United States congressional apportionment

Allocation of congressional districts in the House of Representatives after the 2010 U.S. Census
Allocation of congressional districts after the 2000 U.S. Census
The 435 seats of the House grouped by state (post-2010 Census reapportionment)

United States congressional apportionment is the process[1] by which seats in the United States House of Representatives are distributed among the 50 states according to the most recent constitutionally mandated decennial census. Each state is apportioned a number of seats which approximately corresponds to its share of the aggregate population of the 50 states.[2] However, every state is constitutionally guaranteed at least one seat.

The number of voting seats in the House of Representatives is currently set at 435, where it has been since 1913—except for a temporary (1959–1962) increase to 437 after Alaska and Hawaii were admitted into the Union. The total number of state members is capped by the Reapportionment Act of 1929.[3]

Because the size of a state's total congressional delegation determines the size of its representation in the U.S. Electoral College, congressional apportionment also affects the U.S. presidential election process as well.

Reapportionment

Although the actual reapportionment will normally occur in respect of a decennial census, the law that governs the total number of representatives and the method of apportionment to be carried into force at that time can be created prior to the census.

The decennial apportionment also determines the size of each state's representation in the U.S. Electoral College. Under Article II, Section 1, Clause 2 of the U.S. Constitution, any state's number of electors equals the size of its total congressional delegation (House and Senate seats).

Federal law requires the Clerk of the House of Representatives to notify each state government of its entitled number of seats no later than January 25 of the year immediately following the census. After seats have been reapportioned, each state determines the boundaries of congressional districts—geographical areas within the state of approximately equal population—in a process called redistricting.[4] Any citizen of the State can challenge the constitutionality of the redistricting in their US district court.[5]

Because the deadline for the House Clerk to report the results does not occur until the following January, and the states need sufficient time to perform the redistricting, the decennial census does not affect the elections that are held during that same year. For example, the electoral college apportionment during 2000 presidential election was still based on the 1990 census results. Likewise, the congressional districts and the electoral college during the 2020 general elections will still be based on the 2010 census.

Constitutional texts

The subject of Congressional apportionment is addressed twice in the U.S. Constitution. Initially, the apportionment of House seats was guided by two sentences in Article I, Section 2, clause 3:

Representatives and direct Taxes shall be apportioned among the several States which may be included within this Union, according to their respective Numbers, which shall be determined by adding to the whole Number of free Persons, including those bound to Service for a Term of Years, and excluding Indians not taxed, three fifths of all other Persons.

The Number of Representatives shall not exceed one for every thirty Thousand, but each State shall have at least one Representative;…

Following the end of the Civil War, the first of those provisions was superseded by Section 2 of the Fourteenth Amendment:

Representatives shall be apportioned among the several States according to their respective numbers, counting the whole number of persons in each State, excluding Indians not taxed.[6] But when the right to vote at any election for the choice of electors for President and Vice-President of the United States, Representatives in Congress, the Executive and Judicial officers of a State, or the members of the Legislature thereof, is denied to any of the male inhabitants of such State, being twenty-one years of age, and citizens of the United States, or in any way abridged, except for participation in rebellion, or other crime, the basis of representation therein shall be reduced in the proportion which the number of such male citizens shall bear to the whole number of male citizens twenty-one years of age in such State.

House size

The U.S. population has increased more rapidly than the membership of the House of Representatives.

The size of the U.S. House of Representatives refers to total number of congressional districts (or seats) into which the land area of the United States proper has been divided. The number of voting representatives is currently set at 435. There are an additional five delegates to the House of Representatives. They represent the District of Columbia and the territories of American Samoa, Guam, the Northern Mariana Islands, which first elected a representative in 2008,[7] and the U.S. Virgin Islands. Puerto Rico also elects a resident commissioner every four years.

Controversy and history

Since 1789, when the Federal Government began operating under the Constitution, the number of citizens per congressional district has risen from an average of 33,000 in 1790 to almost 700,000 as of 2008. Prior to the 20th century, the number of representatives increased every decade as more states joined the union, and the population increased. In 1911, Public Law 62-5 raised the membership of the U.S. House to 433 with a provision to add one permanent seat each upon the admissions of Arizona and New Mexico as states. As provided, membership increased to 435 in 1912. As of May 2016, there is approximately one representative for every 720,000 people in the country.

In 1921, Congress failed to reapportion the House membership as required by the United States Constitution. This failure to reapportion may have been politically motivated, as the newly elected Republican majority may have feared the effect such a reapportionment would have on their future electoral prospects.[8][9] Then in 1929 Congress (Republican control of both houses of congress and the presidency) passed the Reapportionment Act of 1929 which capped the size of the House at 435 (the then current number). This cap has remained unchanged for more than eight decades. Three states – Wyoming, Vermont, and North Dakota – have populations smaller than the average for a single district.

Ratio of representation in the House
YearsSourceAvg. Constituents
per Rep.
1793–18031790 Census34,436
1803–18131800 Census34,609
1813–18231810 Census36,377
1823–18331820 Census42,124
1833–18431830 Census49,712
1843–18531840 Census71,338
1853–18631850 Census93,020
1863–18731860 Census122,614
1873–18831870 Census130,533
1883–18931880 Census151,912
1893–19031890 Census173,901
1903–19131900 Census193,167
1913–19231910 Census210,583
1923–19331920 Census210,583
1933–19431930 Census280,675
1943–19531940 Census301,164
1953–19631950 Census334,587
1963–19731960 Census410,481
1973–19831970 Census469,088
1983–19931980 Census510,818
1993–2003 1990 Census 571,477
2003–2013 2000 Census 646,946
2013-2023 2010 Census 709,760

The ideal number of members has been a contentious issue since the country's founding. George Washington agreed that the original representation proposed during the Constitutional Convention (one representative for every 40,000) was inadequate and supported an alteration to reduce that number to 30,000.[10] This was the only time that Washington pronounced an opinion on any of the actual issues debated during the entire convention.[11]

In Federalist No. 55, James Madison argued that the size of the House of Representatives has to balance the ability of the body to legislate with the need for legislators to have a relationship close enough to the people to understand their local circumstances, that such representatives' social class be low enough to sympathize with the feelings of the mass of the people, and that their power be diluted enough to limit their abuse of the public trust and interests.

... first, that so small a number of representatives will be an unsafe depositary of the public interests; secondly, that they will not possess a proper knowledge of the local circumstances of their numerous constituents; thirdly, that they will be taken from that class of citizens which will sympathize least with the feelings of the mass of the people, and be most likely to aim at a permanent elevation of the few on the depression of the many; ...[12]

Madison also addressed Anti-Federalist claims that the representation would be inadequate, arguing that the major inadequacies are of minimal inconvenience since these will be cured rather quickly by virtue of decennial reapportionment. He noted, however,

I take for granted here what I shall, in answering the fourth objection, hereinafter show, that the number of representatives will be augmented from time to time in the manner provided by the Constitution. On a contrary supposition, I should admit the objection to have very great weight indeed.

Madison argued against the assumption that more is better:

Sixty or seventy men may be more properly trusted with a given degree of power than six or seven. But it does not follow that six or seven hundred would be proportionally a better depositary. And if we carry on the supposition to six or seven thousand, the whole reasoning ought to be reversed. ... In all very numerous assemblies, of whatever character composed, passion never fails to wrest the scepter from reason.[12]

Clemons v. Department of Commerce

A 2009 lawsuit, Clemons v. Department of Commerce, sought a court order for Congress to increase the size of the House's voting membership and then reapportion the seats in accordance with the population figures of the 2010 Census. The intent of the plaintiff was to rectify the disparity of congressional district population sizes among the states that result from the present method of apportionment. Upon reaching the U.S. Supreme Court in December 2010, the holdings of the lower district and appellate courts were vacated and the case remanded to the U.S. District Court from which the case originated with instructions that the district court dismiss the case for lack of jurisdiction.

Proposed expansion

The first proposed amendment to the Constitution within the Bill of Rights attempted to set a pattern for growth of the House along with the population, but has not been ratified.

Article the first ... After the first enumeration required by the first article of the Constitution, there shall be one Representative for every thirty thousand, until the number shall amount to one hundred, after which the proportion shall be so regulated by Congress, that there shall be not less than one hundred Representatives, nor less than one Representative for every forty thousand persons, until the number of Representatives shall amount to two hundred; after which the proportion shall be so regulated by Congress, that there shall not be less than two hundred Representatives, nor more than one Representative for every fifty thousand persons.[13]

The proposed Wyoming Rule calls for expanding the House until the standard Representative-to-population ratio equals that of the smallest entitled unit (currently the state of Wyoming). This proposal is primarily designed to address the fact that some House districts are currently nearly twice the size of others; for instance, there are just over 1 million residents in Montana's single district, compared to about 570,000 in Wyoming's. Although a larger House size will generally result in the smallest and largest districts being proportionally closer in size, this is not always the case. Therefore, in some cases, the Wyoming Rule may actually result in an increase in the ratio of the sizes of the largest and smallest districts. For instance, after the 1990 Census and with a House size of 435, the largest district (Montana's at-large district) had 799,065 residents, 76% larger than the smallest district (Wyoming's at-large district with 453,588 residents). The Wyoming Rule would have given a House size of 547 in 1990. Using that size, the largest district (North Dakota's at-large district) would have had 638,800 residents, 92% larger than the smallest districts (Delaware's two districts at approximately 333,084 residents each), which is larger than the 76% figure mentioned above.

On May 21, 2001, Rep. Alcee Hastings sent a dear colleague letter pointing out that U.S. expansion of its legislature had not kept pace with other countries.[14]

In 2007, during the 110th Congress, Representative Tom Davis introduced a bill in the House of Representatives that would add two seats to the House, one for Utah and one for the District of Columbia. It was passed by the House, but was tripped up by procedural hurdles in the Senate and withdrawn from consideration. An identical bill was reintroduced during the 111th Congress. In February 2009 the Senate adopted the measure 61-37. In April 2010, however, House leaders decided to shelve the proposal.[15]

Apportionment methods

Apart from the requirement that the number of delegates for each state is at least one, a state's number of representatives is in principle proportional to population, thus assuring reasonably consistent representation to the people regardless of the state boundaries and populations. No method of calculating a fair distribution of voting power across the various states was known until recently and five distinct apportionment methods have been used since the adoption of the Constitution, none of them producing fully proportional distribution of power among the states.

The current method, known as the method of equal proportions, has been used since the 1940 Census. The Vinton or Hamilton method, used from 1850 to 1900, was susceptible to what is known as the apportionment paradox or Alabama paradox.[16]

The method of equal proportions

The apportionment methodology currently used is the method of equal proportions,[1][17][18][19] so called because it guarantees that no additional transfer of a seat (from one state to another) will reduce the ratio between the numbers of persons per representative in any two states.[20] The method of equal proportions minimizes the percentage differences in the populations of the congressional districts.[21]

In this method, as a first step, each of the 50 states is given its one guaranteed seat in the House of Representatives, leaving 385 seats to assign.

The remaining seats are allocated one at a time, to the state with the highest priority number. Thus, the 51st seat would go to the most populous state (currently California). The priority number is determined by a formula that is mathematically computed to be the ratio of the state population to the geometric mean of the number of seats it currently holds in the assignment process, n (initially 1), and the number of seats it would hold if the seat were assigned to it, n+1.

The formula for determining the priority of a state to be apportioned the next available seat defined by the method of equal proportions is

where P is the population of the state, and n is the number of seats it currently holds before the possible allocation of the next seat. An equivalent, recursive definition is

where n is still the number of seats the state has before allocation of the next, and for n = 1, the initial A1 is explicitly defined as

Consider the reapportionment following the 2010 U.S. Census: beginning with all states initially being allocated one seat, the largest value of A1 corresponds to the largest state, California, which is allocated seat 51. After being allocated its 2nd seat, its priority value decreases to its A2 value, which is reordered to a position back in line. The 52nd seat goes to Texas, the 2nd largest state, because its A1 priority value is larger than the An of any other state. However, the 53rd seat goes back to California because its A2 priority value is larger than the An of any other state. The 54th seat goes to New York because its A1 priority value is larger than the An of any other state at this point. This process continues until all remaining seats are assigned. Each time a state is assigned a seat, n is incremented by 1, causing its priority value to be reduced and reordered among the states, whereupon another state normally rises to the top of the list.

The Census 2010 Ranking of Priority Values[22] shows the order in which seats 51–435 were apportioned after the 2010 Census, with additional listings for the next five priorities. Minnesota was allocated the final (435th) seat. North Carolina missed its 14th seat by 15,754 residents as the 436th seat to be allocated; ten years earlier it had gained its 13th seat as the 435th seat to be allocated based on the 2000 census.[23]

Past apportionments

Note: The first apportionment was established by the Constitution based on population estimates made by the Philadelphia Convention, and was not based on any census or enumeration.

Changes following the 2010 census

On December 21, 2010 the U.S. Census Bureau released its official apportionment results for congressional representation. The changes were in effect for the U.S. elections in 2012.[25]

Gain fourGain twoGain oneNo changeLose oneLose two
1. Texas 1. Florida 1. Arizona
2. Georgia
3. Nevada
4. South Carolina
5. Utah
6. Washington		 (32 states) 1. Illinois
2. Iowa
3. Louisiana
4. Massachusetts
5. Michigan
6. Missouri
7. New Jersey
8. Pennsylvania		 1. New York
2. Ohio
+4 +2 +6 −8 −4
+12 seats gained total −12 seats lost total

Past increases

The size of the U.S. House has increased and decreased as follows:[26]

1789–1800

DateSizeChangeCitationComments
March 4, 178959n/aConst. Art. I, § 2, cl. 3Seats apportioned by the Constitution
November 21, 178964Increase 5North Carolina ratified the Constitution with the seats apportioned by the Constitution
May 29, 179065Increase 1Rhode Island ratified the Constitution with the seat apportioned by the Constitution
March 4, 179167Increase 21 Stat. 191Vermont admitted
June 1, 179269Increase 2Kentucky admitted
March 4, 1793105Increase 361 Stat. 253 (Apportionment Act of 1792)Apportionment of the First Census
June 1, 1796106Increase 11 Stat. 491Tennessee admitted

1801–1850

DateSizeChangeCitationComments
March 1, 1803107Increase 12 Stat. 175Ohio admitted.
March 4, 1803142Increase 352 Stat. 128Apportionment of the Second Census.
April 30, 1812143Increase 12 Stat. 703Louisiana admitted.
March 4, 1813182Increase 392 Stat. 669Apportionment of the Third Census.
December 11, 1816183Increase 13 Stat. 290Indiana admitted.
December 10, 1817184Increase 13 Stat. 349Mississippi admitted.
December 3, 1818185Increase 13 Stat. 430Illinois admitted.
December 14, 1819186Increase 13 Stat. 492Alabama admitted.
March 15, 1820Steady3 Stat. 555Maine admitted, 7 seats transferred from Massachusetts
August 10, 1821187Increase 13 Stat. 547Missouri admitted
March 4, 1823213Increase 263 Stat. 651Apportionment of the Fourth Census
March 4, 1833240Increase 274 Stat. 516Apportionment of the Fifth Census
June 15, 1836241Increase 15 Stat. 51Arkansas admitted
January 26, 1837242Increase 15 Stat. 50Michigan admitted
March 4, 1843223Decrease 195 Stat. 491Apportionment of the Sixth Census, the only time the size of the House was reduced, except for the minor readjustments in 1863 and 1963.
March 3, 1845224Increase 15 Stat. 743Florida admitted.
December 29, 1845226Increase 25 Stat. 798Texas annexed and admitted.
December 28, 1846228Increase 25 Stat. 743
9 Stat. 52		Iowa admitted.
May 29, 1848230Increase 29 Stat. 58
9 Stat. 235		Wisconsin admitted.
March 4, 1849231Increase 19 Stat. 235Wisconsin given another seat.
September 9, 1850233Increase 29 Stat. 452California admitted.

1851–1900

DateSizeChangeCitationComments
March 4, 1853233Steady9 Stat. 432Apportionment of the Seventh Census.
234Increase 110 Stat. 25Additional seat apportioned to California[27]
May 11, 1858236Increase 211 Stat. 166Minnesota admitted.
February 14, 1859237Increase 111 Stat. 383Oregon admitted.
January 29, 1861238Increase 111 Stat. 269Kansas admitted
June 2, 1862239Increase 112 Stat. 411California apportioned an extra seat
March 4, 1863233Decrease 69 Stat. 432Apportionment of the Eighth Census, in accordance with the 1850 act, which provided for an apportionment of 233 seats
241Increase 812 Stat. 353Supplemental apportionment of 8 seats, for an overall increase of 2 seats in the 38th Congress
June 20, 1863Steady12 Stat. 633West Virginia admitted, three seats transferred from Virginia
October 31, 1864242Increase 113 Stat. 32Nevada admitted
March 1, 1867243Increase 114 Stat. 391Nebraska admitted
March 4, 1873283Increase 4017 Stat. 28Apportionment of the Ninth Census, replacing the 1850 act
292Increase 917 Stat. 192Supplemental apportionment added one seat each for nine states
August 1, 1876293Increase 113 Stat. 34Colorado admitted
March 4, 1883325Increase 3222 Stat. 5Apportionment of the Tenth Census.
November 2, 1889328Increase 325 Stat. 679North and South Dakota admitted, with one and two seats respectively.
November 8, 1889329Increase 125 Stat. 679Montana admitted.
November 11, 1889330Increase 125 Stat. 679Washington admitted.
July 3, 1890331Increase 126 Stat. 215Idaho admitted.
July 10, 1890332Increase 126 Stat. 222Wyoming admitted.
March 4, 1893356Increase 2426 Stat. 735Apportionment of the Eleventh Census.
January 4, 1896357Increase 128 Stat. 109Utah admitted.

1901–1950

DateSizeChangeCitationComments
March 4, 1903386Increase 2931 Stat. 733Apportionment of the Twelfth Census
November 16, 1907391Increase 534 Stat. 271Oklahoma admitted
January 6, 1912393Increase 237 Stat. 14 (Apportionment Act of 1911)New Mexico admitted
February 14, 1912394Increase 137 Stat. 14 (Apportionment Act of 1911)Arizona admitted
March 4, 1913435Increase 4137 Stat. 13 (Apportionment Act of 1911)Apportionment of the Thirteenth Census
March 4, 1933435Steady46 Stat. 26 (Reapportionment Act of 1929)Apportionment of the Fifteenth Census[28]
January 3, 1943435Steady46 Stat. 26 (Reapportionment Act of 1929)
54 Stat. 162		Apportionment of the Sixteenth Census

1951–2000

DateSizeChangeCitationComments
January 3, 1953435Steady55 Stat. 761Apportionment of the Seventeenth Census[29]
January 3, 1959436Increase 172 Stat. 345Alaska admitted
August 21, 1959437Increase 173 Stat. 8Hawaii admitted
January 3, 1963435Decrease 22 U.S.C. § 2a
72 Stat. 345
73 Stat. 8		Apportionment of the Eighteenth Census[30]
January 3, 1973435Steady2 U.S.C. § 2aApportionment of the Nineteenth Census
January 3, 1983435Steady2 U.S.C. § 2aApportionment of the Twentieth Census
January 3, 1993435Steady2 U.S.C. § 2aApportionment of the Twenty-First Census

2001–present

DateSizeChangeCitationComments
January 3, 2003435Steady2 U.S.C. § 2aApportionment of the Twenty-Second Census
January 3, 2013435Steady2 U.S.C. § 2aApportionment of the Twenty-Third Census

See also

Notes

  • Delegate counts in italics represent temporary counts assigned by Congress until the next decennial census or by the U.S. Constitution in 1789 until the first U.S. Census.
  • Elections held in the year of a census use the apportionment determined by the previous census.
  1. 1 2 Kristin D. Burnett (2011-11-01). "Congressional Apportionment (2010 Census Briefs C2010BR-08)" (PDF). U.S. Department of Commerce, Economics and Statistics Administration. Retrieved 2015-02-25.
  2. ↑ The populations of Washington, D.C. and federal territories are not included in this figure.
  3. ↑ Public Law 62-5 of 1911, though Congress has the authority to change that number.
  4. ↑ 2 U.S.C. § 2c
  5. ↑ 28 U.S.C. § 2284(a)
  6. ↑ Rendered moot by the Revenue Act of 1924 and Indian Citizenship Act of 1924.
  7. ↑ Bush signs federalization bill, Agnes E. Donato, Saipan Tribune, May 10, 2008.
  8. ↑ "Fair Representation, Meeting The Ideal of One Man One vote" - Michel Balinski and H. Peyton Young -- Page 51
  9. ↑
  10. ↑ Goldberg, Jonah (2001-01-15). "George Will Called Me An Idiot". National Review. Archived from the original on 2009-02-13. Retrieved 2018-04-11.
  11. ↑ Madison's notes on the Constitutional Convention - Tuesday September 17, 1787
  12. 1 2 The Federalist #55
  13. ↑ "Constitutional Amendments Not Ratified". United States House of Representatives. Archived from the original on 27 September 2007. Retrieved 2007-09-30.
  14. ↑ House of Representatives? Hardly., Alcee Hastings, May 21, 2001.
  15. ↑ Marimow, Ann E.; Pershing, Ben (April 21, 2010). "Congressional leaders shelve D.C. voting rights bill". The Washington Post.
  16. ↑ "Congressional Apportionment-Historical Perspective". U.S. Census Bureau. Retrieved 27 October 2013. .
  17. ↑ "The History of Apportionment in America". American Mathematical Society. Retrieved 2009-02-15.
  18. ↑ "2 USC §2a". Cornell University Law School, Legal Information Institute. Retrieved 2008-05-13.
  19. ↑ "Computing Apportionment". U.S. Census Bureau. Retrieved 2009-02-14.
  20. ↑ Edward V Huntington (1921). "The Mathematical Theory of the Apportionment of Representatives". Proceedings of the National Academy of Sciences of the United States of America. 7 (4): 123–7. doi:10.1073/pnas.7.4.123. PMC 1084767. PMID 16576591.
  21. ↑ "Congressional Apportionment". NationalAtlas.gov. U.S. Department of the Interior. Archived from the original on 2008-10-30. Retrieved 2009-02-14.
  22. ↑ "PRIORITY VALUES FOR 2010 CENSUS" (PDF). U.S. Bureau of the Census. Retrieved 2012-06-07.
  23. ↑ "Census 2000 Ranking of Priority Values". U.S. Bureau of the Census. 2001-02-21. Retrieved 2008-05-13.
  24. ↑ Congress failed to pass any reapportionment to implement the 1920 United States Census so despite population shift, distribution of seats from 1913 remained in effect until 1933.
  25. ↑ "APPORTIONMENT POPULATION AND NUMBER OF REPRESENTATIVES, BY STATE: 2010 CENSUS" (PDF). US Census. 2010-12-21. Retrieved 2013-02-23.
  26. ↑ The Size of the U. S. House of Representatives and its Constituent State Delegations, thirty-thousand.org.
  27. ↑ The 1850 Apportionment bill provided a method to be used in future reapportionments, as well as establishing the then-current 233 as the number of seats to be apportioned after future censuses. Due to census returns being incomplete in California, an additional act provided that California retain the same representation it had when admitted, until a new census could be taken. California would otherwise have lost one seat, and so the total number of seats was increased by one to 234.
  28. ↑ Congress failed to reapportion in 1923, following the Fourteenth Census.
  29. ↑ Pub.L. 77–291 amends section 22 of the Reapportionment Act of 1929 by wholly replacing its text.
  30. ↑ The Reapportionment Act of 1929 stated that the "then existing number of Representatives" would be apportioned after each census, which would have dictated an apportionment of 437 seats, but the Alaska Statehood Act and Hawaii Admission Act explicitly stated that the new seats were temporary increases. Both acts included the phrasing That such temporary increase in the membership shall not operate to either increase or decrease the permanent membership of the House of Representatives as prescribed in the Act of August 8, 1911 (37 Stat. 13) nor shall such temporary increase affect the basis of apportionment established by the Act of November 15, 1941 (55 Stat. 761; 2 U. S. C., sec. 2a), for the Eighty-third Congress and each Congress thereafter.

References

  • Balinski, Michael L.; Young, H. Peyton (1982). Fair Representation: Meeting the Ideal of One Man, One Vote. New Haven, CT: Yale University Press. ISBN 0-8157-0090-3.
  • Foster, Robert (1895). Commentaries on the Constitution of the United States: Historical and Judicial. 1. Boston: The Boston Book Co. pp. 329–446.
  • Hamilton, Alexander; Madison, James; Jay, John (1831). The Federalist. Hallowell: Glazier, Masters & Co. ISBN 0-8239-5735-7.
  • Edelman, Paul H. (2006). "Getting the Math Right: Why California Has Too Many Seats in the House of Representatives". Vanderbilt Law Review. Nashville: Vanderbilt University. 102 (March): 297.
  • Kromkowski, Charles A.; Kromkowski, John A. (1991). "Why 435? A Question of Political Arithmetic" (PDF). Polity. 24 (Fall 1991): 129–145. doi:10.2307/3234988. JSTOR 3234988. Retrieved 2013-10-17.
  • Agnew, Robert A. (2008). "Optimal Congressional Apportionment" (PDF). American Mathematical Monthly. Mathematical Association of America. 115 (April): 297–303. JSTOR 27642473.

Further reading

  • Stinebrickner-Kauffman, Taren (2004). "Counting Matters: Prison Inmates, Population Bases, and "One Person, One Vote"". Virginia Journal of Social Policy & the Law. Chicago: Virginia Journal of Social Policy & the Law. 11 (Winter): 229.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.