In order to do so, the customer must purchase an item (the "token product") that is of marginal value, at a price above its actual value. Typical token products include e-books, cell phone boosters, screen savers, or shareware CDs.
Each customer who purchases the token product also has their name added to a waiting list. Each time the total number of people in the waiting list passes a particular threshold, the list "cycles": the person at the top of the list receives their reward item, and the next person in the list moves to the top.
Matrix schemes are generally considered to be a scam, or to represent gambling. This is due to the fact that for each customer to receive their reward item, multiple other customers must join, and those customers will also expect to receive reward items. This is compounded by the fact that the attractiveness of entering the matrix declines rapidly over time, thus meaning that the number of customers is unlikely to cross the thresholds necessary for many reward items to be made available.
For example, in a matrix scheme in which a reward item is sent out each time 10 new customers join, at any given moment 9 out of 10 or 90% of all customers must not have received their reward item. (This is inevitable because, for each customer who received their reward item, 9 others had to join.) Furthermore, eventually the matrix must reach a point by which it will be nearly impossible for new people added to the list to reach the top. The first person to join only needs 9 additional sign-ups, but the second person needs 18 additional sign ups (8 more for the person above him, and then 10 more for himself). The third person on the list needs 27 additional signups (7 for the person on top of the list, 10 for the person directly above him, and then 10 for himself). Then the number of people required continues to grow for each new person joining the list, thus making the value of joining the matrix fall rapidly. This means that at some point no further people will join; the system will halt; and the 90% of customers who, at the moment of the halt, have not yet received their reward item, never will. Meanwhile, the operator profits from the sale of the token products at inflated prices.
Supporters claim that additional revenue streams from advertising are used to keep the lists moving. However, detractors claim that it is impossible to generate enough outside revenue. If the entire world were to join the list, 90% of the world would be unable to cycle if the site did not draw sufficient alternate revenue streams. Adding more people to the list does not change the fact that the majority would receive nothing without these streams.
The operation of matrix schemes thus resembles Ponzi schemes: money from newly arriving investors is taken and used to pay off the return to existing investors.
Matrix scheme operators often claim that the sale of the "token product" obviates them from any blame for fraud or gambling, arguing that the person knowingly paid for that item alone and receiving the reward item is essentially a free bonus to which a buyer has no right or expectation. However, the token product alone could not be reasonably sold for the price listed, and as such legal experts claim that, regardless of what is said, the real product being sold is the "reward" in question in those situations. Steven A. Richards, a lawyer who represents multi-level marketing (MLM) companies for Grimes & Reese in Idaho Falls, Idaho, has stated that often there are no clear legal tests for Ponzi schemes. But if the product sold has no value or very little value, and consumers wouldn’t buy it without the attached free gift, the scheme probably runs afoul of federal and state laws.
When the first 10 people join, the operator has made $140 ($150, less the $10 for the 10 ringtones CDs). They purchase a mobile phone for $100 and send it to the first buyer, leaving a $40 profit. They may then repeat this process for every 10 people that join.
For each person who is sent a phone, 9 others will join the list; thus, at any given moment, only 10% of buyers will have received mobile phones. When the system halts, the 90% who have not received their phones at that point will never receive them, yet the operator will have made a profit of US$40 for every 10 customers who joined the list. Additionally, there will probably be some number of members who have joined since the last phone was sent out (between 1 and 9, since if there were 10 another phone would have been sent out); normally their money would have been used to purchase the next phone, but once the operator knows that no more phones will ever be sent, the operator will can keep all of their money (between $14 and $126).
As an example, suppose that a total of 25 people join such a matrix during its lifetime. The list will proceed as follows:
A Matrix Scheme is easily represented as a simple M/M/1 queue within the context of Queueing Theory In such a system you have a Markovian arrival, Markovian service, and one single server (F. S. Hiller and G. J. Lieberman). Introduction to Operations Research. McGraw-Hill, New York, 1995). In the standard Matrix queue service rates are a function of arrival rates since the time to cycle out of the queue is based on the entry fee into the matrix from arriving members. Also, since members move through the matrix in single file, it is easy to associate the single server.
The basic premise of queueing theory is that when service rates equal or exceed arrival rates overall waiting time within the queue moves towards infinity (Hiller and Lieberman).
The basic formulation includes three formulae. The traffic intensity, ρ, is the average arrival rate (λ) divided by the average service rate (μ):
The mean number of customers in the system (N):
N = ρ/(1-ρ)
And the total waiting time within the queue (T):
T = 1/(μ-λ)
It is possible to see that as arrival rates rise towards service rates the total waiting time (T) and mean number of customers in the system (N) will move towards infinity . Since service time can never exceed the arrival time in the standard matrix, and total waiting time can only be defined if service times exceed arrival times, the only way for the matrix queue to reach stability is for outside income sources to exceed those being entered into the system.
Currently there are no laws specifically naming matrix schemes illegal in the US. However, the US Federal Trade Commission has issued warnings to the public about these sites. In the UK, the Office of Fair Trading has declared some of them to be illegal. On July 1, 2005, two matrix sites, pulsematrix.com and phones4everyone (themobilematrix.com), were declared to be running a form of illegal lottery. Additionally, the US Federal Trade Commission and the UK Trading Standards have issued warnings to the public regarding the ease with which these models can be manipulated for fraudulent purposes.
Many of the original matrix sites, including EZExpo.com, are no longer in operation; some of them closed down while defending civil lawsuits. In 2003 EZExpo and several payment processors were sued in the civil courts for running an illegal lottery in the state of California, with the payment processors abetting the scam. However, the civil case is still ongoing. One result of the lawsuit is that those payment processors and some others no longer accept matrix schemes as customers. Currently, no legal precedent exists regarding the matrix scheme in the US.