Alabama paradox: Difference between revisions
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{{Wikipedia|Apportionment paradox#Alabama paradox}} |
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{{merge|House monotonicity criterion}} |
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| ⚫ | The '''Alabama Paradox''' refers to the pathological scenario of the [[Hamilton method]] in which an increase in the total number of seats in the legislature would cause an electoral district or political party to lose a seat. It is an example of [[House monotonicity criterion|House monotonicity]] failure and can be understood through the [[Balinski–Young theorem]]. |
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For example: |
For example: |
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! Party !! Votes |
! Party !! Votes |
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With 323 seats, the Hamilton method gives: |
With 323 seats, the Hamilton method gives: |
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! Party !! Quotas !! Seats |
! Party !! Quotas !! Seats |
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But with 324 seats: |
But with 324 seats: |
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! Party !! Quotas !! Seats |
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The Alabama Paradox is named after the 1880 observation by U.S. census clerk C.W. Seaton that the state of Alabama would lose one of its 8 seats in the House of Representatives if the size of the House were increased from 299 to 300. |
The Alabama Paradox is named after the 1880 observation by U.S. census clerk C.W. Seaton that the state of Alabama would lose one of its 8 seats in the House of Representatives if the size of the House were increased from 299 to 300. |
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[[Category:Election scenarios]] |
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Latest revision as of 20:56, 22 March 2020
 | It has been suggested that this article be merged with House monotonicity criterion. (Discuss) |
The Alabama Paradox refers to the pathological scenario of the Hamilton method in which an increase in the total number of seats in the legislature would cause an electoral district or political party to lose a seat. It is an example of House monotonicity failure and can be understood through the Balinski–Young theorem.
For example:
| Party | Votes |
|---|---|
| A | 56.7% |
| B | 38.5% |
| C | 4.2% |
| D | 0.6% |
With 323 seats, the Hamilton method gives:
| Party | Quotas | Seats |
|---|---|---|
| A | 183.141 | 183 |
| B | 124.355 | 124 |
| C | 13.566 | 14 |
| D | 1.938 | 2 |
But with 324 seats:
| Party | Quotas | Seats |
|---|---|---|
| A | 183.708 | 184 |
| B | 124.740 | 125 |
| C | 13.608 | 13 |
| D | 1.944 | 2 |
The Alabama Paradox is named after the 1880 observation by U.S. census clerk C.W. Seaton that the state of Alabama would lose one of its 8 seats in the House of Representatives if the size of the House were increased from 299 to 300.