Like many topics of real importance, there has been substantial disagreement about the best way to construct a sample of observations that optimally reflects the population of interest (see Sterba, 2009, for an excellent review). Core to this disagreement is the distinction between model-based and design-based approaches. These two approaches permit us to make inferences from samples back to populations, with differences between the two approaches motivating different sampling designs. Briefly, the model-based approach was first proposed by Fisher (1922) who believed that obtaining a truly random sample from a given population was typically not possible. Instead, Fisher proposed building a statistical model that explicitly linked the substantive theory to the sample data by approximating the mechanism by which the dependent variable was generated. However, the statistical model required the imposition of certain distributional assumptions that many researchers believed to be both subjective and fallible. In response to these concerns, Neyman (1934) developed a design-based approach that introduced randomness via a set of known selection probabilities. This allowed for the selection process to be both controlled and known, avoiding untenable
