Question

The legislature in a state has 59 seats. Apportion these seats to the five counties below using Jefferson's method. County Population Seats received

Adams 131,000

Grant 350,000

Colton 300,000

Davis 347,000

Hayes 236,000

Answer 1

The legislature in a state has 59 seats. Apportion these seats to the five counties below:

Country	Population	Quota	Initial	Final
Adams	131,000
Grant	350,000
Colton	300,000
Davis	347,000
Hayer	236,000
Total	1,364,000

Now Quota is computed using below formula

Country	Population	Quota	Initial	Final
Adams	131,000	5.666
Grant	350,000	15.139
Colton	300,000	12.976
Davis	347,000	15.009
Hayer	236,000	10.208
Total	1,364,000

Now the initial value is taken by truncating the decimal value of quota

Country	Population	Quota	Initial	Final
Adams	131,000	5.666	5
Grant	350,000	15.139	15
Colton	300,000	12.976	12
Davis	347,000	15.009	15
Hayer	236,000	10.208	10
Total	1,364,000		57

The total initial value is 57, whereas the legislature has 59 seats

Hence we compute quota using modified divisor which is near to standard divisor ( truncating decimal values of standard divisor i.e 23000)

Country	Population	Quota	Initial	Final
Adams	131,000	5.695	5
Grant	350,000	15.217	15
Colton	300,000	13.043	13
Davis	347,000	15.086	15
Hayer	236,000	10.26	10
Total	1,364,000		58

Yet we get total initial values as 58 whereas we should get 59. Repeat the above procedure by decreasing the value of modified divisor(21870)

Country	Population	Quota	Initial	Final
Adams	131,000	5.989	5	5
Grant	350,000	16.003	16	16
Colton	300,000	13.717	13	13
Davis	347,000	15.866	15	15
Hayer	236,000	10.791	10	10
Total	1,364,000		59	59

Hence the apportion of 59 seats are done using Jefferson's method.