Social projection is a judgemental heuristic that allows people to make quick and reasonably accurate predictions about others. The first part of this paper presents a review of the status of projection as a highly (though not fully) automatic process, its separateness from superficially similar processes of self-stereotyping, and its implications for intergroup perception. The second part places social projection within the context of the theory of evidential decision making, which highlights the benefits and the liabilities of projection in social dilemma situations. The main benefit is that projection can enhance cooperation within a group by leading individuals to believe that their own behavioural choices will be reciprocated. However, when interpersonal social dilemmas are nested within intergroup dilemmas, differential projection (i.e., strong ingroup projection paired with weak outgroup projection) yields collectively undesirable outcomes.