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Popular understandings of the financial crisis tend to focus on the rents extracted by elite personnel in the financial sector. Professional discussions, however, have addressed the faulty assumptions underlying theory and practice – in particular, the assumption that returns to financial assets follow the Gaussian distribution, in the face of much empirical evidence that these have power law distributions with far higher kurtosis. It turns out that the power law tails of returns to financial assets are also a feature of the distribution of company rates of profit, a discovery that stems from proposals to ‘dissolve’ the traditional transformation problem by abandoning the condition of a uniform rate of profit and instead considering its distribution.Marx himself was aware of the importance of considering the distributional properties of economic variables, based on his reading of Quetelet. In fact, heavy-tailed distributions characterise a wide range of variables in capitalist economies, the best-known probably being the Paretian tail component in distributions of income and wealth. Nor is this simply an empirical fact – such distributions emerge readily from a range of agent-based simulations.Capitalist economies are, in a particular technical sense, complex self-organising systems perpetually on the brink of crisis. This modern understanding is prefigured in Marx’s discussion of how the compulsive character of social relations emerges from the atomistic exercise of human free will in commercial society. The developing literature of probabilistic Marxism successfully applies these insights to the wider fields of econophysics and complexity, demonstrating the continuing relevance of Marx’s thought.

We revisit the model of socialism proposed in our Towards a New Socialism (1993) and attempt to answer various questions that have been raised regarding the connection between our view of socialism and our perspective on capitalism, the process of transition to socialism, the failings of the Soviet model, the relationship between socialism and communism, the role of direct democracy under socialism, and the use of labor-time calculation in a socialist economy. We argue that the contradictions of capitalist property relations, and of the accumulation process on a world scale, are set to present once again the necessity of the abolition of private property during the 21st century, and offer some thoughts on transitional forms that could implement this abolition. We defend the ideas of direct democracy and economic calculation in terms of labor time, and argue that these elements distinguish our proposals from the Soviet model. We trace the demise of the latter both to specifics of the Russian situation and to more general problems of Leninism, notably Lenin’s conception of the council state, and of socialism as a long period during which the productive forces are built up in preparation for an eventual communism.