A Bayesian approach to detecting electoral manipulation

“Manipulating Maps and Winning Elections” is a challenging paper to comment upon. In part, this is because it is, in sum, convincing, and in part because it is merely the tip of Professor Johnston’s iceberg: It rests upon (and cites) a score of his previous works, which have been produced over more than twenty-five years of scholarly activity. In particular, this paper brings to bear data from Johnston’s unique and detailed research into the mechanics and effects of the UK’s system for defining parliamentary constituencies (Rossiter, Johnston, & Pattie 1999), and analytical methods that he has invented or refined (Rossiter, Johnston, & Pattie 1997; Johnston & Pattie, 2000). I do not intend to comment upon every aspect of this article in these remarks. Instead, I will attempt to place that work in a more general analytic framework, and to suggest several methodological refinements and alternative approaches. Since Johnston explicitly draws on the general themes of “generalization and order,” “measurement,” (p. 2) and “understanding of aggregation patterns,” (p. 3) and since he argues that significant insights are to be gained from the “application of mathematical and statistical reasoning,” (p. 19) it is appropriate to put Johnston’s approach into a more formal statistical framework. 1 In the next section of this paper I present