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2023 | OriginalPaper | Chapter

5. Properties of the Apportionment Methods Used in the Primaries

Authors : Michael A. Jones, David McCune, Jennifer M. Wilson

Published in: Delegate Apportionment in the US Presidential Primaries

Publisher: Springer International Publishing

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Abstract

The seven delegate apportionment methods used in the presidential primaries are analyzed and compared, according to whether they satisfy basic properties such as homogeneity and proportionality. We consider how often the delegate apportionment methods satisfy the quota condition and quantify their degree of bias for and against the strongest and weakest candidates by analyzing delegate bias, delegate thresholds, and the behavior of the methods in close elections. These ideas are then related to the sensitivity of the apportionment methods to small changes of the vote totals. We also determine which methods satisfy majority and leader criteria, and discuss the methods’ propensity to support candidate coalitions. We conclude by comparing overall vote share to seat share for the strongest candidates in recent state primaries.

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Footnotes
1
In the context of house seat apportionment, bias may also be a result of a method’s tendency to favor the smaller states at the expense of larger states. This kind of bias does not arise in delegate apportionment, although it is conceivable that a party may wish to favor weaker candidates at the beginning of the primary season, as discussed in Chap. 7.
 
2
The method itself was described too vaguely to categorize as one of the seven apportionment methods we study. The method is based on nearest integer rounding, but there is no indication how to adjust the apportionment if the rounding does not yield a legitimate apportionment.
 
Literature
go back to reference Balinski ML, Young HP (2001) Fair representation: meeting the ideal of one man, one vote, 2nd edn. Brookings Institution Press, Washington, DC Balinski ML, Young HP (2001) Fair representation: meeting the ideal of one man, one vote, 2nd edn. Brookings Institution Press, Washington, DC
go back to reference Jones MA, McCune D, Wilson J (2023) An iterative procedure for apportionment and its use in the Georgia Republican primary. Contemp Math, Amer Math Soc, Providence, RI (to appear) Jones MA, McCune D, Wilson J (2023) An iterative procedure for apportionment and its use in the Georgia Republican primary. Contemp Math, Amer Math Soc, Providence, RI (to appear)
go back to reference Pukelsheim F (2017) Proportional representation: apportionment methods and their applications. Springer, Cham, second edition. With a foreword by Andrew Duff Pukelsheim F (2017) Proportional representation: apportionment methods and their applications. Springer, Cham, second edition. With a foreword by Andrew Duff
go back to reference Rokkan S (1968) Elections: electoral systems. In: Sills DL (ed) International Encyclopedia of the Social Sciences. Crowell, Collier, Macmillan, New York, pp 6–21 Rokkan S (1968) Elections: electoral systems. In: Sills DL (ed) International Encyclopedia of the Social Sciences. Crowell, Collier, Macmillan, New York, pp 6–21
Metadata
Title
Properties of the Apportionment Methods Used in the Primaries
Authors
Michael A. Jones
David McCune
Jennifer M. Wilson
Copyright Year
2023
DOI
https://doi.org/10.1007/978-3-031-24954-9_5

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