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Apportionment in the US Presidential Primaries Read chapter Read first chapter

2023 | OriginalPaper | Chapter

6. Paradoxes

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

In this chapter, we catalog the paradoxes to which the seven delegate apportionment methods are susceptible. Because all of the methods used in the Democratic and Republican primaries are quota-based, they are susceptible to classical paradoxes like the Alabama and population paradoxes. The methods also suffer from other paradoxes that are more relevant in the context of delegate apportionment such as the elimination and aggregation paradoxes. We evaluate the extent to which each method is susceptible to each paradox. We use simulations, data from recent presidential primaries, and simplicial geometry to investigate the likelihood that each paradox occurs. For each paradox, we focus on which candidates are most likely to be affected and on the effect of thresholds.

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previous chapter Properties of the Apportionment Methods Used in the Primaries
next chapter Exploring Alternative Ways to Allocate Delegates
Footnotes
1
Included in the 21 instances is the at-large delegate apportionment in the 2020 Colorado primary. This elimination paradox did not occur in practice because some of the candidates, including Elizabeth Warren, withdrew from the primary, causing them to lose all of their delegates per the CO party rules. If no candidates had formally withdrawn, Warren would have lost an at-large delegate because of the elimination of the weaker candidates.
 
2
The 2020 Iowa Democratic caucuses also produced an elimination paradox: If the 9 at-large delegates were allocated without the 15% threshold, the apportionment would have been \((2,2,2,2,1,0,\dots , 0)\) and Biden would have received another delegate. Thus, this election demonstrates a number of apportionment anomalies; see (McCune 2023).
 
3
Recall that we obtain all of our primary data from thegreenpapers.com. This website contains almost complete district vote data for the candidates that surpass the 15% threshold. There are several states for which the data for candidates who do not surpass the threshold is unavailable; in these states, it is impossible to measure the effects of aggregation when we remove the threshold.
 
4
As discussed in Chap. 4, some of the state party rules were not completely clear. The rules indicated using NIE if there was an under allocation of delegates, but was unclear about how to handle an over allocation. In the example given, we avoid over allocations.
 
Literature
Balinski ML, Young HP (2001) Fair representation: meeting the ideal of one man, one vote, 2nd edn. Brookings Institution Press, Washington, DC
Dančišin V (2017) No-show paradox in Slovak party-list proportional system. Human Affairs 27(1):15–21 CrossRef
McCune D, McCune L, Nelson D (2019) The cutoff paradox in the Kansas presidential caucuses. UMAP J 40(1):21–45
Pukelsheim F (2017) Proportional representation: apportionment methods and their applications. Springer, Cham, second edition. (With a foreword by Andrew Duff)
Metadata
Title
Paradoxes
Authors
Michael A. Jones
David McCune
Jennifer M. Wilson
Copyright Year
2023
Book
Delegate Apportionment in the US Presidential Primaries

Print ISBN: 978-3-031-24953-2

Electronic ISBN: 978-3-031-24954-9

Copyright Year: 2023

DOI
https://doi.org/10.1007/978-3-031-24954-9_6

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