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Proof of Equivalence of Webster's Method and Willcox's Method of Major Fractions

Pat Hunley

ABSTRACT

This note is a simpli cation and expansion of the proof of the equivalence of Webster's method and Willcox's method of major fractions found in Fair Rep- resentation: Meeting the Ideal of One Man, One Vote, by Michel Balinski and H. Peyton Young, p. 103-104. The proof in Fair Representation demonstrates that Webster's method minimizes a function, which Willcox's method of major fractions also happens to minimize; it doesn't directly refer to Willcox's method. In this paper I have modi ed the proof to explicitly show that the two methods are equivalent and to include details, such as unstated lines of reasoning and algebraic steps, omitted from the Fair Representation proof.

CITATION:

Pat Hunley. (2014). Proof of Equivalence of Webster's Method and Willcox's Method of Major Fractions. Center for Statistical Research & Methodology Research Report Series (Statistics #2014-04). U.S. Census Bureau. Available online at <http://www.census.gov/srd/papers/pdf/RRS2014-2014-04.pdf>.

Source: U.S. Census Bureau, Center for Statistical Research & Methodology

Published online: July 17, 2014
Last revised: July 17, 2014

 


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Source: U.S. Census Bureau | Research and Methodology Directorate | Center for Statistical Research & Methodology | (301) 763-3215 (or chad.eric.russell@census.gov) |   Last Revised: August 12, 2014