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Numbers Rule by George Szpiro

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CHAPTER TWELVE

THE QUOTARIANS

We return to the frustrating subject of apportionment. In the preceding chapter I recounted that Kenneth Arrow proved that any election method that satisfies reasonable conditions of rationality—like avoiding cycles—is either imposed or dictatorial, and that Allan Gibbard and Mark Satterthwaite showed that any democratic election method can be manipulated. This chapter will, unfortunately, be the bearer of further bad tidings: a fair and true allocation of seats in Congress is also a mathematical impossibility.

With the size of the House fixed at 435 in 1912, the Alabama Paradox no longer loomed. And after the inclusion of Alaska and Hawaii in 1959 no new states were likely to join the Union, so the New State Paradox ...

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