The sampling method described in the question is stratified sampling. This approach involves dividing a population into smaller groups, known as strata, where the members of each stratum share similar characteristics. In this case, the newspaper publisher has divided the database into strata based on income levels. A sample is then taken from each stratum to ensure that the sample represents the diversity of the entire population. Stratified sampling is particularly useful when the population has distinct subgroups and the goal is to ensure representation from each group. This method is part of the ASQ Manager of Quality/Organizational Excellence Body of Knowledge, which includes various statistical techniques for quality control and improvement1.
References: 1: ASQ, "Sampling in Quality Control"