Congratulations! You’ve made it to graduate school. This means you’re in a select group, about to embark on a great adventure to learn about the world and teach us all some new things. This also means you obviously know how to follow rules. So I have five for you -- not counting the obvious one that to learn new things you’ll need to break some rules. After all, to be a successful academic, you’ll need to cut a new path, and so if you do exactly what your advisors and I did, you won’t get anywhere near as far since we already did it. So here are some rules, but break some of them, perhaps including this one
We clarify the theoretical foundations of partisan fairness standards for district-based democratic electoral systems, including essential assumptions and definitions that have not been recognized, formalized, or in some cases even discussed. We also offer extensive empirical evidence for assumptions with observable implications. Throughout, we follow a fundamental principle of statistical inference too often ignored in this literature -- defining the quantity of interest separately so its measures can be proven wrong, evaluated, or improved. This enables us to prove which of the many newly proposed fairness measures are statistically appropriate and which are biased, limited, or not measures of the theoretical quantity they seek to estimate at all. Because real world redistricting and gerrymandering involves complicated politics with numerous participants and conflicting goals, measures biased for partisan fairness sometimes still provide useful descriptions of other aspects of electoral systems.