A key starting point of quantitative social science is measurement – which encompasses direct observations from personal interviews and field observations, large-scale data collection efforts such as surveys and censuses, structured observations in designed experiments, and summary measures such as the Consumer Price Index. All these form the raw material for larger social science studies, and it is easy to get lost in these analyses and forget where the numbers came from and, even more importantly, what they represent.

We illustrate the choices involved in numerical measurements in the context of a subject of general interest – how people are represented in a political system – that can be studied both at a theoretical and an empirical level. I want to make the case that quantitative summaries can be helpful, as long as we are aware of the choices that must be made in summarizing a complex situation by a single set of numbers.

We want our political system to represent the voters and treat them fairly. At the simplest procedural level, this means giving a vote to each citizen and deciding elections based on majority or plurality rule. In practice, however, we are not all represented equally by the government, and as long as there is political disagreement, there will be some dissatisfaction. It would be appealing to have a mathematical definition of the amount of citizen “representation.