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Social Choice_Lecture 10_Apportionment

# Social Choice_Lecture 10_Apportionment - The Problem of...

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The Problem of Apportionment 1 Matt Van Essen University of Alabama 1 These slides are based on chapter 5 of Taylor and Pacelli (2008) and Chapters 9 and 10 of Szpiro (2010). Van Essen (U of A) Apportionment 1 / 15

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The Problem of Apportionment The US House of Representatives has, at any given time, a °xed size. The current size is 435. Article 1, Section 2 of the Constitution speci°es that these seats should be apportioned among the states ±according to their respective numbers.² In other words, a state with 10% of the population should receive 10% of the seats. Problem: 10% of 435 is 43.5 which is not an integer. How do we give away 0.5 of a seat? Van Essen (U of A) Apportionment 2 / 15
The Problem of Apportionment The number 43.5 is a state³s ideal quota . This is the number of seats a state would get if fractional seats were possible. It is found be multiplying the size of the house by the percentage of the US population found it the state. The ±apportionment problem² refers to the search for a method to replace ideal quotas with whole numbers in a way that is as fair and equitable as possible. Van Essen (U of A) Apportionment 3 / 15

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The Founding Fathers The Problem of Apportionment was very quickly recognized. The following ±Founding Fathers² all proposed ways of dealing with the problem Alexander Hamilton Thomas Je/erson John Quincy Adams Daniel Webster In this lecture we will look at these early proposals, discuss some problems, discuss what properties ±good² apportionment methods should have, and °nally get a glimpse of the fact that no apportionment system will be perfect. Van Essen (U of A) Apportionment 4 / 15
Hamilton³s Method Alexander Hamilton, the Secretary of the Treasury, proposed a method following the °rst US census in 1790.

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