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Emma Holbrook

Honors Thesis

April 22, 2014

Faculty AdvisersDr. KuhlmannDr. Hardwick

Second Reader Dr. Christine Kinsey

Title

Replacing the Apportionment Method of the Electoral College and the House of Representatives: Replacing Huntington-Hill Apportionment with Dean’s method and Re-adjusting to Population Shifts

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Table of Contents

Introduction 3

THESIS STATEMENT 4

UNITED STATES GOVERNMENT APPORTIONMENT USAGE OVERVIEW 4

IMPORTANT TERMINOLOGY FOR APPORTIONING THE HOUSE OF REPRESENTATIVES AND ELECTORAL COLLEGE

8

THE HISTORY OF APPORTIONMENT METHODS 9

THE EFFECT OF FAIRNESS CRITERIA ON APPORTIONMENT METHODS12THE UTILIZATION OF HUNTINGTON-HILL APPORTIONMENT

15RETURNING TO THE WEBSTER METHOD 16MONTANA V. UNITED STATES DEPARTMENT OF COMMERCE: WHEN DEAN METHOD CHALLENGED HUNTINGTON-HILL METHOD 17THE REASONING BEHIND THE DEAN METHOD OF APPORTIONMENT 21

RISKS IN MAKING FUTURE CHALLENGES TO HUNTINGTON-HILL IN COURT 23

REASONS FOR MORE FREQUENT CENSUSES FOR STATE APPORTIONMENT 24

UTILIZATION OF CENSUSES RATHER THAN SAMPLING FOR APPORTIONMENT 27

THE CURRENT HOUSE SIZE FLAWS THE PRESIDENTIAL ELECTION 29

REASON TO TRANSFORM STATE REPRESENTATION IN THE HOUSE OF REPRESENTATIVES AND ELECTORAL COLLEGE: VOTER DISSATISFACTION 32CONCLUSION 35BIBLIOGRAPHY 38

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Introduction:

The United States Constitution was a product of compromise. At the Constitutional

Convention, in 1787, the Framers agreed over a separation of powers and three branches

of federal government. Nevertheless, they could not agree on how the legislative branch

should be constituted. Small states backed the New Jersey plan, while large states backed

the Virginia plan. Finally in the end, a compromise was struck between the two plans.

The final product mandates that representation in the House of Representatives shall be

based on the states’ populations, but it does not specify the exact apportioning method in

which this shall be achieved. This unspecified method has significant implications on the

Presidential Elections also because the number of Electoral votes a state receives is

contingent on the number of members in the House. Since 1787, several different

apportionment methods have been employed, each demonstrating bias. Yet in 1941,

Congress established the permanent method of apportionment known as the Huntington-

Hill method. By examining close elections, evidence portrays how this method fails to

fairly seat the House of Representatives and the Electoral College. As a result, citizens of

Montana proposed new methods of apportionment in the 1990s.

Montana suggested an alternative, the Dean Method, to replace the Huntington-Hill

Method. I argue in this paper, that the Dean Apportionment method acts as a plausible

replacement for apportioning the House of Representatives and the Electoral College.

The replacement of the Huntington-Hill method, accompanied by more frequent censuses

increases citizens’ approval of seating in the Federal government. More frequent censuses

maintain the accurate representations necessary for seating the modern government. Due

to an aging United States population, domestic migration, and the geographically

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heterogeneous effects of foreign immigration, the distribution of population shifts

frequently. Population shifts alter the seating in the House and the Electoral College. In

addition, large House sizes increase citizens’ satisfaction with the House and the

Electoral College because for large House sizes, the relative representation of the states in

the Electoral College becomes closer to their relative representation in the House.

Thesis Statement:

Political results from close elections and controversial United State Supreme Court

cases demonstrate that the Huntington-Hill apportionment method fails to fairly seat the

House of Representatives and the Electoral College. Despite laws preventing replacement

of Huntington-Hill, the Dean method appears to be an attractive replacement. Utilization

of the Dean method, accompanied by more frequent censuses, and a large House size will

increase citizen voter approval in the Presidential Elections as positions in the Electoral

College will more accurately represent the state ratio in the House of Representatives.

United States Government Apportionment Usage Overview:

Apportionment of seats in the House of Representatives causes arguments since

objects are being divided and there is a proportionality criterion for division. The

Apportionment debate, concerning the makeup of the legislature, began at the

Constitutional Convention. At the Convention, small states wanted all states to have the

same number of representatives, whereas larger states wanted some form of proportional

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representation (Tannenbaum 123.) As a result, the House of Representatives was

composed by proportional representation and the Senate had a fixed number of seats

constant for every state. Ernst explains how in, “Article I, Section 2 of the U.S.

Constitution requires that the House of Representatives ‘shall be apportioned among the

several States according to their respective Numbers,’ and that ‘each State shall have at

least one Representative’” (Ernst 1207.) Thus, apportionment was only necessary for the

House of Representatives since seating would be proportional to each state’s population.

In 1787, the Constitutional Convention was authorized by Congress in order to

revise the Articles of Confederation, which been in session since May 25. In his article,

"A Great Compromise Settles the Acrimony the House and Senate are Born Out of

Necessity. A Great Compromise Settles the Acrimony," Michael Schaffer describes how

Paterson, an attorney offered the New Jersey Plan as a blueprint for national government

that has been the center of the meeting's attention up to now (Schaffer, 2003.) The

proposal for government, prepared with the collaboration of delegates from New Jersey,

Connecticut, New York, Delaware and Maryland, called for a one-house Congress with

an equal vote for each state.

The New Jersey Plan takes the larger population of the big states into account in

one important way; Congress would have the power to tax states based on their

population. The New Jersey Plan also proposed a weak executive, with power vested in

several officials elected by Congress. Paterson argues that the New Jersey Plan keeps

with the powers vested in the Constitutional Convention and "the sentiments of the

people," which are not ready for a national government (Schaffer, 2003). Not

surprisingly, given the convention's deepening rift between big-state and small-state

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delegates, the convention heated when debate on the New Jersey Plan began on June 16.

Promoters of the New Jersey Plan believed that the Virginia Plan, which was crafted by

James Madison, would leave the states the authority to deal only with "little local

matters” as the larger states would have more control (Schaffer, 2003). Madison believed

the New Jersey Plan was an effort to secure to the smaller states equality with the larger

states in the structure of the government. On June 19, Madison dissected the Jersey

proposal with relentless precision. When he finished, the convention votes ended in 7 to

3, with the Maryland delegation divided, in favor of the Virginia Plan (Schaffer, 2003.)

Still the vote did not bring harmony because the delegates argued about the number

of seats each state should have in the national legislature. They could not decide if

representation should be based on population or if each state have the same number, so

later, Committee Member Sherman suggested that each state have the same vote in one

house and a vote based on its population of citizens in the other (Schaffer, 2003). After

some discussion, the committee recommended a plan calling for each state to have one

representative for every 40,000 inhabitants (including three-fifths of all slaves) in the first

house of the national legislature and an equal vote in the second house. All bills related to

money began in the first house, the House of Representatives, and were not altered by the

second house, the Senate. On July 16, the compromise, known as the Great Compromise,

the Federal Compromise, and the Connecticut Compromise squeaked through the

convention, 5 to 4, with Massachusetts divided, the New York delegates absent, the New

Hampshire delegates absent, and Rhode Island not participating (Schaffer, 2003).

Historians recognize that the agreement did indeed address the central issue of the

convention, that of balancing the competing interests of different states through

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compromise over representation in the national government (Festa 2020.) It was a

pragmatic arrangement: small states preserved their role as sovereigns through equal

representation in the Senate, while the proportional representation in the House gave

leverage to the larger states who were further mollified by the exclusive origination of

revenue and spending bills in that body (Festa 2020.) Still, some delegates introduced a

set of concerns regarding the proposed selection by Congress because they feared that

giving complete control to the legislative branch would compromise the independence of

the executive (Festa 2023.) Wilson of Pennsylvania thought of a solution similar to

House of Representatives: an appointment by the people to make the executive and the

legislature "as independent as possible of each other” (Festa 2023.) He also proposed,

"the States be divided into districts," where voters choose "Electors" who meet to elect

the "Executive magistracy” (Festa 2023.)

Yet after the Great Compromise incorporated both proportional representation in

the House and equal representation in the Senate, the delegates turned back to the issue of

the executive, this time with a structural model for a balance between federal and state

power. The number of Electors for each state electing for the executive branch is the sum

of a fixed component and proportional component based on the seating for the legislative

branch. Originally, the Virginia Plan, Madison's proposal for a national government,

called for a "National Executive" to be chosen by the "National Legislature" (Festa

2022.) In the New Jersey Plan also advocated selection of the executive by the

legislature, the proportion component corresponds to the number of seats in the House of

allocated to each state. For instance, in 2000, the state of California had 54 seats, while in

the Senate the state had 2 Senators, totaling 56 Electors for the presidential election. The

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convention delegates’ concerns about the independence of the executive office were now

tied to the question of the proper federal balance-animated, as always, by the states'

relative interests. Still, even after the creation of the electoral college, determining an

apportionment method to distribute the seating for each state’s representatives in the

House and Electoral College electors has been a continued debate throughout United

States history.

Important Terminology for Apportioning the House of Representatives and

Electoral College

In order to understand the difference between apportionment methods techniques, it

is essential to understand certain terminology. First, ‘states’ refers to the players involved

in the apportionment, and ‘seats’ is the term utilized to describe the set of M identical,

indivisible objects that are being divided among the N states (Tannenbaum 127.) Used as

the basis for the apportionment of the seats to the states, the ‘population’ is the set of N

positive numbers. The ratio of population to seats, referred to as the ‘standard divisor,’

gives us a unit of measurement for our apportionment calculations; thus, the standard

divisor of people is equivalent to one seat (Tannenbaum 127.)

Another important term to remember, ‘the standard quota’ of a state, is the exact

fractional number of seats that the state would get if fractional seats were allowed. In

order to find a state’s standard quota, divide the state’s population by the standard

divisor. In general, the standard quotas can be expressed as fractions or decimals; one

rounds the standard quotas to two or three decimal places and one uses the notation q1,

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q2,..., qN to denote them to their respective states (Tannenbaum 127.)

When creating an apportionment method, mathematicians realize that there are an

infinite number of possible divisor methods, but only five methods have a significant role

in apportionment history. Other apportionment methods are cast aside due to fairness

criteria checks that I explain later in the paper. For each divisor method, the number of

seats assigned to a state designated based on state’s population. The divisor, denoted as

X, can be thought of as a target district size; the divisor must be the same for each state

(Ernst 1208.)

The History of Apportionment Methods

Alexander Hamilton's method of apportionment was the first to be adopted by

Congress in 1792, but was not then used. Thomas Jefferson persuaded George

Washington and Jefferson's method was then adopted (Bradberry 5.) Subsequently,

abandoned Hamilton's method was re-adopted two generation later.

Hamilton’s method, also known as the method of greatest remainders, was the

apportionment method used for the House and the Electoral College for the first five

censuses through 1830. Congress later grew dissatisfied with Hamilton’s method,

because the method appeared to favor large states (Ernst 1208.) Consequently, due to

dissatisfaction from small states, the method of major fractions, known as the Webster

method, replaced Hamilton’s method in 1840 (Ernst 1208.). Hamilton’s method returned

as the specified method again from 1850 to 1900 because for censuses within this time

period. The apportionment was altered because it is possible for a state to lose seats if the

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House size is increased with a fixed set of state populations when states were apportioned

by Hamilton’s method (Ernst 1208.) The anomaly, known as the "Alabama paradox,"

observed in the 1880 census, is one of a few paradoxes that I will introduce later in the

paper along with Fairness Criteria.

In addition to the altered apportionment allocations, the House and Electoral

College were not automatically fixed in size during the period of use of Hamilton’s

method (Ernst 1209.) Thus, the House was not always fixed as a size of 435 as it is today.

Congress, following each census, after reviewing the allocations with various House

sizes, decided the size of the House of Representatives. Fractional seats were not as

complicated when the size of the House was determined after reviewing the each census.

This process implies that Hamilton’s method of apportionment was a simpler process

than modern methods. Yet simpler does not imply fairer, hence, Congress then decided to

return to Webster’s method for the 1910 census.

Due to fair arguments made by mathematicians, Congress fixed the House size at

435 by law about the time of the 1920 census. Also around this time, Professor Edward

Huntington of Harvard refined Joseph Hill’s unaccustomed method from 1911 to become

the principal advantage of the method of equal proportions (Ernst 1209.) Huntington’s

revision of Hill’s earlier method is named the Huntington-Hill apportionment method.

His method is, as Huntington claims, “the champion of the method of equal proportions”

because Huntington describes, “The "multipliers" (to the fractional seats) are the

reciprocals of the geometric means of consecutive integers; hence the method of equal

proportions may be called also the method of the geometric mean” (Huntington 863.)

Huntington promotes other evidence of fairness from utilization the Huntington-

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Hill method; the method is pairwise optimal with respect to relative differences in both

district sizes and shares of a representative. Pairwise optimal involves making sure that

when switching a seat from one state to another, it does not diminish the fairness of the

apportionment as given by some measure of fairness. In order for a method to be pairwise

optimal with respect to a particular measure of inequity, no transfer of representatives

between any pair of states decreases the amount of inequity between these states. The

case for the Huntington-Hill method consequently rests on these pairwise optimality tests.

Huntington further supports his method as he displays a calculative test made by

the American Mathematical Society to test “the average error.” Huntington promotes his

method also as he states, “It can be shown that in any given case the method which makes

the value of this total or average error a minimum, is precisely the method of equal

proportions” (Huntington 865.) Evidence and fairness criteria support the early argument

of the Huntington-Hill method from the 1920s.

Congress looked to switch to Huntington-Hill as a result of Huntington’s

promotions. Yet the 1930 allocations for the Huntington-Hill and Webster methods were

identical, so Congress had no need to take further action to allocate officially in the name

of the Huntington-Hill method (Ernst 1212.) Thus, under the applicable law, the House

was automatically apportioned under the method last used, the Webster method.

Nevertheless in 1940, apportionment allocations by the Huntington-Hill method

and by the Webster method differed for Arkansas and Michigan. As a result, Congress

officially adopted Huntington's reasoning rather than Webster’s. Congress then declared

that the Huntington-Hill method was the preferred method on the basis of the pairwise

tests, for which it is optimal. Congress described the Huntington-Hill method as

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“mathematically occupying a neutral position with respect to emphasis on larger and

smaller states" (Ernst 1212.) The legislation was enacted apportioning the House by the

Huntington-Hill method in 1941, on a mainly party line vote. This method has been used

ever since and, also under the 1941 law, the Huntington-Hill method’s continued use is

automatic until superseding legislation is enacted.

Consequently, the Huntington-Hill method has been used without any serious

competition from alternative apportionment methods until 1991. At this time, the states of

Montana and Massachusetts initiated separate lawsuits in federal court. I will discuss the

significance of Montana’s lawsuit later.

The Effect of Fairness Criteria on Apportionment Methods

Fairness criteria challenge the acceptance of new apportionment methods. The

fairness criteria are necessary for the legislature’s efforts to apportion votes with a

reliable procedure that will always yield a valid or fair apportionment in any population-

based situation. The federal government, such as the Supreme Court during lawsuits,

turns to the criteria to test incoming challenges by alternate apportionment methods.

The most common fairness criteria were brought up during the first few censuses

when apportioning the House and Electoral College. These fairness criteria entail that no

state be apportioned a number of seats smaller than its lower quota or larger than its

upper quota (Tannenbaum 129). When a state is apportioned a number smaller than it’s

standard quota rounded down, it is a violation of the lower-quota violation. The standard

quota rounded down is its lower quota and the standard quota rounded up is its upper

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quota. An upper-quota violation is when a state is apportioned a number larger than its

upper quota (Tannenbaum 129.) Yet, apportionment methods that violate these criteria

are rarely utilized now.

Other criteria became easily recognizable in later censuses. For example, although

Hamilton's method, both simple and straightforward, clearly stays within fair share quota,

three paradoxes affect this method, consequentially making it unacceptable. The Alabama

Paradox was the first paradox to disqualify, Hamilton's method from House and Electoral

College apportionment allocation. In the Alabama Paradox, a state may unjustly lose

representative seats as the size of the House of Representatives increases, even when the

number of states and their populations remain unchanged (Bradberry 6.) The Alabama

Paradox was recognized as a serious issue that government avoided in further censuses.

Jonathan W. Still describes U.S. government’s focus on this paradox in his article, "A

Class of New Methods for Congressional Apportionment" stating that, “In Balinski and

Young’s terminology, an apportionment method that avoids the Alabama paradox is

"house monotone." While not having the strong intuitive appeal of ‘satisfying quota’ as a

requirement, house monotonicity came to be a political necessity” (Still 402.)

The other two paradoxes are not as well known. The Population Paradox is another

paradox affected by Hamilton’s method. This paradox implies that where there is a fixed

house size and a fixed number of states, it is possible that a given state may lose

representation to a second state even if the first state's population is growing faster than

the second state (Bradberry 6.) The other paradox effecting Hamilton’s method is the

New States Paradox. This paradox states that if a new state enters, bringing in its

complement of new seats, a given state may lose representation to another paradox even

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when there is no change in either of their populations (Bradberry 6.) A state’s

complement of new seats is the number it should receive under the apportionment

method in use.

To prevent violations of the paradoxes introduced, mathematicians Balinski and

Young proposed five axioms to recognize when creating apportionment methods in order

to avoid paradoxes interfering with fairness. Their first axiom was ‘The Population

Monotonicity Axiom,’ which states that no state that increases in population loses a seat

to a state that decreases in population (Bradberry 4.) The next axiom composed was the

‘The Absence of Bias Axiom’ states that each state, over a period of time, will receive its

fair share on average (Bradberry 4.) ‘The House Monotonicity Axiom’ necessitates that

for a fixed population, as the total number of states increases, no state will lose a seat

(Bradberry 4.) Additionally, ‘The Fair Share Axiom’ entails that the number of state's

representative seats is not equal from its fair share. The numbers must differ by one

whole seat or more (Bradberry 4.) ‘The Near Fair Share Axiom’ requires that there are

no transfers of seats between states that bring both states nearer to their fair shares

(Bradberry 4.)

Unfortunately, the most important result in the history of the apportionment

problem is the impossibility theorem stated by Balinski and Young, which declares that

there exists no method of apportionment that satisfies these five axioms (Bradberry 4.)

Thus, no divisor method stays within fair share, but a method can only be population

monotone if and only if it is a divisor method. No method can stay within fair share and

be population monotone.

The ultimate issue is deciding whether a method is fairer by staying within fair

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share or by being population monotone. We will use this question to judge the

Huntington-Hill Apportionment method’s relative fairness compared to alternative

methods.

The Utilization of Huntington-Hill Apportionment

Why is the Huntington-Hill Apportionment method currently used to apportion the

seats for the Electoral College and House of Representatives in the United States?

Huntington explains in his defense of this method that, “The inequality between two

states is thus reduced to the more definite concept of the inequality between two

numbers. The question then comes down to this: what shall be meant by the inequality

between these two numbers” (Huntington 86.) Huntington argues the credibility of his

method by taking the absolute difference between the two numbers, or the relative

difference between them based on the size of the congressional districts. The Method of

the Harmonic Means favors the small states compared to the Method of Major fractions,

while the later method favors the large states (Huntington 91.) The Method of Equal

Proportions may be described as the only method which makes the ratio of population to

representatives and the ratio of representatives to population nearly uniform as possible

among the several states based on "comparison tests” (Huntington 108.) Still, the

Huntington Hill method has caused unlikely outcomes, such as in the 2000 presidential

election. Additionally problematic, the desire to avoid the Alabama paradox when

creating Huntington-Hill apportionment method caused ignorance towards the quota

problem.

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The Equal Proportions Method does not satisfy quota, even though the problem has

not caused much controversy (Still 402.) The four times that the Equal Proportions

Method has been used, only by chance the resulting apportionment satisfied the quota

(Still 402.) But there are no promises those specific apportionments by the Huntington-

Hill method can continue to satisfy the quota. As a result, there will most likely be

lawsuits from affected states when apportionments do not satisfy the quota under the

Huntington-Hill apportionment method. Consequently, many wonder if it is a better

option to replace the apportionment method with another.

Returning to the Webster Method

The method of Webster rounds the quotient population and the divisor to the

nearest integer number; if the U.S. government returned to utilizing the Webster method,

the probability that Webster violates this property called “staying within the quota” is

negligible (Barthélémy and Martin, 93.) Furthermore, the method of Webster is the only

divisor method that respects the property of being “near the quota”. The property of being

“near the quota” says that if a State gives one seat to another State, it is not possible that

the new number of seats of these two States brings them simultaneously nearer their

quota (Barthélémy and Martin, 93.) If the government choses to focus on this property,

the Webster Method will be more qualified to replace the Huntington-Hill Apportionment

method.

Another important property satisfied by the method of Webster concerns a possible

bias. It is certainly a negative characteristic if a method has a persistent bias in favor

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either the small States or the large States. There are several ways of measuring this bias.

One way to measure bias is absolute by asking if a state always receives more seats than

its quota (Barthélémy and Martin, 94.) Additionally, a relative one measure of bias asks

if a state always receives more seats for one citizen than another state (Barthélémy and

Martin, 94.) The only divisor method without either absolute bias or relative bias is the

method of Webster (Barthélémy and Martin, 94.) This theoretical and empirical result is

the fundamental argument for returning to the Webster method. By having a good

balance between population and power implies that every citizen in the country has the

same power whatever the state he or she belongs to. Many suggest this trait is a condition

of democracy.

Montana v. United States Department of Commerce: When Dean Method

Challenged Huntington-Hill Method

The United States Supreme Court opposes any challenge to the apportionment

method of the House of Representatives and Electoral College since 1941. The barrier

against the replacement of methods was demonstrated in the lawsuit initiated by the state

of Montana in federal court challenged the constitutionality of the current method, the

Huntington-Hill method. In Montana v. United States Department of Commerce in 1991,

Montana proposed two methods as alternatives to the method of equal proportions (Ernst

1213.). Montana preferred the method of harmonic means, also known as the Dean

method, and the method of smallest divisors, also known as the Adams method. Both

advantageous to Montana, each method would have given Montana two seats instead of

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the single seat allocated by the Huntington-Hill method (Ernst 1213.) Montana first

succeeded by a two-to-one majority because when the original ruling came from a three-

judge panel in the Montana case, the panel ruled that the method of equal proportions was

unconstitutional. Two of the judges said that the method of equal proportions fails to

minimize the absolute discrepancies among states as to the number of citizens per

representative (Barrett 1992.) The third panel member dissented. Under an alternative

formula urged by sparsely populated Montana, the state would have continued to get two

representatives, while Washington state would have lost one of the nine House seats it

had been allocated.

Yet the Bush administration took charge when the administration appealed the

decision of the three-judge district court in the Montana case to the Supreme Court.

Consequently, in 1992, the Supreme Court unanimously upheld the constitutionality of

the Huntington-Hill method of apportionment. Justice Stevens brought forth the ruling of

the Supreme Court as and rejected Montana's argument that the method of apportionment

must achieve precise mathematical equality (Barrett 1992.) He deferred to Congress by

arguing that Congress deserves broad deference to choose a method of apportionment, as

long as it exercises good faith and he stressed that the current method had been endorsed

by independent scholars as fair and has been accepted for 50 years without significant

problems (Barrett 1992.) Furthermore, Justice Stevens finalized the case by stating that

the principle of equality required for intrastate districting applies to interstate

apportionment and that the court concluded that there is no unsuitability to minimizing

both absolute and relative differences. Stevens furthered that all districts within a state

can be brought closer to the ideal simultaneously, based on the legal reasoning of

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Wesberry v. Sanders in 1964.

In 1964, The U.S. Supreme Court had ruled earlier by the "one person, one vote"

principal, that the intrastate redistricting of congressional districts must provide "equal

representation for equal numbers of people" (Ernst 1213.) By meeting the “one person,

one vote” principle, apportionment must minimize "absolute population variances

between districts" (Ernst 1213.) Though the court based their reasoning on a test designed

for district sizes, they concluded that this test was more reliable than a test than one based

on shares of a representative. Hence, their reasoning is mislead and unreasonable for

apportioning the Electoral College and House of Representatives.

In addition, The Supreme Court assumed that absolute difference is a better

measure than relative difference even though the issue of the best test does not apply for

intrastate redistricting. Differences can be made as close to zero as desired for any of

these methods of measurement, so that argument does not support the utilization of the

absolute difference test. The Montana lawsuit lacked evidence to answer why absolute

difference in district sizes is the appropriate test to cite redistricting cases.

Further, plaintiffs also assume that by measuring absolute population variance

among all districts, they determine the bias of the apportionment methods. As evidence,

the defendants observed that the method of equal proportions that always minimizes the

measure absolute population variance among all districts. The defendants also claim that

the method of Harmonic means results in the smallest such variance. They support the

Huntington-Hill despite the conflicting lack of bias of the Dean Method. This reasoning

disagreement in the claims results from the formula used by the plaintiffs. Their formula

did not take into account the number of districts in each state since it measures variability

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among the mean district sizes of the 50 states. The result fails to take into account the

variance of the sizes of the 435 districts, even though this variance is the criterion

actually stated in the plaintiffs' briefs. (Ernst 1214.)

Even though, Justice Stevens stated that a measure of deviation from the ideal

district size should take into account the number of districts in each state, he then made

the critical observation that "neither mathematical nor constitutional interpretation

provides a conclusive answer" to the question of the best measure of inequality. Either by

pairing absolute or relative difference with either district size or share of a representative,

he concluded: "The polestar of equal representation does not provide sufficient guidance

to allow us to discern a single constitutionally permissible course." Thus, the Supreme

Court concluded that the goal of mathematical equality, while appropriate in the intrastate

context, is illusory for interstate apportionment, since each state must have at least one

representative and districts cannot cross state lines.

Still, the Court ruled that a fair apportionment required some compromise between

the interests of the smaller and larger states, and indicating that Congress had been

delegated the authority in the Constitution to reach this compromise. Justice Stevens

concluded his answer, “The decision to adopt the method of equal proportions was made

by Congress after decades of experience, experimentation, and debate about the

substance of the constitutional requirement…That history supports our conclusion that

Congress had ample power to enact the statutory procedure in 1941 and to apply the

method of equal proportions after the 1990 census.’” (Ernst 1222.)

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The Reasoning Behind The Dean Method of Apportionment

James Dean proposed first proposed his method in 1832. He proposed that the

absolute difference between district sizes between any two states be made as small as

possible for a given House size. If a transfer of one seat from one state to another state

lowers the difference in district sizes for two states, such a transfer should be made

(Neubauer and Gartner 77.)

If the House had been set at 1,285 members after the 1990 census, California would

have received 155 seats under the Huntington-Hill apportionment method. Yet according

to the second condition of Article I, Section 2, of the Constitution, California's share in a

House of that size could only be 153.98. This is an instance of a quota violation, which

would certainly be a hard pill for other states to swallow (Neubauer and Gartner 78.),

such an occurrence would be viewed as a very severe violation of the idea of fairness and

should be avoided at great cost. Even though if we fix a House size and choose Dean's

method we run the risk of violating the quota, quota violations occur for less than 1% of

House sizes for Dean’s method (Neubauer and Gartner 78.)

In Montana v. United States Department of Commerce, the court case mentioned

earlier, Montana claimed that the Dean method minimizes the absolute deviations from

the ideal district size (Edelman 307.) By absolute deviation is the sum of the differences

between the average district size of the states and the ideal district size. Montana

reasoned that when taking the difference between the average district size and the ideal

district for all 50 states, and then adding them together, the sum is be smaller when using

the Dean apportionment than when using any other apportionment (Edelman 307.)

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Consequently, Montana concluded Dean Method was the best method for minimizing the

absolute deviations from ideal district size; Montana furthered that the Dean method

better approximated "one person, one vote" than did the Hill apportionment.

When ruling the case, The Supreme Court focused on computing the differences for

Montana and Washington; Under the Hill Method, the absolute difference between the

population of Montana's single district and the ideal district was 231,189 (Edelman 309.)

The difference between the average Washington district and the ideal was 29,361. The

sum of the deviations from the ideal in the two states was 209,165 under the Dean

Method, while it was 260,550 under the Hill Method. Both absolute deviation and total

deviation are smaller under the Dean apportionment than under the Hill apportionment

just as Montana claimed (Edelman 310.) Still, even though the Dean Method had the

lower absolute deviation, the Court justified Huntington-Hill by throwing up its hands

when its favorite method of analysis contradicted the claims of Montana. The Supreme

Court conclusively chose to turn to a "polestar of equal representation," which can guide

the Court through the apportionment dilemma. That polestar is a measure of minimum

total deviation (Edelman 311.)

The Court's ruling against Montana flawed mathematically on the basis of how

chose best to approximate "one person, one vote” because the Court did not unify its

decision with the other districting cases with the apportionment of Congress (Edelman

311.) For example, in the line of congressional districting cases from Wesberry to

Karcher, the Court established total deviation as the measure of disparity from equal

district size and concluded Article I, §2 requires the apportionment of Congress be one

that achieves the minimum total deviation. The total deviation from the ideal district is

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the one that the Court has established for districting cases to turn to when measuring "one

person, one vote." Minimizing total deviation is the "polestar" for which the Court should

have been searching in Department of Commerce (Edelman 313.)

If the Court was willing to stretch Article I, §2 to apply to intrastate districting in

Wesberry v. Sanders, it surely should apply similar reasoning to interstate districting

(Edelman 320.) The standard set in Wesberry is never directly confined to intrastate

districting. There is no excuse for ignoring our Constitution's plain objective of making

equal representation for equal numbers of people the fundamental goal for the House of

Representatives. It is difficult to believe that this "fundamental goal" applies within a

state but not between states because Wesberry is based on the only clause in the

Constitution that speaks to the apportionment of the House.

Risks in Making Future Challenges to Huntington-Hill in Court

The equal protection argument protecting Huntington-Hill apportionment for the

Electoral College falls short of overcoming the same constitutional roadblocks that have

prevented a general challenge to the Electoral College. For example, the Fourteenth

Amendment does not alter the original federal-state balance, which was created to

remove the states from their constitutional role in selecting the President (Festa 2101.) In

addition, the Article II text and the system of dual sovereignty places a state's choice of

the unit rule, or any other method, above the reach of any judicial interference; only

unilateral action by state legislatures or a constitutional amendment will alter the practice.

The Constitution has been interpreted to place state legislatures ability to choose the

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method beyond the reach of a legal challenge on general majoritarian grounds. In

addition to the textual commitment in Article II, the electors are to be appointed in the

states "in such Manner as the Legislature thereof may direct,” but the federalist structure

of the Constitution contemplates a distinct role for the states in national elections, and

thereby places the Electoral College outside the framework of a challenge on general

democratic principles (Festa 2102.) Critics argue that since the winner receives the entire

electoral vote of the state, those who voted for a different candidate are not represented in

the Electoral College, and their votes are "counted only for the purpose of being

discarded" (Festa 2101.) Yet even though this very premise is subject to challenge on

constitutional and general political science grounds, the argument does fit more

accurately within the framework of a viable equal protection claim.

Still, there are four possible avenues for changing the apportionment method and

reforming the Electoral College: constitutional amendment, unilateral action by state

legislatures, lawsuit, or federal legislation. The first two options are both unlikely to

occur because of the long process involved, but for the other two methods, note that a

state's choice to employ the unit rule would be impermissible if the unit rule is indeed

inconsistent with the Fourteenth Amendment (Festa 2101.) The argument concludes that

while the states' discretion is constitutional, the particular exercise of that discretion to

employ the unit rule is not.

Reasons for More Frequent Censuses for State Apportionment

The Electoral College and the House of Representatives are time-honored; thus, the

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number of seats is based on a census taken every ten years. Each census launches the

process of redistricting, in which each state redraws congressional district boundaries to

make each district roughly equal in population. In some cases of censuses, the frequent

shift of population gives one party a significant electoral advantage. Understanding of

population dynamics at both the state and national levels is key to understanding the

modern population’s movement effect on the censuses taken for the apportionment of

seats in both the House and Electoral College.

The fundamental problem of the census is that the states of the United States are too

disparate in size and influence. The population shifts too dramatically within ten years for

the census to be an accurate representation of each state. In “The Electoral College after

Census 2010 and 2020: The Political Impact of Population Growth and Redistribution”,

Edward M. Burmila displays characteristics of population change as he describes,

“Demographers have long understood these dynamics by isolating the three components

of population change: interstate domestic migration, foreign immigration, and the rate of

natural replacement (births relative to deaths) among static population” (Burmila 837.)

By focusing on the shifts of the population in order to predict future population shifts and

by taking more frequent censuses, the apportionment of seats will more accurately

represent the population of each state in the United States.

Analysis of population dynamics focuses on the baby boom generation. The

boomers highlight the importance of interstate domestic migration to population balance

among states and regions. Census data from domestic migration by immigrants between

2000 and 2007 show that seven of the biggest population gainers are Sun Belt states

(Burmila 838.) The biggest lost of population is almost entirely in the Midwest,

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Northeast, and Plains. Migrants are moving across state lines, resulting in net growth in

Sun Belt states at the expense of traditional northern population centers due to retirees

born in the Baby Boom. This migration trend is expected to continue or intensify as the

boomers reach their mid-sixties (Burmila 838.) The large size of the migrating population

dramatically affects the balance of population among states.

Frost Belt states such as the Upper Midwest, Northeast, and Mid-Atlantic are

predicted to lose representation and electoral votes to the growing Sun Belt states like

Florida, Texas, and Arizona. Sun Belt states are magnets for both domestic and foreign

migration and thus, grow faster than states in other regions. The South is popular as

millions of retirees from the Baby Boom flee the weather of northern states.

By studying components of population change, mathematicians can derive accurate

estimates of population within the next few years based on existing data. Population

projection may reflect trends currently occurring, but it fails to predict future trends, such

as trends due to national disasters (Burmila 838.) It is not possible to predict trends that

will develop in the future accurately. Only predictable trends, such as current migration

due to retiring populations and international immigration, influence the accuracy of these

projections. Burmila argues that, “While perfect accuracy is not possible when making

projections, Census projections based on contemporaneous data and trends have proven

to be reliable over short-time horizons and as predictors of total population for large

geographic units such as states” (Burmila 838.)

Contemporary improvements in data quality and the use of proven methodology

increase the accuracy of current forecasts. Based on these population projections,

Electoral College maps are derived. But creating population projections requires two

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assumptions in order qualify the results (Burmila 838.) The first assumption presumes

that over time, there no major changes in the party system because researchers assume

that the ideological positions of or coalitions making up the major parties will not change.

The second assumption presumes that there are no significant changes in the Electoral

College. For example, researchers presume states that award electoral votes on a winner-

take-all basis to the plurality winner of the popular vote will continue to do so. Luckily

for researchers, most states have unsuccessful referenda when attempting to alter their

Electoral College voting systems.

Utilization of Censuses Rather than Sampling for Apportionment

Sampling changes its results rapidly, exemplified as sampling, rather than a

complete census happened to the networks predictions on election night 2000.  Early in

the evening they all gave Florida to Gore based on exit polls (i.e. sampling) and their

mathematical models (By 2014.)A couple hours later, they pulled it back to undecided,

and then they gave it to Bush, then back to undecided. 

Yet, congressional members reason against the large population by arguing that

censuses leave the door open for undercounting minority groups. In response, Republican

congressional members fight the democratic plan to use sampling, by arguing that

statistics can be manipulated for political purposes and that every person ought to be

physically counted (By 2014.) Republicans argue further that despite the errors the

Census Bureau made in 1940, where 5.4% of the population was not counted in the

Census, undercounting is diminishing over time. Results show that in 1990, only 1.8% of

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the population was missed and no more than 1.4% of the population was missed in the

2000 Census (By 2014.)

The Federal government fought off the possibility for sampling the population

when the Supreme Court barred the use of sampling to reapportion congressional seats.

House Republicans filed the lawsuit in federal court in 1998 in order to prevent the

Clinton administration from relying on statistical sampling to complete a national head

count for the 2000 census. The suit argued that the plan to use sampling violates the

Constitution, which calls for an "actual enumeration" of the population (Vobejda 2014.)

In the Supreme Court ruling in 1999, Justice Sandra Day O'Connor said the government

might not use "statistical sampling in calculating the population for the purposes of

apportionment." Although, O’Connor acknowledged that the law "required that

sampling” shall be used for other purposes.

Hence, under the current census plan, census takers will go door-to-door across the

nation to count those who have not returned their forms in the mail. This traditional

method is referred to as the head count. A few weeks later, in the summer of 2000, census

takers will conduct an intense recount of selected areas, and the bureau will use these

numbers to adjust their tallies (Savage and Anderson 2014.)

Interest in sampling California has made the census in 2000 the most controversial.

The sample involved directly counting 90% of households in a census tract and using that

information to estimate the remaining 10%. Sampling the population extrapolates

information from a random selection of households to reach a total head count.

Republicans argued that the use of sampling would cause "direct and concrete injuries" to

the interests of the House because the population figures could be manipulated to alter the

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chamber's political composition (Vobejda 2014.)

Furthermore, statistical sampling gives much greater discretion to the Census

Bureau because the “correction procedure” of sampling chooses population subgroups

subjectively. For example, the Bureau either treats young urban black males as a

subgroup or separates them by region. The Bureau also decides how many ethnic groups

we want to treat as distinct. By allowing more statistical sophistication, more discretion is

in the hands of the statistician. By letting statisticians within the Bureau to use their

judgment and use statistical techniques to correct for any data problems that may exist

leaves room for the Census officials to make the decisions that determine which state gets

U.S. representatives (By 2014.)

Moreover, by giving the Census this much discretionary power will allow lobbying

groups to interfere with the Census process. For example, lobbyists can write position

papers on how to "improve" sampling techniques. Every adjustment decision on sampling

violates of a group of citizens’ rights. Therefore, since sampling gives the Census Bureau

political power, the sample eventually ends up favoring a powerful lobbying group (By

2014.)

The Current House Size Flaws the Presidential Election

Prior to 1911, the size of the House was determined after each census in order to

ensure that no state would lose a representative under the new apportionment (Neubauer

and Gartner 78.) This principle was used because as more states joined the Union,

population growth altered the relative size of states; oftentimes, states were likely to lose

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representatives to newly admitted states or states experiencing large increases in

population. Losing representatives disturbed the states and consequently, they wanted the

number of representatives in the House to increase with the population, thus avoiding a

reduction in the size of a state's congressional delegation. All existing states were at least

as large as it had been under the prior apportionment. The House size was not increased

following the 1920 and 1930 censuses because in 1941, Congress passed a bill that

placed the issue of House size on autopilot by formally keeping both the same (Neubauer

and Gartner 78.)

The election of the President of the United States depends both on the House size,

which is currently stuck at 435 representatives, along with the seating of states

represented in the House of Representatives. The Electoral College is utilized to elect the

President because the size of each state's delegation to the Electoral College equals the

size of the state's delegation in the House of Representatives plus two for the state’s

senators. The reasons for this method of apportionment of the Electoral College members

are rooted in the Connecticut Compromise of 1787, but many US citizens believe the

presidential election to be flawed in an argument that can be used against the use of the

Electoral College (Neubauer and Zeitlin 721). For example, when the winner of the 2000

presidential election was elected when the House size was fixed at 435, the winner of the

Electoral College votes did not match the popular vote. Furthermore, curious

mathematicians researched that the runner-up for the presidential election, Gore would

have won the election had House size been set at 500, as it was in 1940 (Neubauer and

Zeitlin 722). Because of the bill passed in 1941, the size of the House has been fixed at

435 representatives and has not been changed since.

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The law about the constant small house size flaws the electoral college

representation by states; Since population in the United States increased, the house size

must increase also in order to accurately represent the states. For example, despite to

unchanging house size, the population in the United States increased from about 131

million people in 1940 to about 290 million people in 2000 (Neubauer and Zeitlin 723).

In 1941, there was approximately one representative for every 301,000 citizens, but in

1990, there was approximately one representative for every 572,000 citizens. If the ratio

of House Representatives to United States citizens existed as it did in 1941, then the

House would have about 830 members based on the 1990 census (Neubauer and Zeitlin

723). Since the 2000 presidential election utilized the 1990 census figures, if the

hypothetical House was apportioned with 830 members, the 2000 presidential election

would result with Gore earning 471 electoral votes versus Bush earning 463 votes

(Neubauer and Zeitlin 724). In summation, small House sizes flaw the representation of

states in the Electoral College, flawing the Presidential election.

The previous example implies that there exists a pattern when examining the

hypothetical Electoral Colleges for small House sizes and large House sizes. For large

House sizes the relative representation of the states in the Electoral College becomes

closer to their relative representation in the House (Neubauer and Zeitlin 724). Since

Gore won the popular vote, a fair vote by the Electoral College suggests he would have

won the election for large House sizes. On the other hand, test results prove that smaller

states have a relatively larger percentage of the members, thus are over-represented in the

Electoral College for small House sizes, which explains why Bush won the election with

small House sizes (Neubauer and Zeitlin 725).

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In addition, the current apportionment of the House of Representatives with a

House size of 435 leads to large inequalities among states. For example, the difference in

2000 between the number of representatives between the largest district size, Montana,

and the smallest district size, Wyoming, was 410,012 (Neubauer and Gartner 78.) Yet by

increasing in the House size, House sizes of 932 or 1,761 diminish inequalities in

representation between states. If in 2000, the House size was 932, and the seats were

apportioned accordingly, the difference in number of representatives for the smallest and

largest districts would decrease to 76,667 (Neubauer and Gartner 78.) Furthermore, a

House size of 1,761 would result in a difference of only 15,850 (Neubauer and Gartner

78.)

Reason to Transform State Representation in the House of Representatives and

Electoral College: Voter Dissatisfaction

Young American citizens find the Electoral College an outdated voting process,

evident by the awarded presidency to George Bush which caused increased public

dissatisfaction with our nation's political process (Mathis 2014.) The Electoral College

has become unpopular since the controversial 2000 election; Included in the bill of

charges against the method are that it amplifies the effect of the imbalanced allocation of

electoral votes, and that it fails to "count" the votes within a state that were cast for a

losing candidate (Festa 2013.) The system is controversial because it is the mechanism

that enhances the possibility of having an electoral vote winner, and hence a president,

who received fewer popular votes than the electoral runner-up (Festa 2013.) This

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reasoning is behind Bush’s win; his win comes from the fact that delegate-rich states give

a candidate the upper hand. Though public vote supported Gore, Bush got the push he

needed from the delegates. Political insiders worry our political system is set to, once

again, “ignore the will of the people” (Mathis 2014.) The public doesn’t believe their vote

matters and furthermore concludes that the way we elect national leaders in this country

is troubling; United States citizens argue that through the Electoral College, their

government leaders have chosen a way to silence majority because “in a true democracy,

the voice of the people is all that matters” (Mathis 2014.)

To examine the consequences of the voter dissatisfaction especially following

presidential election in 2000, Richard J. Cebula experiments with voter dissatisfaction in

his article, "Strong Presidential Approval Or Disapproval Influencing the Expected

Benefits of Voting and the Voter Participation Rate" in the Atlantic Economic Journal.

Cebula uses annual data for the years 1960 to 1997 to study how voter participation rate

positively responds to strong public approval or strong public disapproval of the

incumbent President and how currently, disappointment and concern regarding both low

and declining voter participation rates in the US are expressed frequently in the media

and elsewhere. Poll results in the United States reminds citizens that each election year,

fewer voters show up at the polls in America than in most other democracies (Cebula

2014.) Cebula further observes that voter turnout has declined despite the fact that the

most commonly noted barrier to voting, the burdensome registration requirements, has

been substantially lowered (Cebula 2014.) Thus, since election outcomes can have very

profound implications for societal and government resource allocations, the loss of voter

participation carries a price tag. Citizens argue back that there are no benefits of voting.

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The US voter participation rate be increased by changing the electoral system

which displeases the voters; the reduced voter participation reflects reduced expected

voter satisfaction (Cebula 2014.) Bennett Drake furthers in his article in the Boston

Globe that if voting numbers grew significantly, in response, politicians would respond to

the agendas of the people who elected them (Drake 2014.) In other words, measuring the

reaction of nonvoters to campaigns that are not pitched to them in the first place is of

limited value to those in office. Drake further explains that "satisfaction is correlated with

voting, not nonvoting" and low turnout is worrisome despite who is in office and what

they do because voting is seen as much as a mark of citizenship as a process for choosing

representatives (Drake 2014.) In order to make voters feel like their vote matters, each

states electors must accurately reflect the views of the state. As explained earlier, for the

House of Representatives and Electoral College to accurately represent their states the

United States must use of the Dean method when apportioning, record more frequent

censuses, and increase in the House size following each census in order decreasing voter

dissatisfaction by eliminating bias within the voting system.

Conclusion

The Framers agreed that the United States government would utilize a separation of

powers and three branches of government, but did not agree on how the legislative

branch should be constituted. After much debate, a compromise was struck between the

New Jersey and Virginia plans suggested; the final product mandates that representation

in the House of Representatives shall be based on the states populations. Still, the

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compromise did not specify the exact apportioning method in which the representation

would be achieved. The unspecified method had significant implications on the

Presidential elections also; The number of Electoral votes a state receives is contingent

on the number of members in the House. Several different apportionment methods have

been employed, yet each method has demonstrated bias.

In 1941, Congress established the permanent method of apportionment known as

the Huntington-Hill method. Yet, by examining close elections, evidence portrays how

Huntington-Hill fails to fairly seat the House of Representatives and the Electoral

College. The Presidential Election voter turnout parallels the growing belief that United

States citizens are dissatisfied by the elections. Citizens’ dissatisfaction roots from the

displeasure with the Electoral College System, which in turn parallels the House of

Representatives apportionment method. The House of Representatives and Electoral

College candidates play a role in the presidential election as the House of Representatives

is apportioned in response to the population of each state in the United States; The

Electoral College is thus determined by the seating of the House of Representatives. Yet

voters are dissatisfied because they feel their size of their electors in the Electoral College

accurately represents their states’ vote and representation in the US.

In order to accurately represent each state’s citizens, I suggest a reform movement:

changing the apportionment method for the House of Representatives. This reform would

also change the seating in the Electoral College. I also suggest shortening the interval

between each census and consequently each apportionment, and increasing the size of the

House of Representatives. The size of the House would be determined following an

increase in population at each census. Montana suggested an alternative, Dean Method, to

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replace the Huntington-Hill Method and I argue in this paper, that the Dean

Apportionment method acts an improved replacement method for apportioning the House

of Representatives and the Electoral College.

In addition, the more frequent censuses will maintain the accurate representations

necessary for seating the modern government; Due to an aging United States population,

domestic migration, and the geographically heterogeneous effects of foreign immigration,

the distribution of population shifts frequently, consequently altering the seating in the

House and Electoral College.

Large house sizes will also increase voter satisfaction with the Electoral College

because for large House sizes the relative representation of the states in the Electoral

College becomes closer to their relative representation in the House.

In summation, political results from close elections and controversial United State

Supreme Court cases demonstrate that the Huntington-Hill apportionment method fails to

fairly seat the House of Representatives and the Electoral College. Despite laws

preventing replacement of Huntington-Hill, the Dean method appears an attractive

replacement. Utilization of the Dean method, accompanied by more frequent censuses,

and large house sizes will modifies the federal government positions justly, increasing

American citizen voter turnout and satisfaction.

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Bibliography

1.Neubauer, Michael G., and Joel Zeitlin. "Outcomes of Presidential Elections and the House Size." PS, Political Science & Politics 36.4 (2003): 721-5. ProQuest. Web. 22 Apr. 2014.

2.Bradberry, Brent A. "A Geometric View of Some Apportionment Paradoxes.” Mathematics Magazine 65 (1992): 3-17. JSTOR. Web. 27 Jan. 2014. <http://www.jstor.org/stable/2691355>.

3.Gaines, Brian J., and Jeffery A. Jenkins. "Apportionment Matters: Fair Representation in the US House and Electoral College." Perspectives on Politics 7.4 (2009): 849-57. ProQuest. 28 Jan. 2014

4.Barrett, Paul M. "Justices Back Method of Apportionment used to Distribute House Seats to States." Wall Street Journal Apr 01 1992: 0. ProQuest. 28 Jan. 2014

5. Festa, Matthew J. "The Origins and Constitutionality of State Unit Voting in the Electoral College." Vanderbilt Law Review 54.5 (2001): 2099-155. ProQuest. 28 Jan. 2014

6.House, Peggy A. "Stand Up and be Counted: The Mathematics of Congressional Apportionment." The Mathematics Teacher 94.8 (2001): 692-7. ProQuest. 28 Jan. 2014

7.Still, Jonathan W. "A Class of New Methods for Congressional Apportionment." SIAM Journal on Applied Mathematics 37.2 (1979): 401-18. ProQuest. 28 Jan. 2014

8.Balinski, M. L., and H. P. Young. "On Huntington Methods of Apportionment." SIAM Journal on Applied Mathematics 33.4 (1977): 607-12. ProQuest. 28 Jan. 2014

9.Edelman, Paul H. "Getting the Math Right: Why California has Too Many Seats in the House of Representatives." Vanderbilt Law Review 59.2 (2006): 0_11,297-346. ProQuest. 28 Jan. 2014

10. Barthélémy, Fabrice, and Mathieu Martin. "A Comparison between the Methods of Apportionment Using Power Indices: The Case of the US Presidential Elections." Annals of Economics and Statistics 101 (2011): 87-106. JSTOR. Web. 27 Jan. 2014. <http://www.jstor.org/stable/41615475>.

11. Ernst, Lawrence R. "Apportionment Methods for the House of Representatives and the Court Challenges." Management Science 40.10

37

Holbrook

(1994): 1207. ProQuest. Web. 13 Apr. 2014.

12. Iovinelli, Robert. "Using Spreadsheets to Analyze the Historical Perspectives of Apportionment." Mathematics Teacher 91.2 (1998): 176-82. JSTOR. Web. 27 Jan. 2014. <http://www.jstor.org/stable/27970473>. Publisher(s): National Council of Teachers of Mathematics

13. Ladewig, Jeffrey W., and Mathew P. Jasinski. "On the Causes and Consequences of and Remedies for Interstate Malapportionment of the U.S. House of Representatives." Perspectives on Politics 6.1 (2008): 89-107. JSTOR. Web. 27 Jan. 2014. <http://www.jstor.org/stable/20446639>.

14. Quitt, Martin H. "Congressional (Partisan) Constitutionalism: The Apportionment Act Debates of 1842 and 1844." Journal of the Early Republic 28.4 (2008): 627-51. ProQuest. 28 Jan. 2014

15. Burmila, Edward M. "The Electoral College After Census 2010 and 2020: The Political Impact of Population Growth and Redistribution." Perspectives on Politics 7.4 (2009): 837-47. ProQuest. 28 Jan. 2014

16. Chris Frates Denver Post, Staff Writer. "APPORTIONMENT OF ELECTORAL VOTES Backers of Change to Winner-Take- all Concede Defeat." Denver Post Nov 03 2004: 0. ProQuest. 28 Jan. 2014

17. Hamburger, Tom, and Kim Geiger. "Q & A; how the Census Alters the House." Los Angeles Times Dec 20 2010 ProQuest. 28 Jan. 2014

18. Bialik, Carl. "Currents -- the Numbers Guy: Bad Math = Mad Politics." Wall Street Journal Apr 25 2008 ProQuest. 28 Jan. 2014

19. Grimmett, Geoffrey. "Stochastic Apportionment." The American Mathematical Monthly 111.4 (2004): 299-307. ProQuest. 28 Jan. 2014

20. Wright, John R. "Pivotal States in the Electoral College, 1880 to 2004." Public Choice 139.1-2 (2009): 21-37. ProQuest. 28 Jan. 2014

21. Jenkins, Jeffery A. "Partisanship and Contested Election Cases in the House of Representatives, 1789-2002." Studies in American Political Development 18.2 (2004): 112-35. ProQuest. 28 Jan. 2014

22. BRICKETTO, MARTIN C. "Electoral College has Important Role in Choosing Nation's President." Home News Tribune Oct 26 2008 ProQuest. 28 Jan. 2014

23. Neal, Andrea. "Ignorance of Electoral College no Excuse." Indianapolis Star Nov 16 2000 ProQuest. 28 Jan. 2014

38

Holbrook

24. Barbash, Fred. "The Electoral College: Patchwork Built on a Faulty Premise Series: THE SUMMER of '87 Series Number: Occ." The Washington Post (pre-1997 Full text) Aug 31 1987: 0. ProQuest. 28 Jan. 2014

25. Ron Tupa State senator and, Boulder Democrat, sponsor of Senate Bill 51, the Electoral College, reform initiative and Amendment 3. outreach director for. "Electoral College Still Valid? NO: Put Outdated Method in Dustbin of History." Denver Post Dec 12 2004: 0. ProQuest. 28 Jan. 2014

26. Huntington, E. V. "The Apportionment of Representatives in Congress." Transactions of the American Mathematical Society 30.1 (1928): 85-110. JSTOR. Web. 27 Jan. 2014. <http://www.jstor.org/stable/1989268>. Published by: American Mathematical Society Article Stable

27. Huntington, Edward V. "A New Method of Apportionment of Representatives. “Quarterly Publications of the American Statistical Association 17.135 (1921): 859-70. JSTOR. Web. 27 Jan. 2014. <http://www.jstor.org/stable/2965187>.

28. Warren, Jenifer. "California and the West; Test of Census Sampling Method Heightens Debate; Population: Agency Stands by Results, which Counted 54,116 More People in Sacramento than Traditional Technique. State Officials Arrived at Yet another Figure." Los Angeles Times Jan 27 1999: 3. ProQuest. 20 Apr. 2014

29. Vobejda, Barbara. "House Republicans Sue to Prevent Census Sampling." The Washington Post: 0. Feb 21 1998. ProQuest. Web. 20 Apr. 2014 .

30. Savage, David G., and Nick Anderson. "Court Rejects Plan to use Sampling for 2000 Census; Population: Statistical Method can't be used for Reapportionment. Ruling may Cost California a House Seat." Los Angeles Times: 1. Jan 26 1999. ProQuest. Web. 20 Apr. 2014 .

31. By, Edward L. "Census Sampling is Dangerous." Wall Street Journal, Eastern edition ed.: 0. Feb 15 2001. ProQuest. Web. 20 Apr. 2014 .

32. Neubauer, Michael G., and Margo G. Gartner. "A Proposal for Apportioning the House." PS, Political Science & Politics 44.1 (2011): 77-9. ProQuest. Web. 21 Apr. 2014.

33. Edelman, Paul H. "Getting the Math Right: Why California has Too Many Seats in the House of Representatives." Vanderbilt Law Review 59.2 (2006): 0_11,297-346. ProQuest. Web. 21 Apr. 2014.

34. Schaffer, Michael D. "A Great Compromise Settles the Acrimony the House

39

Holbrook

and Senate are Born Out of Necessity. A Great Compromise Settles the Acrimony." Philadelphia InquirerJul 01 2003. ProQuest. Web. 22 Apr. 2014 .

35. Mathis, Greg. "Before Criticizing Other Nations' Election Processes, perhaps we should First Correct our Own." Call & Post: 1. Feb 2008. ProQuest. Web. 22 Apr. 2014 .

36. Cebula, Richard J. "Strong Presidential Approval Or Disapproval Influencing the Expected Benefits of Voting and the Voter Participation Rate." Atlantic Economic Journal 33.2 (2005): 159. ProQuest. Web. 22 Apr. 2014.

37. Drake, Bennett. "WHO VOTES? (AND WHO CARES?) COMMENTATORS LOVE TO COMPLAIN ABOUT THE APATHETIC AMERICAN VOTER. BUT DOES LOW TURNOUT REALLY MATTER?" Boston Globe: 0. May 30 2004. ProQuest. Web. 23 Apr. 2014 .

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