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Pyramid scheme

Pyramid scheme is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Pyramid scheme rather than just read about it. In short: A pyramid scheme or pyramid scam is a fraudulent business model in which participants earn money primarily by recruiting new members rather than by selling products or services to end consumers or by generating genuine investment returns. Pyramid schemes depend on an ever-growing number of recruits, making them inherently unsustainable.

Pyramid scheme — main illustration
Pyramid scheme — illustration

Key takeaways

  • Pyramid scheme belongs to science; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Pyramid scheme to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Pyramid scheme from memory before moving on to harder problems.

Reference excerpt

A pyramid scheme or pyramid scam is a fraudulent business model in which participants earn money primarily by recruiting new members rather than by selling products or services to end consumers or by generating genuine investment returns. Pyramid schemes depend on an ever-growing number of recruits, making them inherently unsustainable. As recruitment inevitably becomes insufficient to sustain the scheme, most participants—particularly those who join later—lose money, while only a small number of people near the top of the pyramid profit. Consequently, pyramid schemes are a form of fraud and are illegal in many countries. Pyramid schemes have existed in various forms since at least the mid-to-late 19th century. Although some multi-level marketing (MLM) companies have been found to operate as pyramid schemes, legitimate MLM businesses are distinguished by compensation based primarily on retail sales to end consumers rather than recruitment.

Concept and basic models In a pyramid scheme, an organization compels individuals who wish to join to make a payment. In exchange, the organization promises its new members a share of the money taken from every additional member that they recruit. The directors of the organization (those at the top of the pyramid) also receive a share of these payments. For the directors, the scheme is potentially lucrative—whether or not they do any work, the organization's membership has a strong incentive to continue recruiting and funneling money to the top of the pyramid. Such organizations seldom involve sales of products or services with value. Without creating any goods or services, the only revenue streams for the scheme are recruiting more members or soliciting more money from current members. The behavior of pyramid schemes follows the mathematics concerning exponential growth quite closely. Each level of the pyramid is much larger than the one before it. For a pyramid scheme to make money for everyone who enrolls in it, it would have to expand indefinitely. When the scheme inevitably runs out of new recruits, lacking other sources of revenue, it collapses. Since the biggest terms in this geometric sequence are at the end, most people will be in the lower levels of the pyramid; accordingly, the bottom layer of the pyramid contains the most people. The people working for pyramid schemes try to promote the actual company instead of the product they are selling. Eventually, all of the people at the lower levels of the pyramid do not make any money; only the people at the top turn a profit. In particular, when the scheme collapses, members in the bottom layers did not have any opportunity to profit from the scheme; still, they have already paid to join. Therefore, a pyramid scheme is characterized by a few people (including the creators of the scheme) making large amounts of money, while subsequent members lose money. For this reason, they are considered scams.

The "eight ball" model

Many pyramids are more sophisticated than the simple model. These recognize that recruiting a large number of others into a scheme can be difficult, so a seemingly simpler model is used. In this model each person must recruit two others, but the ease of achieving this is offset because the depth required to recoup any money also increases. The scheme requires a person to recruit two others, who must each recruit two others, and so on. Prior instances of this scheme have been called the "Airplane Game" and the four tiers labelled as "captain", "co-pilot", "crew", and "passenger" to denote a person's level. Another instance was called the "Original Dinner Party" which labeled the tiers as "dessert", "main course", "side salad", and "appetizer". A person on the "dessert" course is the one at the top of the tree. Another variant, "Treasure Traders", variously used gemology terms such as "polishers", "stone cutters", etc. One version called the Abundance Fractal uses the four elements as the names of tiers: "Fire", "Air", "Earth", and "Water". A more recent variation known as the Living Workshop takes the names of plants, calling the tiers "seed", "sapling", "blossom", and "lotus". Such schemes may try to downplay their pyramid nature by referring to themselves as "gifting circles" with money being "gifted". Others focus on sharing circles or educational themes around "abundance" to divert attention away from the unsustainable structure. Popular schemes such as "Women Empowering Women" do exactly this. Whichever euphemism is used, there are 15 total people in four tiers (1 + 2 + 4 + 8) in the scheme—with the Airplane Game as the example, the person at the top of this tree is the "captain", the two below are "co-pilots", the four below are "crew", and the bottom eight joiners are the "passengers".

The eight passengers must each pay (or "gift") a sum (e.g., $5,000) to join the scheme. This sum (e.g., $40,000) goes to the captain, who leaves, with everyone remaining moving up one tier. There are now two new captains so the group splits in two with each group requiring eight new passengers. A person who joins the scheme as a passenger will not see a return until they advance through the crew and co-pilot tiers and exit the scheme as a captain. Therefore, the participants in the bottom three tiers of the pyramid lose their money if the scheme collapses. If a person is using this model as a scam, the confidence trickster would take the majority of the money. They would do this by filling in the first three tiers (with one, two, and four people) with phony names, ensuring they get the first seven payouts, at eight times the buy-in sum, without paying anything themselves. So if the buy-in were $5,000, they would receive $40,000, paid for by the first eight investors. They would continue to buy in underneath the real investors, and promote and prolong the scheme for as long as possible to allow them to skim even more from it before it collapses. Although the "captain" is the person at the top of the tree, having received the payment from the eight paying passengers, once they leave the scheme they are able to re-enter the pyramid as a "passenger" and hopefully recruit enough to reach captain again, thereby earning a second payout.

Blessing Loom

… excerpt ends here. Continue reading the full article.

Illustrations

Pyramid scheme: The unsustainable exponential progression of a classic pyramid scheme in which every member recruits six new people. To sustain the scheme, the 2.2 billion people in the 12th layer would be required to recruit 13.1 billion more people for the 13th layer, even though there are not nearly enough people in the world to achieve that.
The unsustainable exponential progression of a classic pyramid scheme in which every member recruits six new people. To sustain the scheme, the 2.2 billion people in the 12th layer would be required to recruit 13.1 billion more people for the 13th layer, even though there are not nearly enough people in the world to achieve that.
Pyramid scheme: The "eight-ball" model contains a total of fifteen members. Note that it is a representation of the arithmetic progression 1 + 2 + 3 + 4 + 5 = 15. The pyramid scheme in the picture in contrast is a geometric progression 1 + 2 + 4 + 8 = 15.
The "eight-ball" model contains a total of fifteen members. Note that it is a representation of the arithmetic progression 1 + 2 + 3 + 4 + 5 = 15. The pyramid scheme in the picture in contrast is a geometric progression 1 + 2 + 4 + 8 = 15.
Pyramid scheme: At ten levels deep, the "airplane game" has an 87% loss rate.
At ten levels deep, the "airplane game" has an 87% loss rate.
Pyramid scheme: The "Blessing Loom" is identical to the classic "Airplane Game", with a circular diagram obscuring the pyramid structure.
The "Blessing Loom" is identical to the classic "Airplane Game", with a circular diagram obscuring the pyramid structure.

Worked examples

Example 1 — a first encounter with Pyramid scheme

Start with the simplest possible case. Write down what Pyramid scheme claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Pyramid scheme before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Pyramid scheme ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Pyramid scheme

In research
Pyramid scheme appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Pyramid scheme in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Pyramid scheme is common in secondary-school and first-year university syllabi. It links to neighbouring topics Business models, Confidence tricks, Pyramid and Ponzi schemes, so understanding it makes those chapters shorter.
In everyday life
Look for Pyramid scheme outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Pyramid scheme in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Pyramid scheme means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Pyramid scheme out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Pyramid scheme in simple terms?

A pyramid scheme or pyramid scam is a fraudulent business model in which participants earn money primarily by recruiting new members rather than by selling products or services to end consumers or by generating genuine investment returns. Pyramid schemes depend on an ever-growing number of recruits…

Why does Pyramid scheme matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Pyramid scheme?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Pyramid scheme.

Tags

  • Business models
  • Confidence tricks
  • Pyramid and Ponzi schemes
  • Types of marketing

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