Scriptapedia/Ratio Exercise

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Ratio Exercise

This script is used to elicit feedback loops (especially minor loops) and variables within a causal chain, and in some special cases, this script can initiate mapping after a "Graph Over Time" and "Concept Model" exercise.


Best practices

Primary nature of group task:



Preparation time: 30 minutes

Time required during session: 10 minutes

Follow-up time: 30 minutes


  1. Large erasable white surface (cling sheet wall or white board)
  2. White board markers
  3. Vensim sketch program or camera for the recorder to capture images


This script cannot be completed until the group has defined pairs of stock variables whose ratio/difference makes sense to the group (e.g., class size, caseload, vacancy rate, occupancy rate, etc.)


  • Feedback loops
  • Articulation and mapping of feedback effects


  • Facilitator with modest experience in SD; should be able to lead the group in mapping feedback effects (perhaps more skill is required in recognizing the stock variables and getting the exercise set up)
  • Skilled modelers are needed in the “modeler feedback” follow up where the feedback loops elicited by the group are integrated into more complicated “cleaned up” feedback diagrams
  • Recorder who can operate a camera or sketch the geometry of feedback loops using software such as Vensim


  1. The modeler picks out a pair of stocks to work with first.
  2. The facilitator asks the group to name the ratio or difference (caseload, class size, etc.). The facilitator adds the ratio or difference variable using the exact name that the group has suggested.
    • Different groups use differing terminology for a similar concept. Additionally, some groups use differences and some use ratios (e.g. occupancy rate versus number of vacancies). It is important to use their terms.
  3. The facilitator maps the ratio (or difference variable) with the incoming arrows marked with “+” or “-“ as is causally appropriate.
  4. The facilitator asks, “What would happen if this ratio were to go to zero or get unusually small?” or, “What would happen if this ratio were to become very large? How would the system react?”
  5. The participants then start to tell feedback stories about how the system reacts when this key ratio (or difference) gets out of whack. When loops are completed, the facilitator traces them out for the group adding appropriate “+” or “-“, telling the stories of the loops. These loops are almost always balancing loops.
  6. Steps 2 through 5 are repeated with another set of ratios

Evaluation Criteria:

  • This script will usually fill a white board with lots of feedback loops very quickly
  • Participants will “get the hang” of what feedback loops are and how they work, and they will start to look for them
  • A very good map will have feedback paths that connect to other important stocks in the system (other than simple, first order loops). These insights that pass through other stocks are especially important.


David F. Andersen and George P. Richardson


This script was first developed and used by Richardson and Andersen in the 1990s, and described in Richardson and Andersen (1995).




Richardson, G. P. and Andersen, D. F. (1995), Teamwork in group model building. System Dynamics Review, 11, 113–137.


This script typically develops offline when the modeling team realizes that a strong and clear set of stocks and flows exist to under gird this system and that aging chains of usually service loads (students, patients, clients) can be linked to some resource of stocks (teachers, nurses, caseworkers) so that the pairing of related stocks makes sense. Sometimes the modeling team realizes this quite early on, such as when they have a strong hunch before the session even begins. It is a real “work horse” script, yielding lots of feedback in a reliable fashion. This is a gratifying script to use because it so often, consistently, and quickly populates the public diagram with a dense network of feedback loops.