Estimating effective electoral thresholds

Electoral thresholds determine which parties win seats. Yet existing models of the effective threshold—the vote share at which a party has a 50% chance of winning its first seat in a district—rest on strong simplifying assumptions. I develop a new logical model that derives the effective threshold from two electoral quantities: the district magnitude and the effective number of vote-winning parties. A non-linear Bayesian model fitted to historical electoral data corroborates my theoretical logic and outperforms three existing alternatives in both explanatory power and out-of-sample prediction. The results show that effective thresholds decline with both district magnitude and electoral fragmentation. The model extends the Taageperian programme of parsimonious, interlocking electoral models and provides theoretically grounded propensity scores for studying the causal effects of representation.