Standard quantification processes and most often their analysis are derived from statistics’ technique and approach. Social conventions are at the core of daily life, practical knowledge and coordination between people; statistical conventions are at the heart of cognitive activities developed by statisticians. What does quantification mean when addressed from the wider point of view of social conventions? This article analyzes the differences between social and statistical conventions. It enlarges the concept of objectivity in having recourse to the lenses of the plurality of worlds as defined by the economics of convention (EC), and to the concept of the informational basis of judgement in justice introduced by Amartya Sen. A wider conception of quantification processes in the social world can thus be elaborated, which opens fresh views on what become, in these processes, the concepts of facts and democracy.