The Limitations of Quantitative Methods for Analyzing Gerrymanders: Indicia, Algorithms, Statistics and Revealed Preference

29 Pages Posted: 6 Jul 2007

See all articles by Micah Altman

Micah Altman

Massachusetts Institute of Technology (MIT) Libraries; The Brookings Institution

Michael P. McDonald

University of Florida

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

Altman, Micah and McDonald, Michael P., The Limitations of Quantitative Methods for Analyzing Gerrymanders: Indicia, Algorithms, Statistics and Revealed Preference (July 4, 2007). Available at SSRN: or

Micah Altman (Contact Author)

Massachusetts Institute of Technology (MIT) Libraries ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States


The Brookings Institution ( email )

1775 Massachusetts Ave, NW
Washington, DC 20036
United States


Michael P. McDonald

University of Florida ( email )

PO Box 117165, 201 Stuzin Hall
Gainesville, FL 32610-0496
United States

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