Multiagent systems constitute an independent topic at the intersection between distributed computing and artificial intelligence. As the algorithmic techniques and the applications for multiagent systems have been continuously developing over the last two decades reaching significantly mature stages, many methodological problems have been addressed. In this paper, we aim to contribute to this methodological assessment of multiagent systems by considering the problem of choosing, or recruiting, a subset of agents from a set of available agents to satisfy a given request. This problem, which we call problem of recruitment, is encountered, for example, in matchmaking and in task allocation. We present and study a novel formal approach to the problem of recruitment, based on the algebraic formalism of lattices. The resulting formal framework can support the development of algorithms for automatic recruitment.