It has been shown Moreover, the method of equal proportions is the only one that uses relative differences, the methods of harmonic mean and major fraction being based on absolute differences. In addition, the method of equal proportions gives the smallest relative difference for both average population per district and individual share in a representative. No other method takes account of both these factors. Therefore the method of equal proportions gives the most equitable distribution of Representatives among the states.
An example using the North Carolina and Rhode Island populations illustrates the argument for proportional differences. The first step in making comparisons between the states is to standardize the figures in some fashion. One way of doing this is to express each state's representation in the House as a number of Representatives per million residents.
If the major fractions method had been used, then 14 seats would have been assigned to North Carolina, and 1 would have been given to Rhode Island. Under this scenario, North Carolina has 1.
The absolute difference between these numbers is 0. When 13 seats are assigned to North Carolina and 2 are assigned to Rhode Island using equal proportions , North Carolina has 1. The absolute difference between these numbers is. Major fractions minimizes absolute differences, so in , if this method had been required by law, North Carolina and Rhode Island would have received 14 and 1 seats respectively because the absolute difference 0. Equal proportions minimizes differences on a proportional basis, so it assigned 13 seats to North Carolina and 2 to Rhode Island because the proportional difference between a 13 and 2 allocation The proportional difference versus absolute difference argument could also be cast in terms of the goal of "one person, one vote," as noted above.
The courts' use of absolute difference measures in state redistricting cases may not necessarily be appropriate when applied to the apportionment of seats among states. The courts already recognize that the rules governing redistricting in state legislatures differ from those in congressional districting. If the "one person, one vote" standard were ever to be applied to apportionment of seats among states—a process that differs significantly from redistricting within states—proportional difference measures might be accepted as most appropriate.
If the choice between methods were judged to be a tossup with regard to which mathematical process is fairest, are there other representational goals that equal proportions meets that are, perhaps, appropriate to consider? One such goal might be the desirability of avoiding large districts, if possible.
After the apportionment of , five of the seven states with only one Representative Alaska, Delaware, Montana, North Dakota, South Dakota, Vermont, and Wyoming have relatively large land areas. Arguably, an apportionment method that would potentially reduce the number of very large with respect to area size districts would serve to increase representation in those states. Very large districts limit the opportunities of constituents to see their Representatives, may require more district based offices, and may require toll calls for telephone contact with the Representatives' district offices.
Switching from equal proportions to major fractions may increase the number of states represented by only one member of Congress, although it is impossible to predict this outcome with any certainty using Census Bureau projections for The table that follows contains the priority listing used in apportionment following the Census. Table A-1 shows where each state ranked in the priority of seat assignments. The priority values listed beyond seat number show which states would have gained additional representations if the House size had been increased.
Table A A similar, previous CRS report was authored by [author name scrubbed], who retired in While the current report is modified by the current author, Mr.
Huckabee's contribution, in a large part, remains. Of course, any errors that may appear are due solely to the current author. In part, this debate over the apportionment of power in the early years of this country came from the year experience with the unicameral congress provided for under the Articles of Confederation, which assigned one vote to each state delegation in Congress.
For a thorough discussion, see Charles A. A major controversy occurred even over the fixed, short-term apportionment of seats among the delegates at the Constitutional Convention.
See Kromkowski, pp. Thomas Jefferson recommended discarding the fractions. Daniel Webster and others argued that Jefferson's method was unconstitutional because it discriminated against small states. Webster argued that an additional Representative should be awarded to a state if the fractional entitlement was 0.
Congress subsequently used a "fixed ratio" method proposed by Rep. Samuel Vinton following the census of through , but this method led to the paradox that Alabama lost a seat even though the size of the House was increased in Subsequently, mathematician W. Willcox proposed the "major fractions" method, which was used following the census of This method, too, had its critics; and in Harvard mathematician E. Huntington proposed the "equal proportions" method and developed formulas and computational tables for all of the other known, mathematically valid apportionment methods.
A committee of the National Academy of Sciences conducted an analysis of each of those methods—smallest divisors, harmonic mean, equal proportions, major fractions, and greatest divisors—and recommended that Congress adopt Huntington's equal proportions method. For a review of this history, see U. Also, see Michel L. Article I, Section 2 defines both the maximum and minimum size of the House, but the actual House size is set by law.
Thus, the House after could be as small as 50 and as large as 10, Representatives. The actual language in of Article 1, section 2 pertaining to this minimum size reads as follows: "The number of Representatives shall not exceed one for every thirty Thousand, but each State shall have at least one Representative.
Interestingly, while the Constitution requires a census every ten years, it does not require that an apportionment of seats to the House of Representatives must occur.
This became a statutory requirement with the passage of the Apportionment Act of The apportionment population is the resident population of the 50 states. It excludes the population of the District of Columbia and U. The geometric mean of 1 and 2 is the square root of 2, which is 1. The geometric mean of 2 and 3 is the square root of 6, which is 2. Geometric means are computed for determining the rounding points for the size of any state's delegation size.
Equal proportions rounds at the geometric mean which varies rather than the arithmetic mean which is always halfway between any pair of numbers. Thus, a state which would be entitled to The rationale for choosing the geometric mean rather than the arithmetic mean as the rounding point is discussed below in the section analyzing the equal proportions and major fractions formulas.
Any number in this range divided into each state's population and rounded at the geometric mean will produce a seat House, with the provision that each state receives at least one seat. Report , Washington: GPO, , p.
The limit on the size of the House is a statutory requirement. The House size was first fixed at by the Apportionment Act of 37 Stat. The Apportionment Act of 46 Stat. This requirement to "automatically reapportion" every 10 years was needed because the Constitution, ironically, while requiring a census every 10 years makes no such requirement for apportionments.
Thus, the fact that no apportionment was carried out after the census in no way violated the Constitution or any statutory requirement at the time. By authority of section 9 of PL 72 Stat. Fair Representation , pp.
An earlier major work in this field was written by Laurence F. Daniel Webster proposed this method to overcome the large-state bias in Jefferson's discarded fractions method. Webster's method was used three times, in the reapportionments following the , , and Censuses.
Changing to the Hamilton-Vinton method would have kept Indiana from losing a seat. Hearings were held, but no further action was taken on the measure. Since that time no other bill has been introduced to change the formula. The Hamilton-Vinton method used after the censuses is subject to the "Alabama paradox" and various other population paradoxes.
The Alabama paradox was so named in when it was discovered that Alabama would have lost a seat in the House if the size of the House had been increased from to Another paradox, known as the population paradox, has been variously described, but in its modern form with a fixed size House it works in this way: two states may gain population from one census to the next. State "A," which is gaining population at a rate faster than state "B," may lose a seat to state "B.
Hamilton-Vinton is subject to them, whereas equal proportions and major fractions are not. The absolute value of a number is its magnitude without regard to its sign. For example, the absolute value of -8 is 8. The absolute value of the expression is 2. The absolute value of the expression is also 2. Major fractions best conforms to the spirit of these decisions if the population discrepancy is measured on an absolute basis, as the courts have done in the recent past.
The Supreme Court has never applied its "one person, one vote" rule to apportioning seats of the House of Representatives among states as opposed to redistricting within states. Thus, no established rule of law is being violated. Arguably, no apportionment method can meet the "one person, one vote" standard required by the Supreme Court for districts within states unless the size of the House is increased significantly thereby making districts less populous. Nevada had two seats with a population of , Montana was assigned two seats with a population of , South Dakota's single seat was required by the Constitution with a population of , The vast majority of the districts based on the census of them fell within the range of , to , House of Representatives Using the Estimated Citizen Population: , by [author name scrubbed].
Young and M. Contract No. CRS , Sept. This document is available to Members of Congress and congressional staff from the author of this report. Comparing equal proportions and major fractions using the state populations from the 19 actual censuses taken since , reveals that the small states would have been favored 3. Major fractions would have also favored small states, in these cases, but only.
The American Revolution was, in part, a contest about the very definition of representation. In England, the House of Commons represented every British subject regardless of whether the subject could actually vote for its membership. American colonists, who were used to controlling their local affairs in the directly-elected colonial legislatures, lacked a voice in Parliament and resented the British policies imposed on them.
The Articles of Confederation created the first national congress to represent the interests of the states: each state would appoint between two and seven delegates to the congress, and each state delegation would have one vote. House of Representatives. Approved by the 39th Congress — as H. The Constitutional Convention addressed multiple concerns in the process of designing the new Congress.
The first was the relationship of the least populous states to the most populous. The battle between big and small states colored most of the Convention and nearly ended hopes of creating a national government. If an equality of votes is to be put in its place, the large States say their money will be in danger. When a broad table is to be made, and the edges of planks do not fit the artist takes a little from both, and makes a good joint.
The compromise enabled the Convention, teetering on the brink of dissolution, to continue. The Convention determined that a Census of the population conducted every 10 years would enable the House to adjust the distribution of its Membership on a regular basis. The method, however, proved controversial.
Southern delegates argued that their slaves counted in the population, yielding them more Representatives. Northern delegates countered that slaves were property and should not be counted at all. Before federal income taxes or tariffs, the states contributed to the national government with local taxes, often flat poll taxes on each citizen.
Since constitutional framers had to provide for the funding of the new government, they debated the proper relationship between representation and taxation. A number of ideas have emerged for how best to expand the House.
Some reformers have suggested a one-time, arbitrary fix, like adding 50 seats. Others have argued for a more substantive overhaul, like resizing the House based on the population of the smallest state — often called the Wyoming rule, as Wyoming has occupied this position since Matthew Shugart , a professor emeritus at University of California, Davis, has tried to unpack why this is often the case. Of the 30 major democracies Shugart and his co-authors looked at alongside the U.
Take Canada. But other bigger democracies like Brazil and Japan also have seat counts that fall fairly close to the cube root of their respective populations.
Some countries like the U. And countries like Australia, India and Israel are even more underrepresented than the U. Democracy Read more. But as the chart below shows, the House would have to grow to seats to reflect where the cube root law expects representation in the U.
Regardless of the potential benefits of a bigger House, though, there would likely be steep opposition to expanding it because of some of the tradeoffs — and potential downsides — involved. For instance, a larger House would by necessity mean a bigger government and more spending.
There could also be consequences for governing, too, such as more gridlock and partisanship. Marvin Overby , a political scientist at Pennsylvania State University-Harrisburg who studies Congress and has expressed skepticism toward the promised benefits of House expansion.
He also warned that a bigger House might produce fewer competitive seats thanks to partisan sorting and fewer representatives open to compromise. As such, even more elections may be effectively decided by primaries instead of general elections than they are today, which is already the case in the vast majority of House districts. And with more safe seats, incumbents would likely have an even easier time getting reelected than they currently do.
In , 51 percent of Americans told the Pew Research Center that the size of the House should stay the same, while only 28 percent wanted to expand it another 18 percent actually wanted to shrink it. Legislation introduced in February by Rep. Alcee Hastings of Florida, a Democrat who died in April , aims to establish a bipartisan commission to examine the size of the House, among other things.
But the bill has only four co-sponsors and looks unlikely to go anywhere. Clearly, there are pros and cons to increasing the size of the House, but at the very least, the idea should be more openly debated because, in terms of changes that could be made to our institutions, expanding the House is actually doable.
Nevertheless, it may be time for a change given how unequal districts have become between states and how underrepresented Americans are after more than years of being stuck at House members. Strictly speaking, the House has members : are voting members from each of the 50 states, and six are nonvoting members. The District of Columbia, Guam, the U. This number increased to in to accommodate the statehood of Alaska and Hawaii but returned to in , after the reapportionment process in But historically, Congress has usually passed apportionment acts in the year or two after the census was released, but still in time for elections ahead of the next Congress.
Upon statehood, Congress added two seats for New Mexico and one for Arizona in during the 62nd Congress , which had already passed the Apportionment Act of This brought the total number of House seats to before the House expanded to seats in the 63rd Congress.
Minimizing seat loss had long been a major consideration in the apportionment process, to the point that only a handful of states lost any seats in the five apportionments from to This is why even now the secretary of commerce reports apportionment figures to the president, who then transmits that information to Congress.
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