Power Balance and Apportionment Algorithms forthe

We measure the performance, in the task of apportioning the Congress of the United States, of an algorithm combining a heuristic-driven (simulated annealing) search with an exact-computation dynamic programming evaluation of the apportionments visited in the search. We compare this with the actual algorithm currently used in the United States to apportion Congress, and with a number of other algorithms that have been proposed. We conclude that on every set of census data in this country's history, the heuristic-driven apportionment provably yields far fairer appor-tionments than those of any of the other algorithm considered, including the algorithm currently used by the United States for Congressional apportionment. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for proot or direct commercial advantage and that copies show this notice on the rst page or initial screen of a display along with the full citation. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works, requires prior speciic permission and/or a fee. Permissions may be requested from Publications