Surface volumes of rounding polytopes

Linear Algebra and Its Applications

Volumn 378, Issue 1-3, 2004, Pages 71-91

  Drton, Mathias ^a   Schwingenschlögl, Udo ^b  

^a UNIVERSITY OF WASHINGTON   (United States)

^b UNIVERSITY OF AUGSBURG   (Germany)

Author keywords

Apportionment method; Probability simplex; Proportional representation; Rounding method; Rounding rule; Seat allocation; Seat bias

Indexed keywords

APPROXIMATION THEORY; INVARIANCE; MAPPING; PROBABILITY; SET THEORY; STATISTICAL METHODS; VECTORS;

APPORTIONMENT METHOD; ROUNDING POLYTOPES;

LINEAR ALGEBRA;

EID: 0347476975     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2003.09.005     Document Type: Article

References (20)

1. Athanasopoulos B.D. Probabilistic approach to the rounding problem with applications to fair representation. in: Approximation, Probability, and Related Fields (Santa Barbara, CA, 1993). 1994;75-99 Plenum, New York.
2. Athanasopoulos B.D. Probabilistic approaches to the rounding problem. Serdica. 20:1994;306-327.
3. Balinski M.L., Rachev S.T. Rounding proportions: rules of rounding. Numer. Funct. Anal. Optim. 14:1993;475-501.
4. Balinski M.L., Rachev S.T. Rounding proportions: methods of rounding. Math. Sci. 22:1997;1-26.
5. Balinski M.L., Young H.P. Fair Representation - Meeting the Ideal of One Man, One Vote. second ed. 2001;Brookings Institution Press, Washington, DC.
6. H. Bergold, Wie gerecht sind unsere Verhältniswahlen? Didaktik Math. 7 (1979) 266-278.
7. Bergold H. Mehr Chancen für Außenseiter. Didaktik Math. 18:1990;38-51.
8. Bühler W. Characterization of the extreme points of a class of special polyhedra. Z. Oper. Res. 19:1975;131-137.
9. Dorfleitner G., Klein T. Rounding with multiplier methods: an efficient algorithm and applications in statistics. Statist. Papers. 40:1999;143-157.
10. M. Drton, U. Schwingenschlögl, On methods for rounding probabilities and other fractions, Technical Report 450, Institut für Mathematik, Universitat Augsburg, 2003.
11. Edwards C.H. Jr. Advanced Calculus of Several Variables. 1994;Dover Publications, New York. (Corrected reprint of the 1973 original).
12. Happacher M. The discrepancy distribution of stationary multiplier rules for rounding probabilities. Metrika. 53:2001;171-181.
13. Kopfermann K. Mathematische Aspekte der Wahlverfahren - Mandatsverteilung bei Abstimmungen. 1991;Wissenschaftsverlag, Mannheim.
14. Marshall A.W., Olkin I., Pukelsheim F. A majorization comparison of apportionment methods in proportional representation. Social Choice and Welfare. 19:2002;885-900.
15. Pólya G. Sur la représentation proportionelle en matière électorale. L'Enseignement Math. 20:1918;355-379.
16. Pukelsheim F. Efficient rounding of sampling allocations. Statist. Probab. Lett. 35:1997;141-143.
17. Pukelsheim F., Rieder S. Efficient rounding of approximate designs. Biometrika. 79:1992;763-770.
18. Schuster K., Pukelsheim F., Drton M., Draper N.R. Seat-biases of apportionment methods for proportional representation. Electoral Studies. 22:2003;651-676.
19. Webster R. Convexity. 1994;Oxford University Press, Oxford.
20. Wode D. Über die Wahrscheinlichkeit absoluter Mehrheiten. Didaktik Math. 9:1981;104-110.