  The aim of this paper is twofold. First, three theoretical principles are
formalized: randomization, overrepresentation and restriction. We develop these
principles and give a rationale for their use in choosing the sampling design
in a systematic way. In the model-assisted framework, knowledge of the
population is formalized by modelling the population and the sampling design is
chosen accordingly. We show how the principles of overrepresentation and of
restriction naturally arise from the modelling of the population. The balanced
sampling then appears as a consequence of the modelling. Second, a review of
probability balanced sampling is presented through the model-assisted
framework. For some basic models, balanced sampling can be shown to be an
optimal sampling design. Emphasis is placed on new spatial sampling methods and
their related models. An illustrative example shows the advantages of the
different methods. Throughout the paper, various examples illustrate how the
three principles can be applied in order to improve inference.
