From Reals to Integers: Rounding Functions and Rounding Rules

Friedrich Pukelsheim
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Friedrich Pukelsheim: Universität Augsburg, Institut für Mathematik

Chapter Chapter 3 in Proportional Representation, 2017, pp 59-70 from Springer

Abstract: Abstract A rounding function maps non-negative quantities into integers. Examples are the floor function, the ceiling function, the commercial rounding function, and the even-number rounding function. A rounding rule maps non-negative quantities more lavishly into subsets of integers. Every rounding function or rounding rule induces a sequence of jumppoints, called signposts, where they advance from one integer to the next. Rounding rules map a signpost into the two-element set consisting of its neighboring integers, while non-signposts are mapped to singletons. Prominent examples are the rules of downward rounding, of standard rounding, and of upward rounding. The one-parameter families of stationary signposts and of power-mean signposts are of particular interest.

Keywords: Rounding Rules; Round Function; Round Downwards; Standard Rounding; Upward Rounding (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/978-3-319-64707-4_3

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