Question 14.79

49. The Legis County Board of Supervisors (see Exercise 48) has too many seats for its space in the County Administration building. It has decided to use the Jefferson method of apportionment, with 3000 as divisor.

  1. Calculate the apportionment and find the new house size.
  2. Why would Epsilon Township have a problem with this?
  3. Find the quota for each township based on the house size you determined in part (a).
  4. Would this apportionment satisfy the quota condition?

49.

(a) Divide each township’s population by 3000 and round the quotient down to get the apportionment.

Township Population Seats Quota
Alpha 16,210 5 5.062
Beta 40,052 13 12.508
Gamma 8,284 2 2.587
Delta 48,018 16 14.996
Epsilon 2,711 0 0.847

The house size is the total number of seats apportioned: 36.

(b) Epsilon Township is unrepresented on the Board, but if a divisor less than 2711 had been chosen, it would have a seat.

(c) The standard divisor is the county’s population, 115,275, divided by the house size, 36. This is . The quotas, obtained by dividing the populations by the standard divisor, are shown in the table displayed in the answer for part (a).

(d) No. The upper quota for Delta Township is 15 seats, but it is awarded 16 seats.