Winners and Losers under Proportional Representation
2026-07-10
In elections under proportional representation (PR), proportionality between votes and seats is an ideal never achieved in reality. Discrepancies between votes and seats are most prevalent under the most widely used PR seat allocation formula, D’Hondt/Jefferson. This article provides the first comprehensive model to explain the discrepancies between the national seat allocation and the vote distribution under the D’Hondt rule. The model identifies six systematic factors that drive these deviations, ranging from the bias in the seat allocation rule to differences in the electoral rules (e.g. malapportionment) and party competition across districts. Thus, this model goes beyond the well-known rule that large parties are overrepresented under D’Hondt by providing a quantitative point estimate of this deviation and of between-district inequalities. The model identifies the (expected) beneficiaries and losers of the seat allocation and predicts the magnitude of these penalties and benefits. At the level of political parties, the model predicts the gains and losses in terms of seats, relative to the parties’ proportional share of seats. Empirical tests on 156 elections from 23 democracies, covering 3,653 political parties and 2,139 constituencies, are used to assess its validity and to calculate the resulting substantial effects.