You must have seen them dozens of times. Email messages or messages on the Internet which tell you how, for a relatively small investment, you can make huge amounts of money.  There are countless variations depending on economic climate or country, but the concept and motive is always the same, which is to fool naïve or financially desperate people.

The typical pyramid scheme is similar to a “chain-letter” and the process can be represented to go something like this:

• You receive an email making unbelievable and fabulous claims about how much money you can “earn” simply by participating in a no-brainer process.
   
• You are told to send some amount of money to the people who have joined this scheme ahead of you.  Typically, you are asked to send approximately $5-$10 each to about four or five people, a negligible sum compared to the windfall apparently in store for you.
   
• You are instructed to alter the list of previous participants such that the one at the very top of the list is removed and all the other names are moved up one position. You then add your own name to the bottom of the list.
   
• You are also instructed to send out as many copies of this altered email as you can and to as many people as you can reach, asking each person to do the same.
   
• At the end of the letter, there is a message saying that as new people join the scheme below you, in theoretically exponentially-growing numbers, each one will send you the amount you yourself paid.  It would seem, therefore, that since the number of new participants is growing at an exponential rate, you should collect this payment from a vast number of people.

On the surface the mathematics is very appealing indeed. You do not need a degree in mathematics to know that if that five people send the email to five people each and this continues, the number will increase from five to twenty-five to hundred and twenty five and so on. This type of scheme has been around for as long as fraudulent schemes have existed but it has been given a tremendous boost by the advent of the Internet. It used to take days or weeks for a chain letter to pass from one person’s hands to another but with email, it takes a few seconds. This makes the scheme all the more appealing to ignorant people who think that paying a sum of hundred to two hundred dollars is nothing compared to the vast sums of money they will get in a matter of days. Unfortunately, mathematics does not work so simplistically.

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A hypothetical pyramid scheme

Let us dissect a hypothetical pyramid scheme using a slightly higher level of mathematics and a little common sense. Suppose the list included in this scheme contains five names.  This is how the process works; you are to send just one dollar to each person listed above you, remove the top name, move all the other names up one position and send this modified list to even more people.  Let us assume, for simplicity’s sake, that you get ten people to join, and each of them gets ten people, and so on.

As the pyramid grows below you, here's what theoretically happens:

1. The first level below you has ten people.  They each send you a dollar, so you collect $10.
2. The next level has a hundred people.  (Each of the first ten gets ten more.)  You collect $100.
3. The next level has a thousand people.  You collect $1,000. (2 nd level gets $100 each, 3 rd level $10 each)
4. The next level has 10,000 people, so you collect $10,000. (and so on...)
5. The next level has 100,000 people, so you collect $100,000.
6. At this point, your name drops off the list, and you collect no more.

It seems almost too simple and obvious. Invest a sum of money quickly so as to ensure that you are near the top of the pyramid, send to as money people as possible so as to get that much money and wait for the windfall when they send to more people.

The two basic underlying foundations of this scheme, however, are that there will always be an infinite pool of gullible people who want to cash in and that more and more wealth is being created. This is where the fantasy caves in.

In order to fully understand why pyramid schemes are fundamental flawed, there are two points that you need to take note of.

1. The pyramid must fail because the total number of potential participants is finite and limited.
2. No new wealth is created, the only wealth gained by any single participant is wealth lost by many, many more participants.

The pyramid must fail because the number of potential participants is finite and limited.

The total world population is about 7 billion. Of that, perhaps 5% have Internet access, so that limits us to about 500-1000 million users. If all the people were induced to join one pyramid scheme (something that could never happen) there will still only be about 10 levels to our hypothetical scheme.

That's ten levels, counting the one person at the top who started it.  By the time these ten levels are filled, there will be a total of 1,111,111,111 participants.  The eleventh level would require 10,000,000,000, or ten billion new participants to fill in.  That many people do not exist on this planet yet.

At this point, the pyramid collapses.  When it does, the vast majority of those who had joined (90% of the total) will not have made any return at all.  They will have paid their money to get in, but the promise that they will profit as people join below them will never be fulfilled. This is, of course, making several favourable assumptions all the way. Many people will send to 20 or more people out of sheer eagerness to make money fast, causing the pyramid to break down faster. At the end of the day, only the perpetrator at the top who started the chain stands to benefit. A few more lucky souls may win depending on how many naïve people there are below them.

The crux of the matter is that, very simply, no new wealth is created. The only wealth gained by any participant is wealth lost by other participants.

It is also very important to understand that the underlying principle behind all legitimate business activities is that wealth is created. For example, when a company or individual creates a product which is worth more than the cost of the raw materials needed, wealth has been created. 

Pyramid schemes can hence be defined as illegitimate business ventures because they produce no goods of any significance and they provide no service. Hence, no wealth of any nature is created.  All that is accomplished is that existing wealth is moved around.  Every dollar that one person gains through such a scheme is a dollar that someone else has lost. It is mathematically impossible for more to be taken out of any such scheme than what is put into it.

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Conclusion

This scheme simply does not work, except for those who get in at the first few levels. Using our hypothetical scheme, that would mean the first 20 or so people, including the perpetrator of the scheme. The remaining millions of participants in such a scheme will only lose their original investment without making one cent of profit. This is a very serious act because, for every individual who has been cheated of his money, a fraud has been committed. Every single nation and government has laws against fraud. Apart from being unlawful, it is important to take note that participating in such a scheme is unethical, you would be engaging in something that is dishonest and unethical, and which is very unlikely to make you any profit.

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Reference

A chain letter exposed
http://members.impulse.net/~thebob/ChainLetter/

The U.S. Postal Service's official statement on chain letters
http://www.usps.com/websites/depart/inspect/chainlet.htm

Exploits of Charles Ponzi, from whom the “Ponzi scheme” gets its name
http://www.mark-knutson.com/

Pyramid Schemes, Ponzi Schemes, and Related Frauds
http://members.impulse.net/~thebob/Pyramid.html