Methods to Estimate the Impact of Gerrymandering on the Parliamentary Seat Shares of Parties

The title of this talk is deliberately inaccurate in that gerrymandering - i.e., intentionally drawing the boundaries of similar-size single-member districts in a way that can maximize the likely seat share of a particular party in subsequent elections - is only one of many reasons why a districting plan can unfairly favor one party over the other. However, since it is the most (in)famous of all, it seemed like the best cue to put in the title to convey what this largely methodological talk and discussion, which I hope will eventually lead to a proper research paper, is about. What I will deal with is the topic of much of the scholarly literature on the geography of single-member district elections outside of the US, and asks how we can decompose the total - intended or unintended - partisan bias in a districting plan into various components that may even have contradictory effects on individual parties' fortunes. The possible components differences across electoral districts in population size, turnout, the spatial distribution of voter support and seats that go for 'small' parties and how electorally efficient the geographic distributions of voters for the various 'big' parties are. While multiple methods were proposed to estimate these components, only Brookes method have seen extensive use over the years. This talk is meant to share with you my amazement about how poorly justified this method is, highlight what I suspect the problems with this method are, and test on you whether the alternative estimation techniques to estimate the individual bias components that I developed makes sense. I also intend to present some simulation results that test my methodological propositions.