The following questions review the main ideas of this chapter. Write your answers to the questions and then refer to the pages listed by number to make certain that you have mastered these ideas.
What are the implications of Balinski and Young’s Impossibility Theorem? pg. 329
Reference:
As can be seen from Table 5.45, all four methods of apportionment either violate the quota rule or give rise to one of the paradoxes discussed in this section. Unfortunately, as mathematicians Michel L. Balinski and H. Peyton Young proved (Balinski and Young’s impossibility theorem), there is no apportionment method that satisfies the quota rule and always avoids the Alabama, population, and new-states paradoxes. You may choose or design an apportionment method that obeys the quota rule, but it will be susceptible to at least one of the three paradoxes. You may choose or design an apportionment method that avoids the paradoxes, but then it will violate the quota rule. In other words, there is no perfect apportionment method. The choice of an apportionment method is ultimately a political decision. It is a disappointing realization that the democratic ideal of “one person– one vote” can never be perfectly achieved, although we can come close.
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