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Apportionment is the process by which seats in a legislative body are distributed among administrative divisions, such as states or parties, entitled to representation. This page presents the general principles and issues related to apportionment. The page apportionment by country describes the specific practices used around the world. The page Mathematics of apportionment describes mathematical formulations and properties of apportionment rules.
The simplest and most universal principle is that elections should give each vote an equal weight. This is both intuitive and stated in laws such as the Fourteenth Amendment to the United States Constitution (the Equal Protection Clause).
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Transcription
- WELCOME TO A LESSON ON HAMILTON'S METHOD OF APPORTIONMENT. ALEXANDER HAMILTON PROPOSED THE METHOD THAT NOW BEARS HIS NAME. HIS METHOD WAS APPROVED BY CONGRESS IN 1791, BUT WAS VETOED BY PRESIDENT WASHINGTON. IT WAS LATER ADOPTED IN 1852, AND USED THROUGH 1911. SINCE HE WAS INTERESTED IN THE QUESTION OF CONGRESSIONAL REPRESENTATION, WE'LL USE THE LANGUAGE OF STATES AND REPRESENTATIVES. HAMILTON'S METHOD PROVIDES A PROCEDURE TO DETERMINE HOW MANY REPRESENTATIVES EACH STATE SHOULD RECEIVE. SO THE FIRST STEP IN HAMILTON'S METHOD IS TO DETERMINE HOW MANY PEOPLE EACH REPRESENTATIVE SHOULD REPRESENT. WE DO THIS BY DIVIDING THE TOTAL POPULATION OF ALL THE STATES BY THE TOTAL NUMBER OF REPRESENTATIVES. THIS ANSWER IS CALLED THE STANDARD DIVISOR, OR DIVISOR. STEP TWO, WE DIVIDE EACH STATE'S POPULATION BY THE DIVISOR TO DETERMINE HOW MANY REPRESENTATIVES IT SHOULD HAVE. WE WOULD RECORD THIS ANSWER TO SEVERAL DECIMAL PLACES, AND THIS ANSWER IS CALLED THE QUOTA. SINCE WE CAN ONLY ALLOCATE WHOLE REPRESENTATIVES, HAMILTON RESOLVES THE WHOLE NUMBER PROBLEM AS FOLLOWS: STEP THREE, WE CUT OFF THE DECIMAL PARTS OF ALL THE QUOTAS, AND THESE ARE CALLED THE LOWER QUOTAS. THEN WE ADD THE LOWER QUOTAS. THIS SUM WILL ALWAYS BE LESS THAN OR EQUAL TO THE TOTAL NUMBER OF REPRESENTATIVES. STEP FOUR, ASSUMING THAT THE TOTAL FROM STEP THREE WAS LESS THAN THE TOTAL NUMBER OF REPRESENTATIVES, ASSIGN THE REMAINING REPRESENTATIVES ONE EACH TO THE STATES WHOSE DECIMAL PART OF THE QUOTA WERE LARGEST UNTIL THE DESIRED TOTAL IS REACHED. WE DO WANT TO MAKE SURE THAT EACH STATE ENDS UP WITH AT LEAST ONE REPRESENTATIVE. LET'S TAKE A LOOK AT OUR FIRST EXAMPLE. AGAIN, THE FIRST STEP, WE WANT TO FIND THE DIVISOR, OR STANDARD DIVISOR. SO WE TAKE THE SUM OF THE POPULATION FROM ALL THE STATES, WHICH IS 189,000, AND DIVIDE BY THE TOTAL OF SEATS IN CONGRESS, WHICH IS 30. NOTICE HOW THIS GIVES US A DIVISOR OF 6,300. AND NOW, TO FIND THE QUOTAS WE TAKE EACH STATE POPULATION AND DIVIDE BY 6,300. SO FOR STATE "A" THE QUOTA WOULD BE 27,500 DIVIDED BY 6,300. IF WE ROUND TO FOUR DECIMAL PLACES, THE QUOTA FOR STATE "A" WOULD BE APPROXIMATELY 4.3651. FOR STATE B WE WOULD HAVE 38,300 DIVIDED BY 6,300, SO THE QUOTA FOR STATE B WOULD BE APPROXIMATELY 6.0794, AND SO ON. TO SAVE SOME TIME WE WON'T SHOW ALL THIS DIVISION. SO HERE ARE OUR QUOTAS TO FOUR DECIMAL PLACES, AND NOW FOR THE INITIAL APPORTIONMENT OR INITIAL ASSIGNMENT OF THE SEATS IN CONGRESS, WE REMOVE THE DECIMAL PARTS OF THE QUOTA. WHICH MEANS STATE "A" WOULD RECEIVE 4, STATE B WOULD RECEIVE 6, STATE C WOULD RECEIVE 7, AND STATE D WOULD RECEIVE 12. WE NOTICE HOW THE SUM HERE IS 29, AND WE HAVE A TOTAL OF 30 SEATS. WE NOW ASSIGN THE REMAINING SEAT TO THE STATE WHOSE QUOTA HAS THE LARGEST DECIMAL PART. NOTICE STATE "A" HAS THE LARGEST DECIMAL PART AT .3651, AND THEREFORE STATE "A" RECEIVES ONE MORE SEAT. WHICH MEANS FOR THE FINAL APPORTIONMENT STATE "A" RECEIVES 5 SEATS, STATE B RECEIVES 6, STATE C RECEIVES 7, AND STATE D RECEIVES 12. NOTICE HERE THE TOTAL IS 30. WE'VE USED ALL THE SEATS IN CONGRESS. AND HERE'S THE RESULT IN A NICE TABLE. LET'S TAKE A LOOK AT A SECOND EXAMPLE. HERE A TEACHER WISHES TO DISTRIBUTE 10 IDENTICAL PIECES OF CANDY AMONG 4 STUDENTS, BASED UPON HOW MANY PAGES OF A BOOK THEY READ LAST MONTH, USING HAMILTON'S METHOD. THE TABLE BELOW LISTS THE TOTAL NUMBER OF PAGES READ BY EACH STUDENT. SO IN THIS PARTICULAR QUESTION WE'RE ASKED TO FIND THE DIVISOR, THE QUOTA FOR ANTONIO, AND THE INITIAL APPORTIONMENT FOR ANTONIO. BUT WE'LL ACTUALLY GO AHEAD AND GO THROUGH THIS ENTIRE PROCESS FOR THIS PROBLEM. SO THE FIRST STEP IS TO FIND THE DIVISOR, SO WE'LL SET THIS UP AS A TABLE AS WE SEE HERE. NOTICE HOW WE ALREADY FOUND THE SUM OF THE TOTAL NUMBER OF PAGES, WHICH IS 1,120, AND THERE ARE 10 PIECES OF CANDY TO APPORTION. SO OUR DIVISOR IS 1,120 DIVIDED BY 10, OR 112. SO TO FIND THE QUOTA WE'LL TAKE THE NUMBER OF PAGES EACH STUDENT READ AND DIVIDE BY 112. SO THE QUOTE FOR ALAN WOULD BE 580 DIVIDED BY 112, WHICH WOULD BE APPROXIMATELY 5.1786. FOR ANTONIO THE QUOTA WOULD BE 230 DIVIDED BY 112, GIVING A QUOTA OF APPROXIMATELY 2.0536, AND SO ON. SO AGAIN, HERE ARE OUR QUOTAS. WE FOUND FROM THE PREVIOUS SLIDE THE DIVISOR IS 112, AND THE QUOTA FOR ANTONIO WE NOW KNOW IS 2.0536. AND NOW FOR THE INITIAL APPORTIONMENT WE REMOVE THE DECIMALS FROM THE QUOTA. SO ALAN WOULD RECEIVE 5 PIECES, ANTONIO WOULD RECEIVE 2, ALEX WOULD RECEIVE 1, AND LUCAS WOULD ALSO RECEIVE 1. SO THE INITIAL APPORTIONMENT FOR ANTONIO, WHICH IS WHAT OUR QUESTION ASKED FOR, IS 2. BUT NOTICE HOW THERE ARE 10 PIECES OF CANDY, AND THIS ONLY ADDS TO 9. SO GOING BACK TO THE ORIGINAL QUOTAS, SINCE ALEX HAS THE LARGEST DECIMAL PART IN HIS QUOTA, HE WOULD RECEIVE THE EXTRA PIECE OF CANDY. AND THEREFORE THE FINAL APPORTIONMENT WOULD BE 5, 2, 2, AND 1. NOTICE HOW HERE THE TOTAL IS 10 PIECES, SO WE'VE USED ALL THE CANDY. AND AGAIN, HERE IS THE RESULT IN A NICE TABLE. HAMILTON'S METHOD DOES SATISFY WHAT IS CALLED THE QUOTA RULE. THE QUOTA RULE SAYS THAT THE FINAL NUMBER OF REPRESENTATIVES A STATE GETS SHOULD BE WITHIN ONE OF THAT STATE'S QUOTA. SINCE WE'RE DEALING WITH WHOLE NUMBERS FOR OUR FINAL ANSWERS, THAT MEANS THAT EACH STATE SHOULD EITHER GO UP TO THE NEXT WHOLE NUMBER ABOVE ITS QUOTA OR GO DOWN TO THE NEXT WHOLE NUMBER BELOW ITS QUOTA. AND THEN FINALLY, THERE IS SOME CONTROVERSY WHEN USING HAMILTON'S METHOD. AFTER SEEING HAMILTON'S METHOD, MANY PEOPLE FIND THAT IT MAKES SENSE, AND IT'S NOT THAT DIFFICULT TO USE. SO WHY WOULD ANYONE WANT TO USE ANOTHER METHOD? WELL, THE PROBLEM IS THAT HAMILTON'S METHOD IS SUBJECT TO SEVERAL WHAT WE CALL PARADOXES. THREE OF THEM HAPPENED ON SEPARATE OCCASIONS WHEN HAMILTON'S METHOD WAS USED TO APPORTION THE UNITED STATES HOUSE OF REPRESENTATIVES. AND THOSE THREE PARADOXES ARE NUMBER ONE, THE ALABAMA PARADOX, TWO, THE NEW STATES PARADOX, AND THREE, THE POPULATION PARADOX. WE'LL TALK ABOUT EACH OF THESE IN FUTURE LESSONS. I HOPE YOU FOUND THIS HELPFUL.
Common problems
Fundamentally, the representation of a population in the thousands or millions by a reasonable size, thus accountable governing body involves arithmetic that will not be exact. Although weighing a representative's votes (on proposed laws and measures etc.) according to the number of their constituents could make representation more exact,[1] giving each representative exactly one vote avoids complexity in governance.
Over time, populations migrate and change in number. Governing bodies, however, usually exist for a defined term of office. While parliamentary systems provide for dissolution of the body in reaction to political events, no system tries to make real-time adjustments (during one term of office) to reflect demographic changes. Instead, any redistricting takes effect at the next scheduled election or next scheduled census.
Apportionment by district
In some representative assemblies, each member represents a geographic district. Equal representation requires that districts comprise the same number of residents or voters. But this is not universal, for reasons including the following:
- In federations like the United States and Canada, the regions, states, or provinces are important as more than mere election districts. For example, residents of New York State identify as New Yorkers and not merely as members of some 415th Congressional district; the state also has institutional interests that it seeks to pursue in Congress through its representatives. Consequently, election districts do not span regions.
- Malapportionment might be deliberate, as when the governing documents guarantee outlying regions a specific number of seats. Denmark guarantees two seats each for Greenland and the Faroe Islands; Spain has a number of designated seats and Canada's apportionment benefits its territories. Remote regions might have special views to which the governing body should give dedicated weight; otherwise they might be inclined to secede.
- A lowest common denominator between adjoining voters exists, the "voting place" or "administrative quantum" (for example, a municipality, a precinct, a polling district) traditionally designed for voting convenience, tending to unite small clusters of homes and to remain little changed. [clarification needed] The government (or an independent body) does not organize the perfect number of voters into an election district, but a roughly appropriate number of voting places.
- The basis for apportionment may be out of date. For example, in the United States, apportionment follows the decennial census. The states conducted the 2010 elections with districts apportioned according to the 2000 Census. The lack of accuracy does not justify the present cost and perceived intrusion of a new census before each biennial election.
A perfectly apportioned governing body would assist but does not ensure good representation; voters who did not vote for their district's winner might have no representative who is disposed to voice their opinion in the governing body. Conversely, a representative in the governing body may voice the opinions held by a voter who is not actually their constituent, though representatives usually seek to serve their own constituents first and will only voice the interests of an outside group of voters if it pertains to their district as well or is of national importance. The representative has the power, and in many theories or jurisdictions the duty, to represent the whole cohort of people from their district.
Apportionment by party list
For party-list proportional representation elections the number of seats for a political party is determined by the number of votes. Only parties crossing the electoral threshold are considered for apportionment. In this system, voters do not vote for a person to represent their geographic district, but for a political party that aligns with the voter's philosophy. Each party names a number of representatives based on the number of votes it receives nationally.
This system tallies (agglomerates) more of the voters' preferences. As in other systems parties with very few voters do not earn a representative in the governing body. Moreover, most such systems impose a threshold that a party must reach (for example, some percentage of the total vote) to qualify to obtain representatives in the body which eliminates extreme parties, to make the governing body as orderly in non-proportionate systems. With the minimum votes threshold version, if a subtype of single-issue politics based on a local issue exists, those parties or candidates distancing themselves from a broad swathe of electoral districts, such as marginal secessionists, or using a marginal minority language, may find themselves without representation.
The vast majority of voters elect representatives of their philosophies. However, unlike district systems (or the hybrid models) no one elects a representative that represents them, or their specific region, and voters might reduce personal contact with their representatives.
Apportionment methods for party-list proportional representation include:
- Sainte-Laguë method – optimal seats-to-votes ratio[2]
- Hare quota – optimal seats-to-votes ratio[2] and higher apportionment paradoxes[3]
- D'Hondt method – higher seats-to-votes ratio for larger parties[4]
- Droop quota(s
- Imperiali quota
- Huntington–Hill method
These apportionment methods can be categorized into largest remainder methods and highest averages methods.
Malapportionment
Malapportionment is the creation of electoral districts with divergent ratios of voters to representatives. For example, if one single-member district has 10,000 voters and another has 100,000 voters, voters in the former district have ten times the influence, per person, over the governing body. The malapportionment can be measured by seats-to-votes ratio. Malapportionment may be deliberate, for reasons such as biasing representation toward geographic areas or a minority over equality of individuals. For example, in a federation, each member unit may have the same representation regardless of its population.
The effect might not be just a vague empowerment of some voters but a systematic bias to the nation's government. Many instances worldwide arise in which large, sparsely populated rural regions are given equal representation to densely packed urban areas.[5] As an example, in the United States, the Republican Party benefits from institutional advantages to rural states with low populations, such that the Senate and the Presidency may reflect results counter to the total popular vote.[a]
Unequal representation can be measured in the following ways:
- By the ratio of the most populous electoral district to the least populous. In the two figures above, the ratio is 10:1. A ratio approaching 1:1 means there are no anomalies among districts. In India in 1991, a ratio of nearly 50:1 was measured.[6] The Reynolds v. Sims decision of the U.S. Supreme Court found ratios of up to 1081:1 in state legislatures. A higher ratio measures the severity of the worst anomalies, but does not indicate whether inequality is prevalent.
- By the standard deviation of the electorates of electoral districts.
- By the smallest percentage of voters that could win a majority in the governing body due to disparities in the populations of districts. For example, in a 61-member body, this would be half the voters in the 31 districts with the lowest populations. It is persuasive to show that far fewer than 50% of the voters could win a majority in the governing body. But it requires additional research to conclude that such an outcome is realistic: whether the malapportionment is systematic and designed to bias the body, or is the result of random factors that give extra power to voters whose interests are unlikely to coincide.[7]
Even when electoral districts have similar populations, legislators may draw the boundaries to pursue private agendas; see Gerrymandering.
Another form of malapportionment is called reactive malapportionment, which can come about in three ways. The first is the impact of abstentions, in which a lower turnout in a constituency means fewer votes are needed to win there. This can be seen in the UK through the Labour Party's strength in inner city areas where turnout is lowest. The second is the impact of minor parties, which works in a similar way; more votes going to smaller parties means fewer votes are needed for the two larger parties. This form of malapportionment benefits the largest party in an area where minor parties excel. Finally, the instance of a minor party winning a constituency denies victory to one of the two main parties.[8]
Examples of malapportionment
- 1955 System – In Japan, malapportionment benefits the Liberal Democratic Party, who have ruled for over 60 years (with two brief periods in opposition, totaling 5 years). This has been the subject of multiple Japanese Supreme Court cases.[9][10][11]
- Population of Canadian federal ridings – in the Canadian House of Commons, in 2021, the least populous riding had 26,000 people while the most populous had 209,000 people. Several provinces are significantly overrepresented relative to their population.[12]
- The Constitution of Australia guarantees each of the six founding states an equal number of Senators in the Australian Senate, regardless of population. But this would not necessarily apply to other states, were they admitted.
- Bjelkemander – malapportionment in Queensland, during the 1970s and 1980s, designed to benefit the rural-based Country Party who were able to govern uninhibited during this period. The system was named after Sir Joh Bjelke-Petersen, who was leader of the Country Party and Premier of Queensland for 20 years during this period. Bjelke-Petersen's administration eventually became embroiled in corruption and lost an election to the Labor Party, who removed the malapportionment.
- Playmander – malapportionment existed in South Australia from 1938 to 1968. It was designed to benefit the rural-based Liberal and Country League, allowing them to rule with majority of seats, even when the opposing Labor Party won the popular vote. The system was named after Sir Thomas Playford, who was leader of the LCL and Premier of South Australia for 26 years during this period. The malapportionment was mostly removed by LCL leader Steele Hall who was embarrassed at how undemocratic it was.
- The United States Constitution guarantees each state two Senators in the United States Senate regardless of population. For instance, the state of California has 70 times the population of the state of Wyoming, but each has two Senators, making those who live in California vastly underrepresented. In the 21st century, this system benefits white Americans (who are more likely to live in smaller states) and the Republican Party (there are more small red states, than small blue states), who wield political power disproportionate to their numbers. This has grown more impactful as bipartisanship has become less common, with Senators increasingly voting along party lines.[13]
- Rotten and pocket boroughs in England, Great Britain, or the United Kingdom before the Reform Act 1832, which had a very small electorate and could be used by a patron to gain unrepresentative influence within the unreformed House of Commons.
See also
- Apportionment in the European Parliament
- Apportionment in the Hellenic Parliament
- United States congressional apportionment
Notes
- ^ For instance, although the Republican candidate has won the popular vote in only one of the eight presidential elections from 1992 through 2020 (that in 2004), the Electoral College vote - and, thus, the presidency - has been won by the Republican candidate in three of those eight contests (the additional instances being in 2000 and 2016).
References
- ^ "Toplak, Jurij, Equal Voting Weight of All: Finally 'One Person, One Vote' from Hawaii to Maine?" (PDF). Temple Law Review, Vol. 81, 2009, p. 123-176. Archived from the original (PDF) on 2012-01-27.
- ^ a b Pennisi, Aline (1998). "Disproportionality indexes and robustness of proportional allocation methods". Electoral Studies. 17: 3–19. doi:10.1016/S0261-3794(97)00052-8.
- ^ Balinski, Michel; H. Peyton Young (1982). Fair Representation: Meeting the Ideal of One Man, One Vote. Yale Univ Pr. ISBN 0-300-02724-9.
- ^ Bochsler, Daniel (2010). "Who gains from apparentments under d'Hondt?". Electoral Studies. 29 (4): 617–627. doi:10.1016/j.electstud.2010.06.001.
- ^ Liptak, Adam (March 11, 2013). "Smaller States Find Outsize Clout Growing in Senate". The New York Times. Retrieved December 10, 2016.
- ^ The largest district, Thane, had a population of 1,744,592, while the smallest district, Lakeshadweep, had a population of 31,665.
- ^ "Engine". Localparty.org. Retrieved 2010-04-18.
- ^ Johnston, Pattie, Dorling, Rossiter, Ron, Charles, Danny, David. "Fifty Years of Bias in the UK's Electoral System" (PDF). geog.ox.ac.uk. APSA. Retrieved 24 January 2021.
{{cite web}}: CS1 maint: multiple names: authors list (link) - ^ "Fixing Japan's gerrymander". 29 April 2022.
- ^ "Japan's Electoral Unfairness Goes Deeper than Malapportionment". 5 April 2013.
- ^ "Japan's electoral map favours the ruling party". The Economist.
- ^ "One person, one vote? In Canada, it's not even close". Toronto Star. 13 October 2019.
- ^ "'The Senate is broken': system empowers white conservatives, threatening US democracy". The Guardian. March 13, 2021. Retrieved March 30, 2023.
External links
- Index of articles relating to Boundary Delimitation from the ACE Project
- A guide to the various formulae for apportionment, and statistical differences between them
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This page was last edited on 7 May 2024, at 18:42