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Huntington-Hill Method Method of Equal Proportions Joseph A. Hill, Chief statistician, Bureau of the Census Edward V. Huntington, Professor of Mathematics, Harvard

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Some History Developed around 1911 Endorsed by a National Academy of Sciences Panel in 1929 Signed into law as our apportionment method in 1941 when the House size was set at 435.

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Two Questions to Answer Why was the Huntington-Hill method chosen as our apportionment method? How does it work? We will answer the second question first. (To make our life easier, we will abbreviate the method as HH!)

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Divisor methods and Means The HH method is a divisor method. The difference between it and other divisor methods is how the quotient for each state is rounded. To understand this rounding method, we take a side trip and talk about three different types of means and how they are used to round in 3 different divisor methods.

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Arithmetic Mean The arithmetic mean(AM) of two numbers is their usual ‘average’: AM(12,13) = (12 + 13)/2 = 12.5 Webster’s method uses this number as the cutoff for rounding (round down if the quotient is less than this number.)

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Geometric Mean The geometric mean(GM) of two numbers is the square root of their product: GM(12,13) = √(12∙13) = 12.49 Huntington-Hill uses this number as the cutoff for rounding (rounding down if the quotient is less than this number.)

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Harmonic Mean The harmonic mean(HM) of two numbers is twice the product of the two numbers divided by their sum: HM(12, 13) = 2∙12∙13/(12 + 13) = 12.48 Dean’s Method uses this number as the cutoff for rounding (rounding down if the quotient is less than this number.)

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How do the means compare? Take four number pairs (4 and 5, 6 and 7, 8 and 9, 10 and 11) and calculate each of the three means for that pair. Then compare the sizes of the means and write down your results (GM

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An example Do HH and Dean for a divisor of 270 SchoolPopulation East1500 West1000 North9000 South6000 Central200

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