A Measure of the Population Quality of Legislative Apportionment

This paper attempts to examine carefully the problem of determining a numerical measure which reflects the quality of the population apportionment in a legislative body. We desire a single index, an index which takes advantage of the available population data, and an index which is readily understood. It should be said that we are not concerned with the much more difficult problem of legislative districting—actually drawing district boundaries on a map—but concentrate our attention only on the quality of apportionment in the particular, but important, sense of population equality. In order to accomplish this purpose I review a number of increasingly complex possibilities and eventually arrive at a measure which superficially seems somewhat esoteric, but which turns out ultimately to be easily interpretable. It will be convenient to proceed heuristically with the development by carrying along a small concrete example. For this purpose, consider the six congressional districts of Connecticut.