Balinski–Young theorem: Difference between revisions
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The division of seats in an election is a prominent cultural concern. In 1876, the United States [[W:1876 United States presidential election|presidential election]] turned on the method by which the remaining fraction was calculated. Rutherford Hayes received 185 electoral college votes, and Samuel Tilden received 184. Tilden won the popular vote. With a different rounding method the final electoral college tally would have reversed. However, many mathematically analogous situations arise in which quantities are to be divided into discrete equal chunks. The Balinski–Young theorem applies in these situations: it indicates that although very reasonable approximations can be made, there is no mathematically rigorous way in which to reconcile the small remaining fraction while complying with all the competing fairness elements. |
The division of seats in an election is a prominent cultural concern. In 1876, the United States [[W:1876 United States presidential election|presidential election]] turned on the method by which the remaining fraction was calculated. Rutherford Hayes received 185 electoral college votes, and Samuel Tilden received 184. Tilden won the popular vote. With a different rounding method the final electoral college tally would have reversed. However, many mathematically analogous situations arise in which quantities are to be divided into discrete equal chunks. The Balinski–Young theorem applies in these situations: it indicates that although very reasonable approximations can be made, there is no mathematically rigorous way in which to reconcile the small remaining fraction while complying with all the competing fairness elements. |
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== Notes == |
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The quota rule is incompatible with resisting [[vote management]]. See [[Divisor method#Notes]] for an example. |
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==Related== |
==Related== |
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