Writing Projects

Writing Projects

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Both writing projects require you to use a spreadsheet to compute an apportionment, based on the 2010 census. While hand calculation is theoretically possible, it is not recommended.

The first step is to download the data as an XLS file from the Census Bureau. Go to www.census.gov/population/apportionment/

The spreadsheet with the 2010 apportionment can be found under the “Data” tab. To modify this spreadsheet to suit the purpose of either project, you will need to put in some additional columns. Place the divisor in cell . Start with standard divisor, 710,767, which you may adjust later. Type “Divisor” in cell as a reminder of what you have entered. You can input formulas for the apportionment quotients by entering in cell and copying this expression to the range in column . (The dollar sign in the expression is important; without it, when the expression is copied to cell , for example, it would be , and a divide by zero error would be noted.)

The spreadsheet function can be used to put , for each apportionment quotient , in the next column, . Thus, enter in cell , and copy this formula to the range . You will put the rounding point (Hill-Huntington or Dean) in column . For example, for Hill-Huntington, put in cell , and copy the formula through .

The tentative apportionments go in column . You’ll use the function. The first entry of this function is a logical expression—that is, a statement that the computer can evaluate as true or false. The second entry is evaluated if the expression is true, the third if the expression is false. A state’s tentative apportionment is obtained by rounding its apportionment quotient down if it is less than the rounding point, and rounding it up otherwise. Therefore, enter

in cell , and copy this through cell J61.

The final modification is to put the sum of the tentative apportionments,

in cell J62. When this is done, you can experiment by adjusting the divisor in cell G63. When the value in this cell changes, you will immediately see the changes in the tentative apportionments and their total.

  1. In the reapportionment resulting from the 2010 census, two states, New York and Ohio, lost 2 house seats, and eight other states lost 1 seat. The 12 seats were transferred to states that had experienced dramatic increases in population: Texas got 4 additional seats, Florida received 2 more, and 6 other states got one apiece. If Congress should decide to increase the statutory house size so that no state’s delegation in the House would be reduced, how many seats would have been added to the House, and which states would have gotten them? (Warning: It may be more than 12.)
  2. The Webster method was proposed in 1832 after New York received an apportionment in excess of its upper quota. Two other apportionment methods were proposed in the same year: the method of John Quincy Adams (see Exercise 45 on page 617) and the Dean method (see page 598).

    Suppose that state has population and its tentative apportionment is , while state has population and tentative apportionment . Which of these states is most deserving of the next seat, in the sense that absolute differences in district population are minimized? (Of course, another state may be more deserving, but we are comparing states two at a time.) To see how to answer this question:

    620

    1. Calculate the absolute difference in district populations if gets the seat, so that its apportionment is increased to . Let that value be denoted . Repeat the calculation for the situation when gets the seat, and get a number .
    2. Show that , where and are the harmonic means (you may have to Google this term) of and and of and , respectively.
    3. Which state is entitled to the next seat if the difference calculated in part (b) is negative?
    4. (d) The Dean rounding point for numbers between a whole number and is . Explain why the divisor method that rounds an apportionment quotient down to if is less than the Dean rounding point between and , and up to otherwise, provides the apportionment that minimizes differences in district population.
    5. Find a formula for the Dean rounding point that can be applied to find the rounding point between 0 and 1 without division by 0.
    6. Compare the Dean rounding point with the Hill-Huntington rounding point for . Which is smaller? Is the Dean method more or less biased in favor of small states? Is it possible for any state to get an apportionment of zero with the Dean method?
    7. Compute the apportionment of the House of Representatives according to the 2010 census by the Dean method. How does it differ from the Hill-Huntington apportionment shown on the spreadsheet as you downloaded it?