Constant‐sum sampling: an apology for statistics' “original sin”

Purpose – The purpose of this editorial is to consider the importance of random samples subject to a constant‐sum constraint (that is, a succession of identically distributed random variables that add up to some predetermined constant) in human experience and intuition. Design/methodology/approach – The importance of constant‐sum random samples is motivated by considering the intuition that successive random variables must be negatively correlated to provide the “balance” required by convergence results such as the law of large numbers. Given that the intuition of negatively correlated trials is valid in the context of constant‐sum sampling, we explore the roles of this model in both evolutionary and modern‐day contexts. Findings – The connection between constant‐sum sampling and the intuition that convergence results require negatively correlated random variables suggests that the constant‐sum model played a significant role in the lives of our primitive human ancestors. Because of the continued prevalence of constant‐sum samples in the modern world, it is concluded that the intuition of negatively correlated random variables should not be so quickly and categorically dismissed. Originality/value – The editorial studies the relationship between constant‐sum random sampling and the intuition of negatively correlated random variables, and reveals the important role that the constant‐sum model has played – and still plays – in human cognition.