Social Choice_Lecture 10_Apportionment

2 now allocate the remaining seats according to the

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Unformatted text preview: locate seats accordingly. 2 Now allocate the remaining seats according to the size of the fractional part of the quota (largest to smallest). Van Essen (U of A) Apportionment 5 / 15 Hamilton’ Method s Example Suppose we had the following country with three states and were interested in apportioning 15 seats among them using Hamilton’ method. s Mattville Vanessenberg New Colorado Population 101 200 300 Ideal Quota 2. 520 8 4. 991 7 7. 487 5 Step 1: allocate 2 seats to Mattville; 4 seats to Vanessenberg; and 7 seats to New Colorado. This allocates 13 of the 15 seats. Step 2: Give a seat to Vanessenberg, then give the last seat to Mattville. Van Essen (U of A) Apportionment 6 / 15 Divisor Methods: Je¤erson’ Method s Hamilton’ method was approved by Congress and sent to President s George Washington where it was vetoed.2 Hamilton’ method was immediately met with a counter proposal by s political rival Thomas Je¤erson. It is an example of a “divisor method” of apportionment. 1 2 3 Pick a whole number d (called a divisor) as the desired size of the congressional district. Allocate each state one seat for each congressional district – i.e., divide the state’ population by d , and then round down to the s nearest whole number to get the state’ allocation. s If the number of seats allocated is exactly the House size, you’ re done. If the number of seats allocated is less than the House size, go back to step 1 and repeat the process with a smaller choice of d . If the number of seats allocated is greater than the House size, go back to step 1 and repeat the process with a larger choice of d . 2 This bill was, in fact, the …rst bill in US history to be vetoed. Van Essen (U of A) Apportionment 7 / 15 Je¤erson’ Method s Example Suppose we had the following country with three states and were interested in apportioning 15 seats among them using Je¤erson’ method. s Mattville Vanessenberg N...
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