## Apportionment: References |

Abeles, F., C.L. Dodgson and apportionment for proportional representation, Bull. Ind. Soc. History of Math., 3 (1981) 71-82.

Anderson, M. and S. Fienberg, Who Counts? The Politics of Census-Taking in Contemporary America, Russell Sage Foundation, New York, 2001.

Baily, W., Proportional Representation in Large Constituencies, Ridgeway, London, 1872.

Balinski, M., The problem with apportionment, J. OR Society of Japan, 36 (1993) 134-148.

Balinski, M. and S. Rachev, Rounding proportions: rules of rounding, Numerical Functional Analysis and Optimization 14 (1993) 475-501.

Balinski, M. and S. Rachev, Rounding proportions: methods of rounding, The Mathematical Scientist 22 (1997) 1-26.

Balinski, M. and V. Ramirez, Parametric methods of apportionment, rounding and production, Mathematical Social Sciences 37 (1999) 107-122.

Balinski, M. and V. Ramirez, Mexico's 1997 apportionment defies its electoral law, Electoral Studies 18 (1999 117-124.

Balinski, M. and H. Young, A new method for congressional apportionment, Proc. Nat. Acad. Sci., 71 (1974) 4602-4606.

Balinski, M. and H. Young, The quota method of apportionment, Amer. Math. Monthly 82 (1975) 701-730.

Balinski, M. and H. Young, The Jefferson method of apportionment, SIAM Review 20 (1978) 278-284.

Balinski, M. and H. Young, On Huntington methods for apportionment, SIAM J. Applied Math. 33 (1977) 607-618.

Balinski, M. and Young, Apportionment schemes and the quota method, Amer. Math. Monthly 84 (1977) 450-455.

Balinski, M. and H. Young, Stability, coalitions, and schisms in proportional representation schemes, Amer. Pol. Science Rev. 72 (1978) 848-858.

Balinski, M. and H. Young, Criteria for proportional representation, Operations Research 27 (1979) 80-95.

Balinski, M. and H. Young, Quotatone apportionment methods, Math. of Operations Research, 4 (1979) 31-38.

Balinski, M. and H. Young, The Webster method of apportionment, Proc. Nat. Acad. Sci., 77 (1980) 1-4.

Balinski, M. and H. Young, Apportioning the United States House of Representatives, Interfaces 13 (1983) 35-43.

Balinski, M. and H. Young, Apportionment, in Operations Research and the Public Sector, S. Pollack, M. Rothkopf, and A. Barnett, (eds.), Handbooks in Operations Research and Management Science, Volume 6, North-Holland, Amsterdam, p. 529-556.

Balinski, M. and H. Young, Fair Representation, Yale University Press, New Haven, 1982, (2nd. ed.), Brookings Institution, 2001.

Balinski, M. and H. Young, The Apportionment of Representation, in Fair Allocation, H. Young, (ed.), Proceedings of Symposia in Applied Mathematics, Volume 33, American Mathematical Society, Providence, 1985.

Bennett, S., et al, The Apportionment Problem, COMAP (Consortium for Mathematics and its Applications), Lexington, 1986.

Birkhoff, G., House monotone apportionment schemes, Proc. Nat. Acad. Sciences, 73 (1976) 684-686.

Bliss, G., and E. Brown, L. Eisenhart, R. Pearl, Report to the President of the National Academy of Sciences, Feb. 9, 1929, in Congressional Record, 70th Congress, 2nd session, 70 (March 2, 1929) 4966-67.

d'Hondt, V., La Répresentation Proportionnelles des Partis par un Electeur, Ghent, 1878.

Dixon, R., Democratic Representation: Reapportionment in Law and Politics, Oxford U. Press, London, 1968.

Dodgson, C., The Principles of Parliamentary Representation, Harrison and Sons, London, 1884 (Supplement, 1885, Postscript to Supplement, 1885.)

Droop, H., On Methods of Electing Representatives, Macmillan, London, 1868.

Eisner, M.,, Methods of Congressional Apportionment, UMAP Module 620, COMAP (Consortium for Mathematics and its Applications), Lexington.

Ernst, L, Apportionment methods for the House of Representatives and the court challenges, Management Science 40 (1994) 1207-1227.

Halacy, D., Census: 190 Years of Counting America, Elsevier, New York, 1980.

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Hart, J., Proportional representation: Critics of the British electoral system 1820-1945, Oxford U. Press, Oxford, 1992.

Hoag, C. and G. Hallett, Proportional Representation, Macmillan, New York, 1926.

Humphreys, J., Proportional Representation,, Methuen, London, 1911.

Huntington, E., The mathematical theory of the apportionment of representatives, Proc. of the National Academy of Sciences, 7 (1921) 123-127.

Huntington. E., A new method of apportionment of representatives, Quart. Publ. Amer. Stat. Assoc, 17 (1921) 859-1970.

Huntington, E., The apportionment of representatives in Congress, Transactions of the American Mathematical Society 30 (1928) 85-110.

Huntington, E., Discussion: The Report of the National Academy of Sciences on Reapportionment, Science, May 3, 1929, pp. 471-473.

Huntington, E., The Role of Mathematics in Congressional Apportionment, Sociometry 4 (1941) 278-282.

Lucas, W., The Apportionment Problem, in Political and Related Models, Springer-Verlag.

Mayberry, J. Quota methods for congressional apportionment are still non-unique, Proc. Nat. Acad. Sci. 74 (1978) 3537-3539.

Morse, M. and J. Von Neumann, L. Eisenhart, Report to the President of the National Academy of Sciences, May 28, 1948, Princeton, N.J.

Owens, F., On the apportionment of representatives, Quart. Publ. of Amer. Stat. Assoc. 17 (1921) 958-968.

Oyama, T., On a parametric divisor method for the apportionment problem, J. Operations Research of Japan 34 (1991) 187-221.

Oyama, T. and T. Ichimori, On the unbiasedness of the parametric divisor method for the apportionment problem, J. Operations Research of Japan 38 (1995) 301-325.

Poston, The U.S. Census and Congressional Apportionment, __Society__, (1997), 34(3): 36-44

Rae, D., The Political Consequences of Electoral Law, Rev. Ed., Yale University Press, New Haven, 1971.

Saari, D., Apportionment methods and the House of Representatives, Amer. Math. Monthly,, 85 (1978) 792-802.

Saari, D., The Geometry of Voting, Springer-Verlag, New York, 1994.

Stevens, J., Opinion in United States Department of Commerce v. Montana, 112 Supreme Court 1415, 1992.

Stiill, J. A class of new methods for congressional apportionment, SIAM J. Applied Math. 37 (1979) 401-418.

Willcox, W., The apportionment of representatives, Amer. Econ. Rev. 6 (1916) 3-16

Young, H., Equity, Princeton U. Press, Princeton, 1994.

Apportionment I Apportionment II