Free Essay

The Apportionment Problem

In:

Submitted By Maharadja
Words 1056
Pages 5
Name
Institution
Date

The Apportionment Problem
The apportionment process has generally been motivated by the need to divide resources of a similar nature fairly amongst people who are entitled to different percentages of the total resource.
Several methods of apportionment exist, including Adam's Method, Hamilton's Method, Jefferson's Method, Webster's Method, just to mention a few. For the problem at hand, Hamilton’s method is employed.
The Hamilton Method
The Hamilton Method is an apportionment style named after Alexander Hamilton. It was first used to decide the initial apportionment of the seats in the House of Representatives in 1790.
We shall define the following parameters for Hamilton’s apportionment: Or (this is also known as the average constituency) or So now and then quota being the number of seats each state should receive. For each state the quota is
State 1: q== 2.907807 State 2: q== 6.697633
State 3: q== 18.5566 State 4: q== 16.60052
State 5: q== 0.069336 State 6: q== 16.09638
State 7: q== 8.160086 State 8: q== 15.84233
State 9: q== 10.28396 State 10: q== 4.785339 | Population | Average constituencyS=p/h | Quota | Lower quota | Final Apportionment | State 1 | 15475 | 154.75 | 2.907807 | 2 | 3 | State 2 | 35644 | 356.44 | 6.697633 | 6 | 7 | State 3 | 98756 | 987.56 | 18.5566 | 18 | 19 | State 4 | 88346 | 883.46 | 16.60052 | 16 | 16 | State 5 | 369 | 3.69 | 0.069336 | 0 | 0 | State 6 | 85663 | 856.63 | 16.09638 | 16 | 16 | State 7 | 43427 | 434.27 | 8.160086 | 8 | 8 | State 8 | 84311 | 843.11 | 15.84233 | 15 | 16 | State 9 | 54730 | 547.3 | 10.28396 | 10 | 10 | State 10 | 25467 | 254.67 | 4.785339 | 4 | 5 | Total | 532188 | | 100 | 95 | 100 |

The problem of how to actually deal with the ‘fraction’ seats arises, because seats are discrete objects. Hamilton’s method solves this fraction problem by assigning a lower quota to each state; a value achieved by rounding down the calculated quota to the nearest lower integer. The fractional part of each calculated quota is studied, and starting with the quota with the largest fractional part, seats are then distributed in order from the larges to the smallest. Here we first consider state one for an additional seat, then State 8, 10,2,4 then 3 in that order till all the seats are taken.
Absolute Unfairness between two states is the difference between the average numbers of people per representative in each state. Absolute unfairness in this problem between the best and the worst represented states:
Abs. Unfairness=Average Constituency of Best state – Average constituency of worst state
987.56-3.69= 983.87
Relative unfairness is the relative unfairness divided by the smaller average constituency between the two average constituencies. So between the best represented and the worst represented states:
Relative Unfairness= Absolute unfairness/ smaller Average Constituency
= 983.87/3.69= 266.63
Changes in state boundaries or populations could affect this apportionment. For instance if the population were to increase or the boundary to enlarge causing a population surge, a state could easily lose seats if it is small and growing much faster relative to a bigger state that is growing much slower. This is called the population paradox. It arises due to the rounding down procedure in the apportionment process. For instance, in the table, if state 1 were growing faster than state 2 it could easily lose a seat in the house.
An Alabama Paradox could occur if the total number of seats to be allotted is increased, causing a state to lose a seat. For instance in the table, State 1 could lose a seat if the total number of seats is increased, making the average constituency figure smaller. Increasing number of seats increases the fair share better for larger states than for smaller ones.
The Huntington- Hill method overcomes this Alabama paradox by calculating the geometric mean (the square-root of the product) of the upper and lower quota for each state. If the standard quota equals or exceeds the geometric mean, the standard quota is rounded up, otherwise it is rounded down.
Apportionment is the best way of achieving fair representation. It ensures that everyone receives proportionate representation based on their population size. Bigger populations get to have bigger say in governance since they are the majority. It has measures to that take into account the sizes of the populations in each state, making it fair for everyone.
Alternative Representation Strategy
Another strategy that can be considered for fair representation is the Huntington-Hill apportionment method. This method is also called the ‘Method of Equal Proportions’. It was developed in 1911 by Edward Huntington and Joseph Hill.
The method requires one to calculate the standard divisor, and then acquire each state’s standard quota. Calculate the geometric mean for each state. It then assigns each state an upper quota if rounds up if the standard quota exceeds or equals the fractional part of the geometric mean, or a rounds down the standard quota otherwise. If the sum of the upper/lower quotas equals the house seats, apportion each state its upper/lower quota as determined. It the sum is not equal, obtain a modified divisor in place of the standard divisor and re-do the procedure. This strategy is better than the Hamilton method. It may only violate the quota rule compared to Hamilton’s Method which has more paradoxes.
Conclusion
The Hamilton method of apportion is quite useful as a way of apportioning, but due to the number of errors that arise with the change in population size and house size, this method has undergone improvements resulting in better methods such as the Huntington-Hill Method, which though may not be absolutely perfect, achieve better consistency in representation under various change in variables.

References
Caulfield ,Michael J. Apportioning Representatives in the United States Congress - Hamilton's Method of Apportionment. Gannon University , Mathematical Association of America, 2014. Web . Nov. 28 2014 http://www.maa.org/publications/periodicals/convergence/apportioning-representatives-in-the-united-states-congress-hamiltons-method-of-apportionment
Hodge, Jonathan and Richard Kilmer. The Mathematics of Voting and Elections: A Hands-on Approach. American Mathematical Society, 2005. Electronic. Nov. 28th 2014 Shapiro, Roman. Methods of Apportionment. University of Maryland, Web. Nov. 28 2014. http://honors.cs.umd.edu/reports/shapiro.pdf

Similar Documents

Premium Essay

M3 A1 Lasa2 the Apportionment Problem

...M3_Assignment 1: LASA 2: The Apportionment Problem Argosy University General Education Mathematics | MAT109 A05 November 8, 2014 Abstract This essay determine how 100 congressional seats should be divided among the 10 states of the union. The number of seats in a state should (in any fair distribution) be proportional to its ratio in the population. Therefore rounding according to some (acceptable) rule should be applied. Below you will see the table showing the Hamilton method of apportionment to determine the number of seats each state would receive. Hamilton Method (Named for Alexander Hamilton) Implementing this method is a three-step procedure. 1) Calculate each state's representation and round each one down. 2) Calculate the number of seats to be assigned. 3) Assign the seats to those with the largest fractional parts. Using the numbers I calculated from applying the Hamilton method, I determine the average constituency for each state by the state with the largest critical divisor and that state was allocated the remaining seats. Absolute Unfairness of an Apportionment The absolute unfairness of an apportionment is the absolute value of the difference between the smallest and largest average constituency state A and the average constituency of state B. This concept is also used when deciding which investments are most productive or detrimental. As you can see below the breakdown of the unfairness of an Apportionment. Population/representative=consistency...

Words: 644 - Pages: 3

Free Essay

Tikaya Final Maths Assignment.Doc

...Math’s Assignment Name Date Abstract This assignment will determine how 100 seats should be divided among the ten states. The number of seats in a state should be fairly distributed and in proportion to the ratio of population. The rounding off rule will be applied. 1. Using the Hamilton method of apportionment, determine the number of seats each state should receive. The Standard Divisor= Total Population/Number of seats In our case the total population= 15475+35644+98756+88346+369+85663+43427+84311+54730+25467 Divided by 100(The number of seats) =532188/100 which is equal to 5321.88 Therefore the standard quota= State Population/Standard Divisor Calculated as follows for each individual states |States |State Pop/Std Divisor |Standard Quota |Lower Quota | |1 |15475/5321.88 |2.9 |2 | |2 |35644/5321.88 |6.7 |7 | |3 |98756/5321.88 |18.5 |19 | |4 |88346/5321.88 |16.6 |17 | |5 |369/5321.88 |0.1 |1 | |6 |85663/5321.88 |16.1 |16 ...

Words: 924 - Pages: 4

Premium Essay

The Effect of State Income Tax Apportionment and Tax Incentives on New Capital Expenditures

...JATA Vol. 25, Supplement 2003 pp. 1–25 The Effect of State Income Tax Apportionment and Tax Incentives on New Capital Expenditures Sanjay Gupta and Mary Ann Hofmann ABSTRACT: This study examines how variations in states’ corporate income tax regimes affect new capital investment by business. Using U.S. state-aggregated data from 1983 to 1996, we find in pooled and fixed-effects regressions that new capital expenditures by corporations in the manufacturing sector are decreasing in the income tax burden on property (measured as the product of the statutory tax rate and the property factor weight), and increasing at a decreasing rate in investment-related tax incentives. The effect of the income tax burden on property is more pronounced for states mandating unitary taxation or the throwback rule. Triangulating our empirical findings with prior analytical and simulation studies suggests the following hierarchy for the relative importance of major attributes of state corporate income tax regimes: the unitary or throwback requirement is most influential on incremental capital investment, followed by apportionment weights and tax rates, and, finally, investment-related incentives. Keywords: state taxation; apportionment formula; tax incentives, unitary business principle, throwback rule. JEL Classification: H20; H71. INTRODUCTION he purpose of this study is to provide empirical evidence on the effects of variations in states’ corporate income tax regimes on new capital...

Words: 13848 - Pages: 56

Premium Essay

Case

...Problems In Joint Products 1. B ltd. manufactures product A, which yields two by-products B and C. The actual joint expenses of manufacture for a period were Rs.8,000. It was estimated that profits on each product as a percentage of sales would be 30%, 25% and 15% respectively. Subsequent expenses were: A B C Material 100 75 25 Direct wages 200 125 50 Overheads 150 125 75 450 325 150 Sales 6,000 4,000 2,500 Prepare a statement showing the apportionment of the joint expenses of manufacture over the different products. Also presume that selling expenses are apportioned over the products as a percentage to sales. 2. In a process line of XY Co., three joint products are produced. For the month of May 1999, the following data were available. Products L M N Sales price per kg. 5 10 20 Post-separation point costs 10,000 5,000 15,000 Output in kg 2,500 1,000 1,500 Pre-separation point costs amounted to Rs.20,000 The joint products are manufactured in one common process, after which they are separated and may undergo further individual processing, the pre-separation point costs are apportioned to joint products according to weight. You are required to prepare a statement showing the estimated profit or loss for each product and in total. 3. In the course of manufacture of the main product ‘P’, by products ‘A’ and ‘B’ also emerge. The joint expenses of manufacture...

Words: 880 - Pages: 4

Premium Essay

Tarrant Regional Water District V. Herrmann: Case Study

...between Oklahoma, Texas, Arkansas and Louisiana that divides water rights from the Red River and its tributaries. Texas believes that Oklahoma has denied them rightful access to water under the compact. Interpreting the compact differently, Oklahoma says they have a concern to safeguard their water supply for future generations. The argument between these four states on how to manage the water has been going on for nearly 60 years. Congress authorized Oklahoma, Texas, Arkansas and Louisiana to draft a compact to ensure fair access to water in the Red River Basin in 1955. After being signed by the states in 1978, the compact was ratified by Congress in 1980. The Red River Compact declares that each of the four states gets an “equitable apportionment of water” from the Red River and its tributaries (Red River Compact, 1980)....

Words: 1791 - Pages: 8

Premium Essay

Bkaf3092

...MFRS 4 insurance contracts MFRS 111 -1 insurance Industry MFRS 4 insurance contracts 1. Introduction 2 main parties in the insurance business: 1- the insured and 2) the insurer. The insured is the individual or organization, which had agreed to contribute an amount of money and been relieved from the risks The insurer is usually an organization, which manages the money and undertakes the risks. MFRS 111 -3 Introduction • The insurance business can be broadly categorized into two classes, the general insurance and the life insurance. • life insurance business is involved in life insurance policies. • general insurance business is involved in policies other than life insurance policies such as marine, motor vehicles, fire and theft. • Takaful -Islamic insurance, which also offers life and general insurance, but is managed according to the syariah laws. MFRS 111 -4 2. Definitions • Several terms used in General Insurance Business. • Acquisitions cost are commissions and agency related expenses incurred in securing premium on general insurance policies. • Claims are demand by any party for payment by the insurer of a policy benefit on account of an alleged loss resulting from an event or events alleged to be covered by a policy of insurance. MFRS 111 -5 2. Definitions • Premium is the amount payable to an insurer under a policy as consideration for the obligations assumed by the insurer. •   • Reinsurance is an arrangement whereby the re-insurer...

Words: 3267 - Pages: 14

Free Essay

Multistate Accounting

...MULTISTATE CORPORATE TAX COURSE John C. Healy | Michael S. Schadewald 2014 EDITION CPE CoursE! BONUS Earn CPE Credit and stay on top of key Multistate Corporate Tax issues. Go to CCHGroup.com/PrintCPE 2014 EDITION MULTISTATE CORPORATE TAX COURSE John C. Healy | Michael S. Schadewald ii Contributors Authors ........................................................... John C. Healy, MST, CPA Michael S. Schadewald, PhD, CPA Technical Review ....................................................... Sharon Brooks, CPA Production Coordinator ................................................... Gabriel Santana Production ......................................................................... Lynn J. Brown Layout & Design..................................................................Laila Gaidulis This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold with the understanding that the publisher is not engaged in rendering legal, accounting, or other professional service. If legal advice or other expert assistance is required, the services of a competent professional person should be sought. © 2013 CCH Incorporated. All Rights Reserved. 4025 W. Peterson Ave. Chicago, IL 60646-6085 800 344 3734 CCHGroup.com No claim is made to original government works; however, within this Product or Publication, the following are subject to CCH’s copyright: (1) the gathering, compilation...

Words: 105989 - Pages: 424

Premium Essay

Partisan Gerrymandering Case Study

...question. Should the judiciary be able stay out of partisan gerrymandering because of the lack of standard in regards to a constitutional violation set by the Courts, or if the judiciary should review such claims to correct a problem in the political process? Supreme Court Justices have gone back on forth on the issue many times. In Veith v. Jubelierer, the Court dismissed a challenge to partisan gerrymandering and a plurality said that much suits are inherently nonjusticiable political questions. Veith has set the standard for how Courts should interpret partisan gerrymandering, but this does not mean that all cases should immediately be dismissed. A majority of Justices said that such challenges can be heard if there is a manageable legal standard. However, Justice Scalia and Thomas always think that partisan gerrymandering is a nonjusticiable political question....

Words: 714 - Pages: 3

Premium Essay

Inventory Control

...Materials Materials are the principle component in production and transform into finished goods. The basic substances used in the process of production and from which a product is made are termed as materials. The term material is fairly comprehensive. It in includes not merely raw materials but work-in-process or semi finished goods, finished goods and consumable stores also because they may use to the process of production. Types of Materials Direct Materials: Materials that became a part of the units produced and incur expenditure, that are easily traced to the units of output and included in the cost goods sold. Example: Timber in cases of furniture making. Indirect Materials: Materials that are not directly associated with production and are part of operating expenses. Example: Bottom in case of shirt making. Material control Material control is a systematic control over the purchasing, storing and using of material to minimize the possible cost. Material control may be defined as the level of material maintenance so as to ensure uninterrupted production and minimizing the investment of funds. Objectives of material control Material controls basically aims at efficient purchases, storage and consumption of materials. The following are the major objectives of material control: ➢ To ensure better quantity of material at right quantity at right time for efficient and uninterrupted production of output. ➢ To maintain the cost of materials...

Words: 4216 - Pages: 17

Premium Essay

Proceess

...Process costing (a) Describe the characteristics of process costing (b) Describe situations where the use of process costing would be appropriate (c) Calculate the cost per unit of process outputs (d) Explain the concepts of 'normal and abnormal' losses and 'abnormal' gains (e) Prepare process accounts, involving normal and abnormal losses and abnormal gains (f) Calculate and explain the concept of equivalent units (g) Apportion process costs between work remaining in process and transfers out of a process using the weighted average and FIFO methods (h) Prepare process accounts in situations where work remains incomplete (i) Prepare process accounts where losses and gains are identified at different stages of the process The basics of process costing Process costing is a costing method used where it is not possible to identify separate units of production, or jobs, usually because of the continuous nature of the production processes involved. It is common to identify process costing with continuous production such as the following. • Oil refining • Foods and drinks • Paper • Chemicals Process costing may also be associated with the continuous production of large volumes of low-cost items, such as cans or tins. Features of process costing (a) The output of one process becomes the input to the next until the finished product is made in the final process. (b) The continuous nature of production in many processes means that there will...

Words: 8300 - Pages: 34

Premium Essay

Week 6

... Problem 1 Demand Curve-right a) Stock market boom that increases consumption spending b) Increase in government defense expenditures c) Increase in money supply Supply Curve-right a) Increased immigration b) Decrease in minimum wage c) Less generous unemployment insurance Problem 2 Researchers have not reached a consensus about just how these two events are linked. The question still remains on how to interpret the negative correlation between wealth and the saving rate over a long period. The movements are consistent with the “wealth effect”, in which an increase in wealth directly causes households to increase their consumption and decrease their saving. Chart Higher prices ^ Agrregrate demanded Lower Prices Less Output More Output Demanded demanded Problem 3 Classical economists viewed the economy as inherently stable and self adjust to deviations from its long-term growth trend, whereas Keynes viewed it as unstable and required government intervention to get back on track. Problem 4 Formula?? MPC * additional income ? * 20 billion Problem 5 Yes. The MPC is the fraction of each dollar of disposable income not spent on consumption. If a poor person doesn’t spend the money then it’s considered MPS however the millionare can spend money but the difference remaining can be that equal to the poor person’s MPS. Hence MPS =.25 and MPC=.75 from a $1. Problem 6 Formula MPC...

Words: 558 - Pages: 3

Premium Essay

Abc Costing

...Coverdrive Ltd Case Study: Activity Based Costing Situation At a recent management meeting at Coverdrive Ltd, the members of the senior management team discussed the introduction of a new product to the company’s range of high quality, hand made cricket bats. A major agenda item was pricing. The management accountant, since his appointment, had given much thought to pricing policy and one of his concerns was that of dealing with the recovery of overhead within a full cost pricing policy. The discussion centred around the traditional method currently in use, compared and contrasted with ABC, Activity Based Costing a technique which re-examines the problem that has faced accountants for decades – that of allocation and absorption of overhead. Traditional pricing method has been based upon absorption costing and the treatment of overhead usually followed a set procedure. ( Cost centres are identified and established within the organisation. ( Cost centres may be producing or service centres. ( Wherever possible a direct charge is made to a cost centre ie allocated overhead. ( Where overhead is jointly incurred it is apportioned to the cost centres on an equitable base. ( The overhead cost for the service centre is then transferred to producing centres. ( The total overhead cost for each producing centre is then divided by for example, machine or labour hours per the cost centre. ( An overhead recovery rate results. ( This is then used to...

Words: 1460 - Pages: 6

Premium Essay

Athens Electoral System

...drawing lots. The third electoral college elected 45 people, which were reduced to form a fourth electoral college of 11 by drawing lots. Finally, the fourth electoral college elected a final electoral body of 41 members, who ultimately elected the Doge. Despite its complexity, this method was effective as it made it hard to become Doge and made sure the winner reflected the opinions of both majority and minority factions. This process continued in the politics of the Republic of Venice for over 500 years, from 1268 to 1797. Electoral systems constantly kept evolving as time went on. During the 18th century, apportionment was a new approach that came into prominence due to the United States Constitution. Apportionment was the idea that the amount of members in the United States House of Representatives was determined accordingly to the state's population. The only problem is the Constitution does not specify any certain method of actually doing this. Alexander Hamilton and Thomas Jefferson began suggesting their own ideas which differed according to whether they favored the large or small states. The United States had a revolutionary method of congress: having a legislative branch with two independent parts, the Senate and the House of Representatives. By having one legislative branch in which each former colony would have equal numbers of representatives (two senators for each state) and one legislative branch based on population, a compromise was reached. Representation is...

Words: 1482 - Pages: 6

Free Essay

History 11 Study Guide

...History 11 exam 2 study guide 1) Explain the structure of the US Gov. under the new constitution and describe the compromises that led to its ratification? What problems do you think remained for the united states under this constitution? The structure of the US Gov under the new constitution sets out the powers of the United States does and what the State powers are as well. In addition Madison is setting up a competion between the US Gov and the States. The US gov can coin money, make taxes, make treaties. State Powers can create taxes, make treaties, but can’t coin money. Many of the powers of the States are often duplicated from the Us Gov. powers. Also there is the 3 branch concept which consist of Executive branch (President, Enforce laws),Legislative Branch (Congress, Make Laws), and Judicial Branch( Interept Laws). These branches will also compete with each other. Example of congress fighting with the president on raising the national debt ceiling. In addition the Judicial branch will sometimes get involved because they have the power to declare a law constitutional or unconstitutional which is the final say. In addion the Judicial Branch can also interpret laws made by the legislative Branch.The compromise that led to the ratification are Virginia Plan:being a large state, because virgina had a larger population.the viginians did not think it was fair for a state to have 3times less population to have a equal vote as a larger state such as virginia.They wanted more...

Words: 2690 - Pages: 11

Free Essay

California Water Crisis

...necessity and the biggest user of water in California is, you got it, the agriculture industry. Before 1922, 6 of the 7 states, including California, which are visited by the Colorado River, signed the Colorado River Compact. This was an agreement among the states governing the allocation of the water rights to the river’s water. California’s rapid growth in population and agriculture began to cause concern for other Colorado River Basin states who feared that California would established priority rights to the river water. The Imperial Valley, located in Southern California, was already relying heavily on the Colorado River for significantly agricultural development (www.usbr.com 2012). For years, California has had their fair share of problems regarding the amount of water that had supposed to been allocated to them or surplus water that the other states never used. In the 1930’s, Southern California’s rights to the river water were thought to be settled and solidified when several agencies signed water delivery contracts with the Secretary of the Interior. The contracts stated the priorities, to use and store California’s portion of the California River water. Over the past 25 years or so, more than 20 cases of Indian land and water rights have been settled and there is still work to be done. Many Indian tribes now occupy the Colorado River with rightful claims to water. Most of the many Indian tribes reside in the state of Arizona. The Navajo Nation is one of the...

Words: 537 - Pages: 3