1Demonstration 1 of 4
Two negative links make a reinforcing loop
If both links in a loop describe opposition, is the loop balancing?
Going once around the loop multiplies the signs. Two negatives multiply to a positive, so a disturbance comes back in the direction it started. One negative returns it reversed.
Each link has a polarity: +1 when source and target move in the same direction, -1 when they move in opposite directions. A loop is reinforcing when it holds an even number of negative links, and balancing when the number is odd.
Predict first. With overtime lowering morale and morale lowering overtime, is the loop reinforcing or balancing?
Choose an example
Constructed example: the chapter's overtime and morale pair, with polarities varied for this reader.
Calculated values
- Overtime to morale
- opposite direction (-)
- Morale to overtime
- opposite direction (-)
- Negative links in the loop
- 2
- Loop polarity
- reinforcing
Count the negative links: 1 + 1 = 2, which is even. The product of the signs gives the same answer, (-1) x (-1) = 1, so the loop is reinforcing. Two negatives make a reinforcing loop, a spiral rather than a correction.
Use the idea
Before calling a loop a correction, count its negative links rather than relying on the impression that each link opposes something.
Where the conclusion applies
Each polarity holds all else constant, and the horizon is the same for both links. The rule says nothing about how fast the loop acts or whether it settles.
Check your understanding: If overtime raises morale (+) and morale lowers overtime (-), is the loop reinforcing or balancing?
Chapter 8 source: section "Polarity, and where intuition fails". Demonstration C08-D01.
2Demonstration 2 of 4
An audit counts what the picture rests on
How many arrows in a six-arrow diagram lack observation or a recorded time effect?
The audit reads fields stored beside each sign. Changing the evidence level or recording a delay changes the unsupported and time counts but not the loops, because loops come from which links exist and from their signs.
Each link is tagged observed, inferred, assumed or proposed. Assumed and proposed links count as unsupported. A link whose delay is unrecorded has no time semantics.
Predict first. If inventory to shipments is upgraded from assumed to observed, how many arrows are unsupported?
Choose an example
Constructed example: the chapter's six links and its printed audit, with evidence levels and time records varied for this reader.
Calculated values
- Links
- 6
- Loops
- 3
- Reinforcing
- 0
- Balancing
- 3
- Unsupported
- 2
- No time semantics
- 2
Unsupported arrows are those resting on assumption or proposal: 1 (inventory to shipments is assumed) + 1 (shipments to inventory is proposed) = 2. Arrows with no recorded time semantics: 1 + 1 = 2. The loop count is unchanged at 3, all 3 balancing, because evidence and timing notes do not alter the signs.
Use the idea
Keep an evidence record under every diagram, so the mixture of observed and assumed arrows is visible to the audience.
Where the conclusion applies
Four evidence levels as the chapter defines them, and a graph of exactly these six links. An observed label is only as good as the record behind it.
Check your understanding: If both inventory to shipments and shipments to inventory are upgraded to observed, how many arrows are unsupported?
Chapter 8 source: section "A graph that audits itself". Demonstration C08-D02.
3Demonstration 3 of 4
One more arrow closes loops nobody counted
How many feedback loops does a diagram have after one more arrow is drawn?
A new arrow from a downstream variable to an upstream one closes a path through every arrow between them. Its sign decides whether each newly closed loop reinforces or balances.
A loop is a closed path that follows the arrows and visits each variable once. Each loop is reported once. The extra arrow is tagged assumed.
Predict first. After adding shipments to backlog, are there more or fewer than 3 loops?
Choose an example
Constructed example: the chapter's six links plus one extra arrow chosen for this reader.
Calculated values
- Extra arrow
- shipments to backlog (+)
- Loops before
- 3
- Loops after
- 4
- New loops
- 1
- Reinforcing
- 1
- Balancing
- 3
Before the extra arrow there are 3 loops. Adding shipments to backlog closes 1 more: backlog > production > inventory > shipments > backlog is reinforcing. Total 3 + 1 = 4. Reinforcing 1, balancing 3, summing to 1 + 3 = 4. One drawn arrow can add loops that were never discussed, which is why the loops are enumerated by code rather than by eye.
Use the idea
When someone adds an arrow to a shared diagram, enumerate the loops it creates before agreeing to it.
Where the conclusion applies
Only the loops of this seven-arrow graph, and a sign that holds all else constant. Loop strength and delay length are not in the count.
Check your understanding: Before the extra arrow there are 3 loops and the extra arrow closes 1 new loop. How many loops are there in total?
Chapter 8 source: section "A graph that audits itself". Demonstration C08-D03.
4Demonstration 4 of 4
Remove the weakest arrow
Which loops stop closing when the least supported arrow is deleted?
Each loop is a closed path, so deleting any one arrow on it opens the loop. Deleting an unsupported arrow also lowers the unsupported count, but the picture's other loops stay.
The full diagram has six links. Removing an arrow breaks every loop that uses it. Inventory to production is negative in the chapter's diagram; the control can make it positive.
Predict first. If shipments to inventory (proposed) is removed, how many loops remain?
Choose an example
Constructed example: the chapter's six links with one removed, following its remove-one-arrow exercise.
Calculated values
- Arrow removed
- none
- Links
- 6
- Loops
- 3
- Reinforcing
- 0
- Balancing
- 3
- Unsupported
- 2
- No time semantics
- 2
Loops: 3 - 0 = 3. Unsupported arrows: 2 - 0 = 2. Nothing is removed, so this is the full diagram. With inventory to production negative, the production and inventory loop has one negative link, so it is balancing. Reinforcing 0 + balancing 3 = 3.
Use the idea
Delete the weakest arrow, write what would justify restoring it and who would hold that evidence, then see whether the conclusion changes.
Where the conclusion applies
Loops are counted from the links listed. Whether the diagram's conclusion survives depends on what it concluded, which the count cannot say.
Check your understanding: With inventory to shipments removed, how many loops remain out of 3?
Chapter 8 source: section "Remove one arrow". Demonstration C08-D04.