Risk-taking in social Parrondo’s games can lead to Simpson’s paradox

Abstract

Parrondo’s paradox (inspired by the flashing Brownian ratchet) and Simpson’s paradox (a statistical phenomenon) are two popular paradoxes that have attracted immense interest across many fields ranging from decision theory, evolutionary biology to social dynamics. In this article, we show that risk-taking behaviour through aggregate decision-making on Parrondo’s games can lead to the emergence of Simpson’s paradox. By partitioning the network of individuals according to risk-taking behaviours, we show that it is possible that the trend of capital losses from playing Parrondo’s games reverses when these groups are combined—the signature of Simpson’s paradox. This work reports on the emergence of the double paradox on a scale-free network and a social network, with the potential to uncover such instances in other social settings as well.