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Unformatted text preview: ew Colorado Population
300 Ideal Quota
2. 520 8
4. 991 7
7. 487 5 Set d=35; Step 2: 101 = 2. 885 7, 200 = 5. 714 3, 300 = 8. 571 4. So 2
seats to Mattville, 5 seats to Vanessenberg, and 8 seats to New Colorado. Van Essen (U of A) Apportionment 8 / 15 Divisor Methods: Adam’ Method
Politically, Je¤erson’ method won out and was used to apportion the
House of Representatives for more than 50 years.
However, by rounding down, Je¤erson’ method systematically favors
larger states. Example
A reduction from 49.9 to 49 leaves a state only 2% short of their ideal
quota whereas a reduction from 4.9 to 4 leaves a state 20% short.
John Quincy Adams (from Mass.) noticed the problem and proposed
altering Je¤erson’ method. His method is identical to Je¤erson’ in
every way except, instead of rounding down, he rounds up to the
nearest whole number.
Adam’ method favor’ small states.
Van Essen (U of A) Apportionment 9 / 15 Divisor Methods: Daniel Webster’ Method of
Apportionment Proceed exactly like Je¤erson’ method but, where Je¤erson rounds
down and Adam rounds up, simply round to the nearest integer as
one would normally do.
Webster’ method was used for 10 years where it was replaced by the
rediscovered Hamilton method. Van Essen (U of A) Apportionment 10 / 15 Properties
What properties would we like in an apportionment method? De…nition (Monotonicity Property)
A method of apportionment satis…es the monotonicity property if no state
receives fewer states than a state with less (or the same) population. De…nition (Quota Property)
A method of apportionment satis…es the quota property if the number of
seats allocated to a state never di¤ers from its ideal quota by more than 1. De…nition (Population Property)
A method of apportionment satis…es the population property if, following
a census, no state should gain in population and lose a seat while some
other state loses population and gains a state.
Van Essen (U of A) Apporti...
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- Spring '12