This paper examines the rise of algorithmic systems – that is, systems of data-driven governance (and social-credit-type) systems – in the form of ratings systems of business respecting human rights responsibilities. The specific context is rating or algorithmic systems emerging around national efforts to combat human trafficking through so-called Modern Slavery and Supply Chain Due Diligence legal. Section 2 provides a brief contextualisation of the problems and challenges of managing compliance with emerging law and norms against forced labour and, in its most extreme forms, modern slavery. Section 3 examines the landscape of such algorithmic private legal systems as it has developed to date in the context of forced labour ratings systems. There is a focus on the connection between the power to impose the normative basis of data analytics and the increasingly tightly woven-in connection between principal actors in this endeavour.