Question 14.75
45. John Quincy Adams, the sixth president of the United States, proposed that the House of Representatives should be apportioned by a divisor method based on the rounding rule that rounds each fraction up to the next whole number.
- Is it likely that the initial tentative apportionment will be final?
- Will the divisor that produces the correct apportionment be greater than or less than the standard divisor?
- Does the method favor small states or large states?
- Can the Adams method apportion any state zero seats?
- The Adams method can violate the quota condition. Explain why it can never apportion to a state more than its upper quota.
45.
(a) No
(b) The divisor will have to be greater than the standard divisor.
(c) It favors small states.
(d) No, because an apportionment quotient between 0 and 1 must be rounded up to get .
(e) The Adams method always uses a divisor that is greater than the standard divisor. Therefore the apportionment quotients are less than the quotas that are obtained by dividing populations by the standard divisor. In other words, if is the quota for some state, and is the apportionment quotient for the same state, then . It follows that . But is the Adams apportionment and is the upper quota; hence the Adams method cannot exceed the upper quota for any state.