A pyramid scheme is a business model in which payment is made primarily for enrolling other people into the scheme. Some schemes involve a legitimate business venture, but in others no product or services are delivered. A typical pyramid scheme combines a plausible business opportunity (such as a dealership) with a recruiting operation that promises substantial rewards. A recruited individual makes an initial payment, and can earn money by recruiting others who also make a payment; the recruiter receives part of these receipts, and a cut of future payments as the new recruits go on to recruit others. In reality, because of the geometrical progression of (hypothetical) recruits, few participants in a pyramid scheme will be able to recruit enough others to recover their initial investment, let alone make a profit, because the pool of potential recruits is rapidly exhausted.
Although they are illegal in many countries, pyramid schemes have existed for over a century. As recently as...
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References and Further Reading
Bhattacharya P, Gastwirth J (1983) A non-homogeneous Markov model of a chain letter scheme. In: Rizvi M, Rustagi J, Siegmund D (eds) Recent advances in statistics: papers in honor of Herman Chernoff. Academic, New York, pp 143–174
Gastwirth J (1977) A probability model of a pyramid scheme. Am Stat 31:79–82
Gastwirth J, Bhattacharya P (1984) Two probability models of pyramids or chain letter schemes demonstrating that their promotional claims are unreliable. Oper Res 32:527–536
Mahmoud H (1994) A strong law for the height of random binary pyramids. Ann Appl Probab 4:923–932
Mahmoud H, Smythe RT (1991) On the distribution of leaves in rooted subtrees of recursive trees. Ann Prob 1:406–418
Naruk H (1975) Memorandum of decision: State of Connecticut versus Bull Investment Group, 32 Conn. Sup. 279
Smythe RT, Mahmoud H (1994) A survey of recursive trees. Theor Probab Math Stat 51:1–27
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Smythe, R.T. (2011). Pyramid Schemes. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_464
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