Social Choice_Lecture 10_Apportionment

520 8 4 991 7 7 487 5 set d35 step 2 101 2 885 7 200

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Unformatted text preview: ew Colorado Population 101 200 300 Ideal Quota 2. 520 8 4. 991 7 7. 487 5 Set d=35; Step 2: 101 = 2. 885 7, 200 = 5. 714 3, 300 = 8. 571 4. So 2 35 35 35 seats to Mattville, 5 seats to Vanessenberg, and 8 seats to New Colorado. Van Essen (U of A) Apportionment 8 / 15 Divisor Methods: Adam’ Method s Politically, Je¤erson’ method won out and was used to apportion the s House of Representatives for more than 50 years. However, by rounding down, Je¤erson’ method systematically favors s larger states. Example A reduction from 49.9 to 49 leaves a state only 2% short of their ideal quota whereas a reduction from 4.9 to 4 leaves a state 20% short. John Quincy Adams (from Mass.) noticed the problem and proposed altering Je¤erson’ method. His method is identical to Je¤erson’ in s s every way except, instead of rounding down, he rounds up to the nearest whole number. Adam’ method favor’ small states. s s Van Essen (U of A) Apportionment 9 / 15 Divisor Methods: Daniel Webster’ Method of s Apportionment Proceed exactly like Je¤erson’ method but, where Je¤erson rounds s down and Adam rounds up, simply round to the nearest integer as one would normally do. Webster’ method was used for 10 years where it was replaced by the s rediscovered Hamilton method. Van Essen (U of A) Apportionment 10 / 15 Properties What properties would we like in an apportionment method? De…nition (Monotonicity Property) A method of apportionment satis…es the monotonicity property if no state receives fewer states than a state with less (or the same) population. De…nition (Quota Property) A method of apportionment satis…es the quota property if the number of seats allocated to a state never di¤ers from its ideal quota by more than 1. De…nition (Population Property) A method of apportionment satis…es the population property if, following a census, no state should gain in population and lose a seat while some other state loses population and gains a state. Van Essen (U of A) Apporti...
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