. Its construction took a single person several years. Another
example is the World3 model in *Limits to Growth*, which
contains about 300 variables and 20 stocks. It took 17 researchers
2 years to construct the model.

Understanding the behavior of difficult complex social system problems well enough to even begin to hypothesize a realistic solution, with a high probability of working the first time, is impossible without understanding the feedback loops involved.

## A quick introduction to how feedback loops work

The universe contains only two kinds of feedback loops: reinforcing and balancing, also called positive and negative feedback loops. Once you grasp how they work you are well on your way to understanding the foundation of systems thinking.

A feedback loop occurs when a change in something ultimately comes back to cause a further change in the same thing. If the further change is in the same direction it’s a positive or reinforcing loop. If it’s in the opposite direction it’s a negative or balancing loop, also called a goal-seeking loop.

An example of a reinforcing loop is Population Growth. As *population* goes up, so does *births per year.* As that goes up, so does future population. The loop goes round and round, growing exponentially until the loop hits its limits, which are not shown.

An example of a balancing loop is Constrained Population Growth. Here the contraint is *carrying capacity*, which is the maximum number of people a system can support. *Population* will grow until it reaches this constraint, also known as a limit or target. Let's call this one a limit.

In a balancing loop the gap equals the limit minus the actual state. Suppose the *carrying capacity* is 100 people and *population* starts at 10. That causes a *population gap* of 90. This increases *births per year* to a high rate. As that goes up, so does *population*. As *population* rises, the *population gap* falls. This lowers the birth rate, which (over a long period of time) lowers *population*, which increases the gap, which increases the birth rate, and so on until the gap approaches zero. This behavior causes *population* to gradually approach the *carrying capacity* of the system, since the system can support a limited number of people. In practice population will tend to overshoot carrying capacity and suddenly collapse, due to long delays in environmental degradation.

Every time a balancing loop goes around, it behaves in the opposite manner than it did before, since a balancing loop contains an odd number of inverse relationships. A reinforcing loop contains an even number of inverse relationships. A solid arrow indicates a direct relationship. A dashed arrow is an inverse relationship. Understanding how balancing loops behave can be tricky at first. If so, do what we did. Draw a few reinforcing and balancing loops on paper. Trace them around until things start to become clear.

Another example of a balancing loop is a Thermostat. Suppose you set the *target temperature* to 65 degrees. The higher the target the greater the *temperature gap*. The greater the gap the more *heat* that flows into the system. That increases the *temperature*. As this goes up the temperature gap goes down. It keeps going down until the gap is zero, at which point the system has reached the target.

These are causal loop diagrams. They can't be simulated but are very useful for simple or high level feedback loop modeling.

Arrows indicate that one node influences another. Solid arrows are a direct relationship. One node varies directly with another. If A goes up then so does B, or if A goes down then so does B. Dashed arrows are an inverse relationship. If A goes up then B goes down and vice versa. As simple as models like these are, they can allow problem solvers to understand the relevant behavior of complex systems well enough to solve surprisingly difficult problems.

The main challenge in social problem analysis is to figure out what the most important feedback loops driving a system’s behavior are and then what they should be. While large social systems contain millions of loops, the decisive behavior of any specific problem is controlled by only a few of these loops. These determine the basic structure of a system, which is the shape of the important loops defining the system’s behavior of interest. The First Law of Modeling states that if you don’t understand a system’s key feedback loops then you don’t understand the system. But once you do understand them you are a giant step closer to controlling the system’s behavior.

Feedback loops control the behavior of a system over time, as shown by the graphs above. *Reinforcing loops cause either runaway (1) exponential growth or (2) exponential decline. *For example, the world’s population began growing exponentially when its limits were suddenly raised by the fruits of the Industrial Revolution and modern technology. *Balancing loops cause (2) goal-seeking behavior.* Iin a balancing loop a quantity such as temperature will grow rapidly for awhile and then slow down, as it homes in on its goal.

A balancing loop with a delay causes *(4) oscillation* around the goal of the loop. The loop is continually overshooting and undershooting the goal due to the information delay. It learns too late when it should correct its growth or decline. For example, most thermostats oscillate around their temperature goal by a few degrees.

All realistic models have at least one reinforcing and one balancing loop. An exponential growth loop combined with a goal seeking loop and a small delay causes (5) *S-shaped growth with small overshoot*. As the delay for correction to the goal grows, the overshoot becomes so large that the perfect approach to the goal shown in graph 5 becomes impossible. The results is (6) *S shapped growth with large overshoot and collapse*. This is the plight of *Homo sapiens* today. Due to high systemic change resistance, solution delay has caused large overshoot. The larger the overshoot becomes the more likely a large collapse becomes.

NOTE - The above six graphs were reconstructed from nearly identical ones in John Sterman's *Business Dynamics: Systems Thinking and Modeling for a Complex World*, page 108. Sterman makes the important point that "The most fundamental modes of behavior are exponential growth, goal seeking, and oscillation." The additional three graphs are merely combinations or variations of the three fundamental modes.