Rounding proportions: Rules of rounding

Svetlozar T. Rachev, Michel L. Balinski

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Failure to add to 1—to be “justified” to 1—occurs frequently in reported sets of rounded data. The probabilities for different rules of rounding vectors and tables to give “justified” results under varying assumptions concerning the probabilistic structure of the data are computed. This extends the pioneering work of Mosteller Youtz, and Zahn (1967) and Diaconis and Freedman (1979) wh< assessed the probability that conventionally rounded proportions add to 1. In particular, it is shown that other rules of rounding can improve upon the conventional rule.

Original languageEnglish
Pages (from-to)475-501
Number of pages27
JournalNumerical Functional Analysis and Optimization
Issue number5-6
StatePublished - Jan 1 1993


  • apportionment
  • rounding vectors rounding tables rounding proportionss probability metrics


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