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The truth of a theory is in your mind, not in your eyes.

In H. Eves Mathematical Circles Squared, Boston: Prindle, Weber and Schmidt, 1972.

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# Apportioning Representatives in the United States Congress

The winds of change were blowing again in 1832.  Former President John Quincy Adams, now a Representative from Massachusetts, proposed an inverse of Jefferson’s method:

He proposed a House size of 250 and a divisor of 50,000 at the time.  See the spreadsheet 1832 Adams for an illustration of the procedure.  The file is set to a House size of 250, but ultimately the Congress passed a size of 240.  If you save this or any other file linked to this article, you may play with the numbers yourself.  In this case, the divisor may be adjusted until the rounded total of 240 is achieved.

If you experimented with the Adams file, you may have noticed the bias inherent in the method:  it favors the smaller states at the expense of the large ones.  We can see this by looking at a variant of the example that we had showing the bias in Jefferson’s method:

Increasing the divisor by 7,000 causes the larger quotient to decrease by about 1.65, while at the same time making the smaller quotient decrease by only about 0.5.  The small states can let the large ones reduce their quotas at a faster rate until the predetermined number of House seats is achieved.

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Caulfield, Michael J., "Apportioning Representatives in the United States Congress," Loci (November 2008), DOI: 10.4169/loci003163