This paper advances the position that sociology needs to develop an approach to research which focuses on fundamental social problems. In doing so it shares many of the intellectual values and goals of political arithmetic while seeking to move methodologically beyond it. Since such problems are complex they will require, typically, interdisciplinary input and a concomitant approach to the development and appraisal of theories. We are not, therefore, advocating the primacy of sociology but arguing that it has a distinctive part to play in addressing the fundamental problems of the twenty-first century. However, a policy-oriented sociology has also to take up the task, so clearly defined by the tradition of political arithmetic, which is to hold governments to account. Consequently a central principle of a new policy science is that it should contribute to democratic debate about policy.