The Limitations of Quantitative Methods for Analyzing Gerrymanders: Indicia, Algorithms, Statistics and Revealed Preference
29 Pages Posted: 6 Jul 2007
Date Written: July 4, 2007
Simply put, all current quantitative methods are deeply flawed: Threshold rules based on indicia that are hypothesized to be correlated with gerrymanders, such as compactness, margins of competition, and estimated electoral responsive, are at best effective only locally and at worst literally impossible to satisfy. Automatic maximization rules using these indicia or other automatable algorithms universally ignore the political context in which they are applied and thus yield politically biased results despite the appearance of neutrality. The most sophisticated methods, which use computationally-intensive sampling from real districting populations, avoid these problems, but suffer from intractable computational issues and (often) from implausible formulation of the "null" hypothesis.
We place evaluating intent as a motive behind a redistricting plan into a formal quantitative micro-economic framework to evaluate existing and emerging methods, and find that these methods are statistically flawed. In place of classical statistical tests, we formalize a method of revealed preferences to probe intent by comparing aspects of plans that were feasible, but not selected. This method has been used in an informal, ad-hoc, manner in redistricting cases, but is not well documented and has never been rigorously analyzed. Our method has five advantages. First, it is easily interpretable. Second, it can be applied using only the data available to the original planners and does not require estimating the outcomes of hypothetical elections. Third, lacking sophisticated optimization technology, the basic method can be applied using hand drawn maps. Fourth, it is more consistent with the knowledge that distracters had than statistical methods because it does not implicitly assume that a districting authority was aware of all possible plans. Finally, it is the only quantitative method for determining intent, so far proposed, that is statistically sound.
Keywords: redistricting, gerrymander, competitiveness, compactness, hypotheis tests, bias, responsiveness, automated redistricting
JEL Classification: C11, P16
Suggested Citation: Suggested Citation