Statistical aspects of equitable apportionment

Bruce D. Spencer*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


Two problems that arise in apportioning the U.S. House of Representatives are: (a) fractional numbers of representatives cannot be allocated, so states receive different per capita representation, and (b) the state population sizes are known only with error. Both problems are addressed in a unified way with decision theory. Although the method currently in use, equal proportions, has poor properties when the populations are assumed perfectly known, it performs surprisingly well in the presence of modest errors in the data. The converse is true for the quota method. Previously developed qualitative notions of bias in apportionment methods are extended to provide a quantitative definition of bias. The new definition accounts both for bias in the apportionment method and for bias arising from imperfect population measurements. Illustrative estimates of the bias against states with large black populations are developed.

Original languageEnglish (US)
Pages (from-to)815-822
Number of pages8
JournalJournal of the American Statistical Association
Issue number392
StatePublished - Dec 1985


  • Allocations
  • Bias
  • Equal proportions
  • Equity
  • Loss functions
  • U.S. congress

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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