Question

The legislature in a state has 34 seats. Apportion these seats to the six counties below using Jefferson's method. County Population Seats Received Adams 480,000 Grant 296,000 Colton 130,000 Davis 298,000 Hayes 164,000 McKinley 326,000 Get help: Video

Answer 1

Total population is $1694000$ and standard divisor is $\text{SD}=\frac{1694000}{34}\approx 49823.53$

Picking a slightly smaller divisor, we take $d=49800$

Corresponding divisors for each are:

$\text{Adams}=\frac{480000 }{49800 }\approx 9.64=9$ (after rounding down)

Similarly for the others, we get $\text{Grant}:5,\text{Colton}:2,\text{Davis}:5,\text{Hayes}:3,\text{Mckinley}:6$

Total seats allotted is $9+5+2+3+5+6=30$

We have a remainder that's pretty large, so we pick a modified (lower) divisor say $d=45000$

For which we get

${\color{Red} \text{Adam}:10,\text{Grant}:6,\text{Colton}:2,\text{Davis}:6,\text{Hayes}:3,\text{Mckinley}:7}$ as the final allocation

$\blacksquare$

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