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

Author

Listed:
  • J. L. Gastwirth

    (George Washington University, Washington, D.C.)

  • P. K. Bhattacharya

    (University of California, Davis, California)

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.

Suggested Citation

  • J. L. Gastwirth & P. K. Bhattacharya, 1984. "Two Probability Models of Pyramid or Chain Letter Schemes Demonstrating that Their Promotional Claims are Unreliable," Operations Research, INFORMS, vol. 32(3), pages 527-536, June.
    • Handle: RePEc:inm:oropre:v:32:y:1984:i:3:p:527-536
    DOI: 10.1287/opre.32.3.527
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    Citations

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    Cited by:

    1. Hosam Mahmoud, 2022. "Profile of Random Exponential Recursive Trees," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 259-275, March.
    2. Antler, Yair, 2018. "Multilevel Marketing: Pyramid-Shaped Schemes or Exploitative Scams?," CEPR Discussion Papers 13054, C.E.P.R. Discussion Papers.
    3. Altok, S. & Işlak, Ü., 2017. "On leaf related statistics in recursive tree models," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 61-69.
    4. Antler, Yair, 2023. "Multilevel marketing: pyramid-shaped schemes or exploitative scams?," Theoretical Economics, Econometric Society, vol. 18(2), May.
    5. Yong Shi & Bo Li & Guangle Du, 2021. "Pyramid scheme in stock market: a kind of financial market simulation," Papers 2102.02179, arXiv.org, revised Feb 2021.
    6. Yarong Feng & Hosam Mahmoud, 2018. "Profile of Random Exponential Binary Trees," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 575-587, June.

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