The line of heterodox economic thinking named “the economics of conventions” emerged in the 1980s in France. Four among its six founding fathers had a strong background in statistics and were working at INSEE (the French National Institute of Statistics and Economic Research). However, the numerous and fruitful researches in the line of this new paradigm have only slightly used the quantitative methods (above all econometrics) that are widely spread in mainstream economics as well as in other heterodox movements, e.g. the French school of regulation. In order to provide a rationale for this paradox, we are lead to set the development of the economics of conventions within a broader history of economics and social sciences. Indeed, from the 1980s onwards, social sciences have gone through a movement of bifurcation that brought about a deep change in the scientific and political status of quantification. Monitoring this movement leads to address the issue of the relationships between the search for theoretical reflexivity and the social demand for expertise addressed to economics.