Exercise #1
Hamilton y n n
Lowndes y n n
Jefferson n y y
Webster n y y
Hill-Huntington n y y
Exercise #2
The authors suggest that the 'quota method' of Balinski and Young cited on page
119 satisfies both.
Exercise #3
None exists, since no divisor method satisfies the quota property, and only
divisor methods ('generalized divisor methods', according to the text on page
119) satisfy the population property.
Exercise #4
On page 119 the authors assert that Webster's method satisfies both.
Exercise #5
Jefferson's Method
(State pop natquota initial )
(A 14978 14.9603 14 )
(B 12991 12.9757 12 )
(C 9260 9.24909 9 )
(D 5453 5.44657 5 )
(E 4624 4.61855 4 )
(F 2753 2.74976 2 )
(Total 50059 (1001.180) 46 )
Jefferson Quota property fails:
natural divisor: 1001.1800
threshold divisor: between 924.8000 and 999.3077
(State threshhold final )
(A 998.533 16 )
(B 999.308 14 )
(C 926 9 )
(D 908.833 5 )
(E 924.800 4 )
(F 917.667 2 )
(Total (927.128) 50 )
Exercise #7
"Hamilton's Method"
(State pop natquota initial )
(A 1676 7.38868 7 )
(B 1454 6.40999 6 )
(C 921 4.06025 4 )
(D 778 3.42983 3 )
(E 615 2.71124 2 )
(Total 5444 (226.833) 22 )
(State frac final )
(A 0.388685 7 )
(B 0.409993 6 )
(C 6.024982E-2 4 )
(D 0.429831 4 )
(E 0.711242 3 )
(Total 24 )
"Hamilton's Method"
(State pop natquota initial )
(A 1676 7.69655 7 )
(B 1454 6.67708 6 )
(C 921 4.22943 4 )
(D 778 3.57274 3 )
(E 615 2.82421 2 )
(Total 5444 (217.760) 22 )
(State frac final )
(A 0.696547 8 )
(B 0.677076 7 )
(C 0.229427 4 )
(D 0.572741 3 )
(E 0.824210 3 )
(Total 25 )
Exercise #9
"Lowndes's Method"
(State pop natquota initial )
(A 11167 10.9803 10 )
(B 7536 7.41003 7 )
(C 3356 3.29990 3 )
(D 1332 1.30973 1 )
(Total 23391 (1017.000) 21 )
(State relfrac final )
(A 9.803343E-2 10 )
(B 5.857564E-2 7 )
(C 9.996722E-2 4 )
(D 0.309735 2 )
(Total 23 )
"Lowndes's Method"
(State pop natquota initial )
(A 11160 11.0372 11 )
(B 7536 7.45304 7 )
(C 3360 3.32301 3 )
(D 1200 1.18679 1 )
(Total 23256 (1011.130) 22 )
(State relfrac final )
(A 3.377428E-3 11 )
(B 6.472063E-2 7 )
(C 0.107671 3 )
(D 0.186791 2 )
(Total 23 )
Review Exercises:
Exercise #3
"Hamilton's Method"
(State pop natquota initial )
(Canyon Hills 1050 55.7983 55 )
(Magnolia 924 49.1025 49 )
(Ramona 917 48.7305 48 )
(Townsend 841 44.6918 44 )
(Woodcrest 502 26.6769 26 )
(Total 4234 (18.818) 222 )
(State frac final )
(Canyon Hills 0.798299 56 )
(Magnolia 0.102504 49 )
(Ramona 0.730515 49 )
(Townsend 0.691781 45 )
(Woodcrest 0.676901 26 )
(Total 225 )
"Lowndes's Method"
(State pop natquota initial )
(Canyon Hills 1050 55.7983 55 )
(Magnolia 924 49.1025 49 )
(Ramona 917 48.7305 48 )
(Townsend 841 44.6918 44 )
(Woodcrest 502 26.6769 26 )
(Total 4234 (18.818) 222 )
(State relfrac final )
(Canyon Hills 1.451454E-2 55 )
(Magnolia 2.091909E-3 49 )
(Ramona 1.521906E-2 49 )
(Townsend 1.572229E-2 45 )
(Woodcrest 2.603466E-2 27 )
(Total 225 )
Jefferson's Method
(State pop natquota initial )
(Canyon Hills 1050 55.7983 55 )
(Magnolia 924 49.1025 49 )
(Ramona 917 48.7305 48 )
(Townsend 841 44.6918 44 )
(Woodcrest 502 26.6769 26 )
(Total 4234 (18.818) 222 )
(State threshhold final )
(Canyon Hills 18.7500 56 )
(Magnolia 18.4800 49 )
(Ramona 18.7143 49 )
(Townsend 18.6889 45 )
(Woodcrest 18.5926 26 )
(Total (18.689) 225 )
Webster's Method
(State pop natquota initial )
(Canyon Hills 1050 55.7983 56 )
(Magnolia 924 49.1025 49 )
(Ramona 917 48.7305 49 )
(Townsend 841 44.6918 45 )
(Woodcrest 502 26.6769 27 )
(Total 4234 (18.818) 226 )
(State threshhold final )
(Canyon Hills 18.9189 56 )
(Magnolia 19.0515 49 )
(Ramona 18.9072 49 )
(Townsend 18.8989 44 )
(Woodcrest 18.9434 27 )
(Total (18.899) 225 )
Hill-Huntington's Method
(State pop natquota initial )
(Canyon Hills 1050 55.7983 56 )
(Magnolia 924 49.1025 49 )
(Ramona 917 48.7305 49 )
(Townsend 841 44.6918 45 )
(Woodcrest 502 26.6769 27 )
(Total 4234 (18.818) 226 )
(State threshhold final )
(Canyon Hills 18.9197 56 )
(Magnolia 19.0526 49 )
(Ramona 18.9082 49 )
(Townsend 18.9001 44 )
(Woodcrest 18.9468 27 )
(Total (18.900) 225 )
Exercise #4
"Hamilton's Method"
(State pop natquota initial )
(Dole 42 7.56000 7 )
(Forbes 20 3.60000 3 )
(Buchanan 18 3.24000 3 )
(Gramm 10 1.80000 1 )
(Alexander 6 1.08000 1 )
(Keyes 3 0.540000 0 )
(Lugar 1 0.180000 0 )
(Total 100 (5.556) 15 )
(State frac final )
(Dole 0.560000 8 )
(Forbes 0.600000 4 )
(Buchanan 0.240000 3 )
(Gramm 0.800000 2 )
(Alexander 8.000000E-2 1 )
(Keyes 0.540000 0 )
(Lugar 0.180000 0 )
(Total 18 )
"Lowndes's Method"
(State pop natquota initial )
(Dole 42 7.56000 7 )
(Forbes 20 3.60000 3 )
(Buchanan 18 3.24000 3 )
(Gramm 10 1.80000 1 )
(Alexander 6 1.08000 1 )
(Keyes 3 0.540000 0 )
(Lugar 1 0.180000 0 )
(Total 100 (5.556) 15 )
(State relfrac final )
(Dole 8.000000E-2 7 )
(Forbes 0.200000 3 )
(Buchanan 8.000000E-2 3 )
(Gramm 0.800000 2 )
(Alexander 8.000000E-2 1 )
(Keyes undefined 1 )
(Lugar undefined 1 )
(Total 18 )
Jefferson's Method
(State pop natquota initial )
(Dole 42 7.56000 7 )
(Forbes 20 3.60000 3 )
(Buchanan 18 3.24000 3 )
(Gramm 10 1.80000 1 )
(Alexander 6 1.08000 1 )
(Keyes 3 0.540000 0 )
(Lugar 1 0.180000 0 )
(Total 100 (5.556) 15 )
(State threshhold final )
(Dole 5.25000 8 )
(Forbes 5 4 )
(Buchanan 4.50000 3 )
(Gramm 5 2 )
(Alexander 3 1 )
(Keyes 3 0 )
(Lugar 1 0 )
(Total (5.000) 18 )
Webster's Method
(State pop natquota initial )
(Dole 42 7.56000 8 )
(Forbes 20 3.60000 4 )
(Buchanan 18 3.24000 3 )
(Gramm 10 1.80000 2 )
(Alexander 6 1.08000 1 )
(Keyes 3 0.540000 1 )
(Lugar 1 0.180000 0 )
(Total 100 (5.556) 19 )
(State threshhold final )
(Dole 5.60000 7 )
(Forbes 5.71429 4 )
(Buchanan 7.20000 3 )
(Gramm 6.66667 2 )
(Alexander 12.0000 1 )
(Keyes 6.00000 1 )
(Lugar 1.000000E+31 0 )
(Total (5.600) 18 )
Hill-Huntington's Method
(State pop natquota initial )
(Dole 42 7.56000 8 )
(Forbes 20 3.60000 4 )
(Buchanan 18 3.24000 3 )
(Gramm 10 1.80000 2 )
(Alexander 6 1.08000 1 )
(Keyes 3 0.540000 1 )
(Lugar 1 0.180000 1 )
(Total 100 (5.556) 20 )
(State threshhold final )
(Dole 5.61249 7 )
(Forbes 5.77351 3 )
(Buchanan 7.34848 3 )
(Gramm 7.07107 2 )
(Alexander 1.000000E+31 1 )
(Keyes 1.000000E+31 1 )
(Lugar 1.000000E+31 1 )
(Total (5.774) 18 )