The forthcoming article “The Achilles Heel of Plurality Systems: Geography and Representation in Multi-Party Democracies” by Ernesto Calvo and Jonathan Rodden is summarized here:
The most recent elections in Britain and some of its former colonies have yielded some rather striking asymmetries between votes and seats. In the UK, the Conservatives came close to an outright majority with 36 percent of the votes. The Canadian Conservatives preside over a legislative majority in spite of winning less than 40 percent of the vote. In India, the BJP recently took a commanding 62 percent of the seats with only 39 percent of the votes.
These are only the most recent examples of what Graham Gudgin and Peter Taylor referred to as the “Achilles Heel” of plurality electoral systems in their classic work on political geography: when more than two parties compete in electoral systems with winner-take-all districts, the geographic distribution of partisan support across districts can lead to surprisingly large asymmetries between votes to seats.
This paper provides a theoretical model that attempts to capture the most crucial aspects of this problem, and develops a corresponding empirical model that allows us to estimate the relationship between a party’s territorial support and its representation in the legislature.
We capture a perennial problem, well known to the Liberals in the UK and the NDP in Canada, whereby small parties can do very well in transforming votes to seats when they emerge and consolidate with sufficient geographic concentration that they can form majorities in their “heartland” constituencies. However, as such parties attempt to expand their support base and become national parties, they are unable to transform votes to seats, and their widespread incursions into other districts generate knock-on effects for the other parties as well, increasing the disproportionality of the whole electoral system.
We also uncover some interesting subtleties about the representation of the larger, established parties as their support surges and declines over time. The historical development of one of the parties—like the Democrats in the United States or Labour in Great Britain—leaves it with a set of extremely safe districts while their main opponent’s support is more dispersed. This relative geographic concentration allows them to suffer fewer seat losses during their periods “in the wilderness.” Yet we also see that this underlying geographic concentration is something they must shed if they are able to win crucial centrist districts and win elections.
Thus the ebb and flow of geographic support distributions for the major parties are not mirror images of one another, and votes do not flow between parties in a uniform way across constituencies from one election to the next. Our paper provides useful insight into the transformation of votes to seats for different types of parties as their support waxes and wanes.