Two Probability Models of Pyramid or Chain Letter Schemes Demonstrating that Their Promotional Claims are Unreliable

Operations Research · 1984 · Volume 32 · Issue 3

Abstract

A variety of chain letters and pyramid schemes continue to be offered to the public. This article reviews two probability models which were developed in response to requests by attorneys faced with prosecuting promoters of such ventures. The two models were designed to establish the fraud underlying a quota pyramid scheme (which places a limit on the maximum number of participants) and a chain letter in which a participant could sell only two letters (unless he purchases a new letter). The models emphasize how dependent a participant's potential earnings are to his time of entry in the process and show that although a small percentage of participants (some early entrants) will make money, most will lose so that pyramid scheme investors, as a class, are defrauded.

Keywords

563 diffusion approximation of a nonhomogenous Markov chain, 567 nonhomogeneous Markov model of a chain letter scheme, 570 pyramid or chain letter schemes

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