If the population of state A is twice the population of state B, then the Hamilton-Hare apportionment method guarantees that A gets twice as many seats as state B.

Question

If the population of state A is twice the population of state B, then the Hamilton-Hare apportionment method guarantees that  A gets twice as many seats as state B.

BlackTom AI · Accepted Answer

The statement presents a claim about the Hamilton-Hare (largest remainder) apportionment method.
Option 1: True. Under Hamilton-Hare, seats are allocated based on quotas proportional to population, then floors are taken and remaining seats assigned by largest remainders. If state A's population is exactly twice that of state B (p_A = 2 p_B), then their quotas satisfy q_A = 2 q_B. However, simply having a ratio of quotas does not guarantee that the final seat count will maintain exactly a 2:1 ratio after floors and remainder distribution; the integer rounding can produce either exactly twice as many seats (in some cases) or more than twice as many seats for A depending on the fractional parts.
Option 2: False. In fact, the proportional relationship at the quota level does not guarantee a strict 2:1 seat ratio after applying the largest remainder procedure. If q_B = x (with fractional part), q_A = 2x. After flooring, you get a_A = floor(2x) and a_B = floor(x). The value floor(2x) can equal 2 floor(x) or 2 floor(x) + 1 if the fractional part of x induces an extra remainder favorable to A. Consequently, A may end up with exactly twice as many seats or more than twice, but not guaranteed to be exactly double in all cases.
Option 3: (Not applicable here due to there being only two options in a true/false question, but if considered, one would analyze edge cases where additional distributions could alter the ratio.)
Option 4: (Similarly, any extra distinctions would hinge on edge cases of fractional parts and total seats, but the core point remains that the guarantee does not hold uniformly.)
In summary, because the largest remainder method can allocate an extra seat to A based on remainders, the claim that A is guaranteed to receive exactly twice as many seats as B is incorrect.

VPM Spring 2025 Final B QB

If the population of state A is twice the population of state B, then the Hamilton-Hare apportionment method guarantees that A gets twice as many seats as state B.

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