The Theory of Apportionment and Just-In-Time Sequences
The apportionment problem and theory have their roots in the proportional representation system intended for the House of Representatives of the United States where each state receives seats in the House proportionally to its population. This chapter reviews these results of the apportionment theory that are most relevant to the topic of just-in-time optimization. It follows the excellent expositions of the basics of the theory presented in the books by Balinski and Young , and Young . However, the chapter also includes new results obtained since these publications — especially in the context of the theory's new applications presented in this book.
The apportionment theory has been developed to address the problem of fair representation or “meeting the ideal of one man, one vote” as Balinski and Young put it in the title of their book. This ideal is clearly a fundamental one yet, as one feels, unattainable, and thus the apportionment problem is not just a problem in mathematics.
KeywordsParametric Method Impossibility Theorem Divisor Function House Size Population Monotone
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