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How can we make complexity work as part of a programme of engaged social science? This article attempts to answer that question by arguing that one way to do this is through a reconstruction of a central tool of a distinctively social science – the comparative method – understood as a procedure for elucidating the complex and multiple systems of causation that generate particular trajectories towards a desired future from the multiple sets of available futures. The article distinguishes between ‘simplistic complexity’ and ‘complex complexity’. ‘Simplistic complexity’ seeks to explain emergence in complex systems as the product of simple rules and defines complex science as the process of establishing such rules. It can and does serve as the basis of technocratic social engineering in the interest of the powerful. In …