Question

The following table shows how the average constituency changes for two regional governing boards, joshua and salinas, when a new representative is added to each board.
joshua's
average
constituency salinas's
average
constituency
joshua receives
new board
member 1232 1520
salinas receives
new board
member 1448 1333
(a) determine the relative unfairness of an apportionment that gives a new board member to joshua rather than to salinas. round to the nearest thousandth.


(b) determine the relative unfairness of an apportionment that gives a new board member to salinas rather than to joshua. round to the nearest thousandth.


(c) using the apportionment principle, determine which regional governing board should receive the new board member.
joshua
salinas

Answer 1

The relative unfairness of an apportionment that gives a new board member to joshua rather than to salinas will be

How to calculate the values?

The relative unfairness of an apportionment that gives a new board member to joshua rather than to salinas will be:

= (1520 - 1232)/1232

= 288/1232

= 0.234

The relative unfairness of an apportionment that gives a new board member to salinas rather than to Joshua will be:

= (1448 - 1333)/1333

= 115/1333

= 0.086

The regional governing board that should receive the new board member is Salinas.

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