I have neglected to publish a link that has been available since December–the article announcing the datasets used in Votes from Seats (national and district) was published in Research & Politics (open access).
Cory L. Struthers, Yuhui Li, Matthew S. Shugart, “Introducing new multilevel datasets: Party systems at the district and national levels” (December 20, 2018). https://doi.org/10.1177/2053168018813508
For decades, datasets on national-level elections have contributed to knowledge on what shapes national party systems. More recently, datasets on elections at the district level have advanced research on subnational party competition. Yet, to our knowledge, no publicly accessible dataset with observations of the party system at both national and district levels exists, limiting the ease with which cross-level comparisons can be made. To fill this gap, we release two corresponding datasets, the National Level Party Systems dataset and the District Level Party Systems dataset, where the unit of analysis is the party system within either the national or district jurisdiction. More than 50 elections in the two datasets are overlapping, meaning they include observations for a single election at both the district and national levels. In addition to conventional measures such as the effective number of parties, we also include underutilized variables, such as the size of the largest party, list type, and the vote shares for presidential candidates in corresponding elections.
The datasets themselves can be accessed directly at Dataverse.