Volume
23
Issue
3
Abstract
This article investigates the interplay between apportionment functions and order-theoretic structures on population and allocation vectors. We define a class of functions, called apportionment maps, that respect population monotonicity, house monotonicity, and size monotonicity. A central focus is placed on the preservation or violation of majorization under these functions, with particular attention to the Jefferson method and related divisor schemes. By applying tools from convex analysis and the theory of Schur-convex functions, we characterize the extent to which fairness criteria are preserved under apportionment.
First Page
259
Last Page
268
Recommended Citation
Chang, Stanley
(2026)
"The Jefferson-D’Hondt method and majorization,"
The Mathematics Enthusiast: Vol. 23
:
No.
3
, Article 7.
DOI: https://doi.org/10.54870/1551-3440.1692
Available at:
https://scholarworks.umt.edu/tme/vol23/iss3/7
Digital Object Identifier (DOI)
10.54870/1551-3440.1692
Publisher
University of Montana, Maureen and Mike Mansfield Library
