Opportunities as chances: maximising the probability that everybody succeeds

Opportunities in society are commonly interpreted as `chances of success'. Within this interpretation, should opportunities be equalised? We show that a liberal principle of justice and a limited principle of social rationality imply that opportunity profiles should be evaluated by means of a `Nash' criterion. The interpretation is new: the social objective should be to maximise the chance that everybody in society succeeds. In particular, the failure of even only one individual must be considered maximally detrimental. We also study a refinement of this criterion and its extension to problems of intergenerational justice.