1 / 9

Huntington-Hill Method Method of Equal Proportions

Huntington-Hill Method Method of Equal Proportions. Joseph A. Hill, Chief statistician, Bureau of the Census Edward V. Huntington, Professor of Mathematics, Harvard. Some History. Developed around 1911 Endorsed by a National Academy of Sciences Panel in 1929

colin-dickson
Download Presentation

Huntington-Hill Method Method of Equal Proportions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

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

  2. 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.

  3. 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!)

  4. 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.

  5. 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.)

  6. 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.)

  7. 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.)

  8. 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<HM<AM, say). • What do you notice? Test your conjecture with another pair like 37 and 38.

  9. An exampleDo HH and Dean for a divisor of 270

More Related