New quota-based apportionment methods: The allocation of delegates in the Republican Presidential Primary

• Published in: Mathematical social sciences 2020-11, Vol.108, p.122-137
• Main Authors: Jones, Michael A., McCune, David, Wilson, Jennifer M.
• Format: Article
• Language: English
• Subjects: Bias; Candidates; Delegate apportionment; Delegates; Elections; Geometry; Hamilton’s method; Polls & surveys; Presidential elections; Presidents; Primaries & caucuses; Quota methods; Republican primary
• ISSN: 0165-4896; 1879-3118
• DOI: 10.1016/j.mathsocsci.2020.05.001

We survey the apportionment methods used by the Republican Party in their 2012 and 2016 state presidential primaries, with a focus on the seven methods that are proportional. All of the proportional methods are quota-based, and all but one are new (or at least previously unstudied). After comparing the apportionment methods for three candidates using simplicial geometry, we evaluate how they differ in bias toward the top and bottom vote-getting candidates. We also compare the methods by how they distinguish among candidates in close elections. We use the bias comparisons to suggest which methods should be used at different junctures in the primary season. We discuss how these new methods were implemented in practice and summarize how successful these methods were in making the Republican delegate process more proportional. •We survey the 2012 & 2016 Republican presidential primary apportionment methods.•The geometry of the seven quota-based delegate apportionment methods is analyzed.•We classify the methods used by each state in the 2016 Republican primaries.•We compare the biases of the methods using close elections and thresholds.•Implementation of the methods, including the effect of cutoffs, is discussed.