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Galton, F. (1907) Vox Populi (Voice of the People). Nature, 75, 450-451.
https://doi.org/10.1038/075450a0

has been cited by the following article:

  • TITLE: Crowdsourced Sampling of a Composite Random Variable: Analysis, Simulation, and Experimental Test

    AUTHORS: M. P. Silverman

    KEYWORDS: Crowdsourcing, Computer Modeling of Crowds, Monte Carlo Simulation, Large-Scale Sampling, Log-Normal Random Variable, Log-Normal Distribution

    JOURNAL NAME: Open Journal of Statistics, Vol.9 No.4, August 15, 2019

    ABSTRACT: A composite random variable is a product (or sum of products) of statistically distributed quantities. Such a variable can represent the solution to a multi-factor quantitative problem submitted to a large, diverse, independent, anonymous group of non-expert respondents (the “crowd”). The objective of this research is to examine the statistical distribution of solutions from a large crowd to a quantitative problem involving image analysis and object counting. Theoretical analysis by the author, covering a range of conditions and types of factor variables, predicts that composite random variables are distributed log-normally to an excellent approximation. If the factors in a problem are themselves distributed log-normally, then their product is rigorously log-normal. A crowdsourcing experiment devised by the author and implemented with the assistance of a BBC (British Broadcasting Corporation) television show, yielded a sample of approximately 2000 responses consistent with a log-normal distribution. The sample mean was within ~12% of the true count. However, a Monte Carlo simulation (MCS) of the experiment, employing either normal or log-normal random variables as factors to model the processes by which a crowd of 1 million might arrive at their estimates, resulted in a visually perfect log-normal distribution with a mean response within ~5% of the true count. The results of this research suggest that a well-modeled MCS, by simulating a sample of responses from a large, rational, and incentivized crowd, can provide a more accurate solution to a quantitative problem than might be attainable by direct sampling of a smaller crowd or an uninformed crowd, irrespective of size, that guesses randomly.