The matchmaking paradox: a statistical explanation
Iddo Eliazar, Igor M. Sokolov · Journal of Physics A Mathematical and Theoretical · 2010
Medical surveys regarding the number of heterosexual partners per person yield different female and male averages—a result which, from a physical standpoint, is impossible. In this paper we term this puzzle the 'matchmaking paradox', and establish a statistical model explaining it. We consider a bipartite graph with N male and N female nodes ( N ≫ 1), and B bonds connecting them ( B ≫ 1). Each node is associated a random 'attractiveness level', and the bonds connect to the nodes randomly—with probabilities which are proportionate to the nodes' attractiveness levels. The population's average bonds-per-nodes B / N is estimated via a sample average calculated from a survey of size n ( n ≫ 1). A comprehensive statistical analysis of this model is carried out, asserting that (i) the sample average well estimates the population average if and only if the attractiveness levels possess a finite mean; (ii) if the attractiveness levels are governed by a 'fat-tailed' probability law then the sample average displays wild fluctuations and strong skew—thus providing a statistical explanation to the matchmaking paradox.