The vexing problem of measuring the quality of government has parallels in many applied sciences. The choice of measures depends on classical statistical questions of reliability and validity. It also depends on the potential uses of the measures. We will discuss four dimensions of the choice:  resource allocation, incentive effects, "representation" of groups, and "fundraising effects." An example (allocating aid) shows that econometric tools can help us qualitatively with this choice, but the richness of the decision problem outstrips the data and tools.