The question, of course, is what a member House of Representatives would look like. My suspicion is that it would be much more representative of the population it represents, with enough seats for a healthy variety of people from more than two parties and many walks of life, rather than the litany of lawyers and businessmen who make up the current roster. And democracy has a deep bench. Just over 1, people will appear on a ballot in November, and thousands more made a respectable run in the primaries.
Some are more qualified than others, but many would make reasonable lawmakers. The smaller the districts get, the lower the cost of entry becomes.
Even if no number of seats can nullify the name recognition that an incumbent enjoys, the natural churn of members would increase, as would the odds of surprise upsets of the Eric Cantor variety. A cast of nearly a thousand, in other words, would be chaos of the best variety. Wrangling members would be a nightmare for the House leadership and a dream for democracy. Instead of the dreary sequence of party-line votes we witness now, CSPAN coverage would be replaced by a rowdy, delightfully turbulent process with uncertain outcomes.
It is easy to forget that nothing contributes more to an active and attentive Congress than a biannual super-dose of entropy. Want to check the math? Write to Chris Wilson at chris. Thus, this intuitive way to apportion fails because, by definition, it does not take into account the constitutional requirement that every state have at least one seat in the House and the statutory requirement that the House size be fixed at The current apportionment method the method of equal proportions established by the act satisfies the constitutional and statutory requirements.
Although an equal proportions apportionment is not normally computed in the theoretical way described below, the method can be understood as a modification of the rounding scheme described above.
First, the "ideal" sized district is found by dividing the apportionment population by to serve as a "trial" divisor. Then each state's apportionment population is divided by the "ideal" district size to determine its number of seats. Rather than rounding up any remainder of. A geometric mean of two numbers is the square root of the product of the two numbers.
For example, for the apportionment, the "ideal" size district of , had to be adjusted upward to between , and , 11 to produce a member House. Because the divisor is adjusted so that the total number of seats will equal , the problem of the "floating" House size is solved.
The constitutional requirement of at least one seat for each state is met by assigning each state one seat automatically regardless of its population size. Although the process of determining an apportionment through a series of trials using divisions near the "ideal" sized district as described above works, it is inefficient because it requires a series of calculations using different divisors until the total is reached.
Accordingly, the Census Bureau determines apportionment by computing a "priority" list of state claims to each seat in the House. During the early 20 th century, Walter F. Willcox, a Cornell University mathematician, determined that if the rounding points used in an apportionment method are divided into each state's population the mathematical equivalent of multiplying the population by the reciprocal of the rounding point , the resulting numbers can be ranked in a priority list for assigning seats in the House.
Such a priority list does not assume a fixed House size because it ranks each of the states' claims to seats in the House so that any size House can be chosen easily without the necessity of extensive re-computations. The traditional method of constructing a priority list to apportion seats by the equal proportions method involves first computing the reciprocals 14 of the geometric means the "rounding points" between every pair of consecutive whole numbers representing the seats to be apportioned.
It is then possible to multiply by decimals rather than divide by fractions the former being a considerably easier task. For example, the reciprocal of the geometric mean between 1 and 2 1. These reciprocals for all pairs 1 to 2, 2 to 3, 3 to 4, etc.
In order to construct the "priority list," each state's apportionment population is multiplied by each of the multipliers. The resulting products are ranked in order to show each state's claim to seats in the House. For example, see Table 2 , below assume that there are three states in the Union California, New York, and Florida and that the House size is set at 30 Representatives. The first seat for each state is assigned by the Constitution; so the remaining 27 seats must be apportioned using the equal proportions formula.
The apportionment populations for these states were 37,, for California, 19,, for New York, and 18,, for Florida. Once the priority values are computed, they are ranked with the highest value first. The resulting ranking is numbered and seats are assigned until the total is reached. By using the priority rankings instead of the rounding procedures described earlier in this paper under " The Formula in Theory ," it is possible to see how an increase or decrease in the House size will affect the allocation of seats without the necessity of additional calculations.
Table 1. Multiplier a. More specifically, for this example in Table 2 , the computed priority values column six for each of the three states are ordered from largest to smallest. By constitutional provision, seats one to three are given to each state. The next determination is the fourth seat in the hypothesized chamber.
California's claim to a second seat, based on its priority value, is 26,, Based on the priority values, California has the highest claim for its second seat and is allocated the fourth seat in the hypothesized chamber. Table 2. Notes: The Constitution requires that each state have at least one seat. Consequently, the first three seats assigned are not included in the table.
Table prepared by CRS. Next, the fifth seat's allocation is determined. California's claim to a third seat, based on the computed priority value, is 15,, Again, California has a higher priority value, and is allocated its third seat, the fifth seat in the hypothesized chamber.
Next the sixth seat's allocation is determined in the same fashion. California's claim to a fourth seat, based on the computed priority value, is 10,, As New York's priority value is higher than either California's or Florida's, it is allocated its second seat, the sixth seat in the hypothesized chamber. Next, the seventh seat's allocation is determined.
Again, California's claim to a fourth seat, based on the computed priority value, is 10,, As Florida's priority value is higher than either of the other states, Florida is, finally, allocated its second seat, the seventh seat in the hypothesized chamber.
This same process is continued until all 30 seats in this hypothesized House are allocated to the three states. From Table 2 , then, we see that if the United States were made up of three states and the House size were to be set at 30 members, California would have 11 seats, New York would have 10, and Florida would have 9.
Any other size House can be determined by picking points in the priority list and observing what the maximum size state delegation would be for each state. A priority listing for all 50 states based on the Census is in the Appendix to this report. It shows priority rankings for the assignment of seats in a House ranging in size from 51 to seats.
The equal proportions rule of rounding at the geometric mean results in differing rounding points, depending on which numbers are chosen. For example, the geometric mean between 1 and 2 is 1. Table 3 , below, shows the "rounding points" for assignments to the House using the equal proportions method for a state delegation size of up to The rounding points are listed between each delegation size because they are the thresholds that must be passed in order for a state to be entitled to another seat.
The table illustrates that, as the delegation size of a state increases, larger fractions are necessary to entitle the state to additional seats.
The fact that higher rounding points are necessary for states to obtain additional seats has led to charges that the equal proportions formula favors small states at the expense of large states.
In Fair Representation , a study of congressional apportionment, authors M. Balinski and H. Young concluded that if "the intent is to eliminate any systematic advantage to either the small or the large, then only one method, first proposed by Daniel Webster in , will do. The NAS concluded that "the method of equal proportions is preferred by the committee because it satisfies Table 3. Notes: Any number between , and , divided into each state's population will produce a House size of if rounded at these points, which are the geometric means of each pair of successive numbers.
A bill that would have changed the apportionment method to another formula called the "Hamilton-Vinton" method was introduced in In order to reapportion the House using Hamilton-Vinton, each state's population would be divided by the "ideal" sized congressional district ,, divided by , in , for an "ideal" district population of , Any state with fewer residents than the "ideal" sized district would receive a seat because the Constitution requires each state to have at least one House seat.
The remaining states in most cases have a claim to a whole number and a fraction of a Representative. Each such state receives the whole number of seats it is entitled to.
The fractional remainders are rank-ordered from highest to lowest until seats are assigned. For the purpose of this analysis, we will concentrate on the differences between the equal proportions and major fractions methods because the Hamilton-Vinton method is subject to several mathematical anomalies.
Prior to the passage of the Apportionment Act of 2 U. Each of the major competing methods—equal proportions currently used and major fractions—can be supported mathematically.
Choosing between them is a policy decision, rather than a matter of conclusively proving that one approach is mathematically better than the other. A major fractions apportionment results in a House in which each citizen's share of his or her Representative is as equal as possible on an absolute basis.
In the equal proportions apportionment now used, each citizen's share of his or her Representative is as equal as possible on a proportional basis. Featured Resources for National History Day Historical Highlight August 07, The admission of Ohio as a state. House of Representatives About this object. Office of the Historian: history mail. Officials from the House are commonly referred to as congressmen, congresswomen or representatives. How the seats are split is contingent on the population size of the states, and D.
This explains why New York 27 representatives has far more representatives than does Montana one representative. Does it matter how many representatives a state has? Yes, for a few important reasons.
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