Where is the Post in First-Past-the-Post (and Beyond)? A Logical Model of the Effective District-Wide Threshold

I present a new model of the effective district-wide threshold: the vote share at which any given party has a 50/50 chance of winning its first seat in a district. To derive my model, I rely only on simple combinatorics. The resulting expression suggests both that, all else being equal, we should expect parties to be more likely than not to win at least one seat in a district and that the effective district-wide threshold depends only on the district’s magnitude and the number of vote-winning parties. Using district-level data from 375 elections in 110 countries, I then estimate a non-linear Bayesian model that strongly corroborates my theoretical logic. As such, the model that I present here serves both to advance the broader Taageperan research agenda of interlocking electoral models and allows for new quasi-experimental research designs that exploit as-good-as-random variation around electoral thresholds.