A hypothetical example illustrating Hamilton's method The result is called the standard divisor (SD). This is the raw number of seats that should be allotted to each state. Fairness in representation has been a passionate issue since the origin of the Unites States of America. This lesson reviews his method. Webster’s time was short-lived, however. Just remember to choose something close to your standard divisor. APPORTIONMENT is a FORTRAN90 program which demonstrates some of the methods used to apportion seats in the United States House of Representatives. Webster proposed that “…let the rule be, that the population of each It states that apportioning should be accomplished through the selection of a divisor such that the ultimate traditionally-rounded quotas will sum to the exact number of seats to be assigned. It was then replaced by Hamilton method and in 1911 the Webster method … Over time, there have been many different proposals for how to fairly calculate each state's seat quota, the number of voting seats apportioned to the state. Webster's Method Finding Suitable Divisor Daniel Webster proposed his apportionment method in 1832.It was adopted by the Congress in 1842, and then replaced by Alexander Hamilton's in 1852. How to use apportionment … Remember that in traditional rounding, you round up if the number is 5 or greater and round down if the number is less than 5. This example should not mislead one into thinking that Huntington-Hill always does a better job. The different, methods of apportionment are considered, and a preferred method of apportionment discussed with reasons that support the assertions. Okay, so our standard calculations didn't come out exact; that means we are off to the modified versions. If the sum of the quotas is too high, then choose a larger modified divisor; if the sum is too low, choose a smaller modified divisor. I found that the correct MD is 20.15. The larger the number you divide by, the smaller the result and vice versa. We've gone through all the standard calculations, but our result is not correct. :�J!����0Mp0��z�а�iȬB/�/��^"��Q�J���C֗�P��/��% T���T��T��CA�MxM'j�(0�T�_ ���2��YTّr � �� The Webster and Huntington-Hill apportionment methods Using Webster's apportionment method to solve problems, steps in the Huntington-Hill apportionment approach and geometric mean Friday Get access risk-free for 30 days, Maria has a Doctorate of Education and over 20 years of experience teaching psychology and math related courses at the university level. In 1842 the method was adopted (Act of June 25, 1842, ch 46, 5 Stat. It was adopted and used by the House of Representatives for many years. Not only that, it proposed scrapping Jefferson’s method in favor of that of Webster. No, you can't. We will illustrate Webster's method of apportionment by using the data in this example. Earn Transferable Credit & Get your Degree, Adams' Method of Apportionment in Politics, Jefferson's Method of Apportionment in Politics, Balinski & Young's Impossibility Theorem & Political Apportionment, Huntington-Hill Method of Apportionment in Politics, The Alabama, New States & Population Paradoxes, The Quota Rule in Apportionment in Politics, Hamilton's Method of Apportionment in Politics. The only difference is that we use the term 'modified' to indicate that it is not calculated with the original standard divisor. Sciences, Culinary Arts and Personal !�A ��3�. In the 1880s and 1890s, House sizes were chosen so that the calculations based on Hamilton’s method and Webster’s method would agree: 325 seats in the 1880s and 356 in the 1890s. Webster's Method proposed that a divisor should be chosen such that the sum of the rounded quotas is equal to the number of seats to be apportioned. Since all remainders are less than .5, ordinary rounding will allot 20 seats instead of the required 21. Webster, Sainte-Laguë, and Schepers Webster proposed the method in United States Congress in 1832 for proportional allocation of seats in United States congressional apportionment. Log in here for access. We can begin by computing the exact quota that each state is entitled to: A's value is given by (684/1100)(10) = 6.22 �B�a�""! An error occurred trying to load this video. 4.1 Apportionment Problems and Apportionment Methods There are two key elements of the dictionary de nition of the word apportion: To get an idea of where interesting issues might arrise with apportionment problems, let’s look at an example. Discrete Math: Apportionment Methods. How Long Does IT Take to Get a PhD in Business? Webster’ s Method In 1832 Daniel Webster entered his method in the list of candidates for fair apportionment. Jefferson’s method was under-representing New England states, where Webster was from. Which brings us to the next step in our process. (� ���0B@����B�!&��z�� Daniel Webster proposed his method of apportionment in the 1830s. imaginable degree, area of Huntington's method agreed with Webster's in 1930, and since 1940 it has been the law of the land. Finally, the apportionment method might have a choice of which seat allocation to choose for the exact quotas which lie on the borders between two or more possible regions. Advantages of Self-Paced Distance Learning, Advantages of Distance Learning Compared to Face-to-Face Learning, Top 50 K-12 School Districts for Teachers in Georgia, Those Winter Sundays: Theme, Tone & Imagery. ��I80��_zzkۦ���4A�Gw�]"W��SV�ꨆI5�O� 4t��^vJoH'_W��0��)]�vz����+����I�A�ԞC��I֓�i/�Ҧ�A8@�DBB-V��ZOI�D�����M�M���]o_�>�}�\t���^Xp�i}]kip�z��Z㏎�a������x���^>����������띖�_����A�N!2LU#2�dY%Nk"P��dRvAe]/���| � ��N�5� ib� �,���U�����ȡd��+ I use this example only to illustrate the distinction between relative and absolute difference ideas. The Huntington-Hill method starts out similarly to Webster’s method since some quotas are rounded up and some quotas are rounded down. © copyright 2003-2020 Study.com. 1/2]). We will look at the following Apportionment methods: Hamilton Webster In the past, different apportionment methods have been used in an attempt to distribute house of representatives’ seats in a manner that makes the most sense and is fair to all. study just create an account. An example is the ‘Adams method’ of apportionment, which is similar to the Webster and Jefferson methods, except that the number of seats is rounded up. In our example, we would have an SD of 1517 / 75 = 20.2267. Adams' method works by always rounding up. The standard divisor is 8.02 School Enrollment Standard Q Rounded Q A 520 64.84 65 B 312 38.90 39 C 614 76.56 77 D 158 19.70 20 Totals 1604 200 201 Example: Webster Method 2012 Pearson Education, Inc. Slide 16-3-18 Solution (continued) Quick review of what we know so far…. Already registered? Lowndes’s Method Same as Hamilton’s Method until the step of apportioning the surplus seats. Because this can go on for a while, I won't list all my modified divisors here. courses that prepare you to earn Since my sum based on the standard calculations is too low, I needed a smaller modified divisor (MD). Example: 250 seats are being apportioned among 6 states. The Jefferson method is also known as the greatest divisor Use Webster’s method to apportion the 25 seats in Hamiltonia from Example \(\PageIndex{2}\). Revisit the last example and apportion the 200 computers to the four schools using the Webster method. Measuring the absolute difference in representatives per person would be the basis for defending why the Webster apportionment is better. In 1842 the method was adopted (Act of June 25, 1842, ch 46, 5 Stat. Webster's method rounds to the nearest integer, that is, sets a = Lpi/A + 1/21. Webster's Apportionment Method. Lowndes’s Method looks at relative fraction. Webster’ s Method In 1832 Daniel Webster entered his method in the list of candidates for fair apportionment. stream And the lower quota is the next smaller whole number. Forexample,Adams'methodrounds upall fractions (that is, sets as = rpi/A]); Jefferson's method drops all fractions (that is, sets as = Lpi/XJ); and Webster's methodroundstothenearestinteger(that is, setsas =[pi/A + 1/2]). This apportionment is known as the Jefferson apportionment, and in this example the results are the same as what we got by using Webster's method. In this lesson, we will learn the method proposed by Daniel Webster in the 1830s. | {{course.flashcardSetCount}} Jefferson, of course, had political reasons for wanting his method to be used rather than Hamilton’s. Step 2. The specific calculation to determine how many seats each state should receive is called apportionment. While the proposed method may seem a bit incomprehensible, the definitions of the terms become clear in the calculations. ;DHh��N�5���D(�DAߢ"��DN�"� � ��p���!���h����-���d��A�C�@��m&�]��:N�� � otD��]���6 `�����6�{im��]ZW�]�i�6�{��oZ]W�Z����KV�մ�~���u�S��N��W����:�������]���������a���z������������x�ߤ�Kk����ׇ��iaֺ�ֽ����k���ok]��w�C�����0����C�o��k�__�+� �u��u�����u^�.�!��M�t��k���o�����a|&�?��_�Y�3��T��_p������@�¿�䚑�����_�A_��?�B?O������� ��D��}=��=+�����O��K�_�l����9��������K�/��5�Rl&o���Z�_K�sU����6C�_��_I�[��j��}j�d6�ii�����׻�����].׿ma�j�T�K�ikWҵ��^�o�_� State 1940 Apportionment population Hill-Huntington apportionment Webster apportionment Michiga n 5,256,106 17 18 Arkansa s 1,949,387 7 6 One way to test the fairness of an apportionment is to calculate the following fraction for each state. [�K��?�A�փ~B�%��[���T�6��a֗Z��]i�_����������^=j�lt������6������FEk���=k�Z�'����������ת��D;_��_�?^��zޗ�]]k�����/ꟿ���֞oT���iKʮu��J�Z�VG���O�|]�k���u���-׭{I4��Ӫ���T��]iQ�n�zT�P�R����i�+��a(a%��:I��t�zXK��im+I;��Ұ��vJ� ݄���0X`�l%!��!��V�GT�0�UqLW�Q�t�b�7kkA�M5�U���j�aj��v�Up�U��/�a5����4�!�T�Ma�@����XA��i��!,&U4&B�A�&� ��a��%�DA�&B-�i�&Š�4B�%š�����������pC�r��-���� d@�hY]J$Ð��@��Äiɰ0�8W;�@̖U��FJC;;uM�� 0�8 �j ���2;Gt���&S����� T0�-������� �A�h&�5��X�t�����6&�\:�M����w��~�w����K��W��v����������בR=7��~�z�=5���몮�O״�������]���s"���I{�����K"�2 ������X�=�d����O�2��uC�O��ԫ-U~a��hC ��B�=��� �m��иz$?M;���~������t�'�#�����A�]�� DIz"Cd��A�z��]���艏�ǰ���A�6�����$DǪ��7��7�_uo��Wj��A�Ko��N�z^�{�ȉ�����o_�����w��^T��%�a�_i��K���n�4G���z�}_������O�U������U����t�z�^������� i��&�z�^��i>�����A���?WZo�a���hB���iX2���/��/��8yN�����\������u��Z�������U��߿����_�B��Y����w���D���UW��������_�]z��k����;��k�^�k�������_�t�J�ֽu���^����u{��SEk��ۥi=k�]�O�^�����}zM�iv�4;ȋ�N�gjڦ�|C��q 7 ��`�+N����=iZKiæ�6�v�ȸlb���{IU�i�.4�� `����i��]4ծ�:����l���`�~���o�h0�(O�1Z�O���� ���a5�! State Population Quota Hamilton apportionment A 7,270,000 14.24 14 B 1,230,000 2.41 3 C I 2 220,000 4.35 4 Total 10,720,000 21.00 21 Table 2. Any apportionment of items to a sample, in which the items apportioned is greater than the upper quota of that sample, violates the Quota Rule. AppliedMathematicalSciences: BalinskiandYoung Bias Whyhas Huntington's method been retained for U.S. Con-gressional apportionment fromamongthefive historic divisor methods?If oneinspects examples, it is immediatelyevident that, as application of Adams'methodis succeededbyappli- cation of Dean's, and then Huntington's, Webster's andJef- ferson's, solutions tendmoreandmoreto favor large states over I use this example only to illustrate the distinction between relative and absolute difference ideas. Let's get to the calculations required for Webster's Method of Apportionment. 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Create an account to start this course today. Quiz & Worksheet - Webster's Method of Apportionment in Politics, Over 83,000 lessons in all major subjects, {{courseNav.course.mDynamicIntFields.lessonCount}}, Biological and Biomedical The Plurality-with-Elimination Election Method, The Pairwise Comparison Method in Elections, Quartiles & the Interquartile Range: Definition, Formulate & Examples, How to Calculate the Probability of Combinations, Introduction to Statistics: Help and Review, Accuplacer Arithmetic Test: Practice & Study Guide, Pennsylvania Grades 4-8 - Math Subject Concentration (5158): Practice & Study Guide, Introduction to Statistics: Tutoring Solution, TExES Mathematics 7-12 (235): Practice & Study Guide, CSET Math Subtest I (211): Practice & Study Guide, High School Algebra II: Tutoring Solution, CSET Math Subtest II (212): Practice & Study Guide, High School Precalculus: Tutoring Solution. Finally, it was replaced by Huntington-Hill's method in 1941. What Are Preference Ballots and Preference Schedules? All rights reserved. A modified divisor is literally a divisor chosen through trial and error in order to return exact results from the modified rounded quotas. The difference is that the cut-off for rounding is not 0.5 anymore. Webster's Method Finding Suitable Divisor Daniel Webster proposed his apportionment method in 1832.It was adopted by the Congress in 1842, and then replaced by Alexander Hamilton's in 1852. Find the apportionment of each state by rounding its quota the conventional way. Apportionment definition is - an act or result of apportioning; especially : the apportioning of representatives or taxes among the states according to U.S. law. This example should not mislead one into thinking that Huntington-Hill always does a better job. What do we do? Parador's Congress: Webster's Apportionment 50,000) 1,646000 32.92 154,000 3.08 138.72 139 Standard quota (SD = Nearest integer Modified quota (D Nearest integer 4.6 Webster's Method Daniel Webster (1782 1852) Law,'er, Statesman, Senator from Massachusetts Method used in 1842, 1901, 1911, 1931 Basically a compromise between Jefferson and Adams `!�A yS�:��S����" �0@�30���˜���S� `\�)�! Starting with the original calculation, repeated below: A: 322/39.48 = 8.156028369 B: 256/39.48 = 6.484295846 Remember, when rounding, go up if the decimal is .5 or higher and go down if it is less than .5. Log in or sign up to add this lesson to a Custom Course. If you recall, Webster's Method mentioned that rounding should be used. #�~�����?�D6lOP^�C_�7T��������7$����߿���Az��������?�}��_Z������ګ����������������������ֿ�������-J �CM�����^��������k����y������Z���_r4��~����>����MB�����7�yA��@�S����d@l�z׽����������k���kZ�������_������������_]=�����t�����~����]/_^��������^��������M���������������~�W_����������]��-�޿���o���/�K��/���[az�[��]I�I]OV���u������ ?��5���m/���n�T��������w.����IuV@��v����uM&§k�v��0����K�0�����]?��m+W����n�_� /�Nت�(j��&�j�0¦�����a �0[JL0��M�� ���,���hN�ZP�TՄ Sj+A��X�P�c�մv�a$�&8WqP�$��oT�TS�FQK�����P ab�6( `\TSN QE �" p�k��l/ "uT�D5�C ��H4�0�M��!�+L44�0�I��MCOM`�� Visit the Contemporary Math page to learn more. As a member, you'll also get unlimited access to over 83,000 Any divisor method may be described in similar terms by using a divisor X. Jefferson's method was used for the apportionments based on the censuses of 1790 through 1830. Try refreshing the page, or contact customer support. We start with standard calculations and then move on to the modified calculations, only if we need them. How Long Does IT Take To Get a PhD in Philosophy? Did you know… We have over 220 college Apportion: To divide and assign in due and proper proportion or according to some plan. Enrolling in a course lets you earn progress by passing quizzes and exams. What is the Difference Between Blended Learning & Distance Learning? We want a total of 75 seats in our pretend House of Representatives. In fairness to Webster, the two methods did agree on the 1852 apportionment. flashcard set{{course.flashcardSetCoun > 1 ? How Long Does IT Take To Get a PhD in Law? All other trademarks and copyrights are the property of their respective owners. Thus, we have given away exactly 25 seats as required. Webster's Method of Apportionment is one such method proposed and adopted by the House. Balinski and H.P. If a country had 4 states, and a planned 20-seat Hous… During this period the debate centered around the statistical fact that Jefferson's method was systematically giving large states more than their share, that is, the method is biased in favor of large population states. You should have the ability to do the following after this lesson: To unlock this lesson you must be a Study.com Member. Select a subject to preview related courses: Here's a hint: the next divisor should go in the same direction as the direction you are off the target. Webster proposed traditional rounding based on the arithmetic mean. Today, states are allotted voting seats in the House of Representatives based on population. Webster proposed that “…let the rule be, that the population of each Measuring the absolute difference in representatives per person would be the basis for defending why the Webster apportionment is better. The size of the house of representatives is set in order to calculate the divisor, but can be increased in the final apportionment if a large number of states have fractions above 0.5. Choose a modified divisor for step 1 then simply repeat steps 2 - 3 until the sum of the rounded quotas equals the number of seats. Study.com has thousands of articles about every Step 1: Divide the total population by the number of seats available. 3 0 obj �0@@�(7%�t��&��i�P� � �s(�A�H�;0���* �A���� h24 �!��U� �� xA�Lx ��A����0�4� AL`���p�j�0@�@��A����A�|&�n���4��P�t �M0��h4�MSM�0� Bi���i�k����4�M��C�a=5���A��O�:�~��ӵ…Mt�P����ޚ�����, ߤ���M�h0��MSib�m��u�6�nL ��A�����D� The apportionment methods are Jefferson’s method, Hamilton’s method, Webster’s method, Hill’s method, Dean’s method, and Adams’s method. Methods that have been proposed include: Alexander Hamilton's method; Thomas Jefferson's method; John Adam's method; Daniel Webster's method; �k�� 4����DF�SU^�4�P������aD! In the 1850s it was Hamilton’s method, the one vetoed by Washington, that was adopted. ���N����Kᄛ Z���[��iޝ����{r GG�0�0�lR 6)����i.��i����a��w{a6)��iZ Webster's Method; Province A B C D E F Total; Population : Number of seats: Standard divisor: Modified divisor: Modified Exact quota: Modified Rounded quota credit by exam that is accepted by over 1,500 colleges and universities. It was then replaced by Hamilton method and in 1911 the Webster method … 's' : ''}}. Not sure what college you want to attend yet? The sum of the quota results is the determining factor for if we need the modified versions of the calculations. 2 0 obj The proposal passed. This apportionment is known as the Jefferson apportionment, and in this example the results are the same as what we got by using Webster's method. and career path that can help you find the school that's right for you. Property Ownership & Conveyance Issues in Washington, Zeroes, Roots & X-Intercepts: Definitions & Properties, Manufactured Housing Rules in New Hampshire, Quiz & Worksheet - Analyzing The Furnished Room, Quiz & Worksheet - Difference Between Gangrene & Necrosis, Quiz & Worksheet - A Rose for Emily Chronological Order, Quiz & Worksheet - Nurse Ratched Character Analysis & Symbolism, Flashcards - Real Estate Marketing Basics, Flashcards - Promotional Marketing in Real Estate, Middle School Language Arts: Lessons & Help, DSST Principles of Statistics: Study Guide & Test Prep, CLEP Introductory Psychology Exam: Study Guide & Test Prep, High School US History: Tutoring Solution, Middle School World History Curriculum Resource & Lesson Plans, Polynomial Functions Basics: Help and Review, Quiz & Worksheet - Authority in Centralized & Decentralized Organizations, Quiz & Worksheet - Principles of Total Quality Management, Quiz & Worksheet - Unfreezing, Changing & Refreezing in Lewin's Model, Quiz & Worksheet - Germinal, Embryonic & Fetal Development, Formal Organization Structure: Utilitarian, Normative & Coercive, The Gram-Schmidt Process for Orthonormalizing Vectors, How to Become a National Board Certified Teacher, Tech and Engineering - Questions & Answers, Health and Medicine - Questions & Answers, Working Scholars® Bringing Tuition-Free College to the Community, State A - MQ= 453 / 20.15 = 22.48, modified lower quota = 22, State B - MQ = 367 / 20.15 is 18.21, modified lower quota is 18, State C - MQ = 697 / 20.15 which equals 34.59, modified upper quota this time of 35, Explain what the standard divisor is and what the standard quota is, Distinguish between the upper quota and the lower quota, Explain how to use Webster's Method of Apportionment. A simple example is shown in Table 2. :D���i�S�!�C�/zAU' �D+�i��_�H6�Ht�H��"CD$a���_n����h/mP[T������iGK |BJ�/���-/�K������zTZZ�R]��A��$�����Zm/Ҡ����R�*�����Ri/�I��O Brc�+�]�_ߴ�%N�,r1�]. Okay, now we have all the information we need to execute Webster's Method of Apportionment. The Webster Method is a modified version of the Hamilton/Vinton method. Applying such a system to post-election assignments would ensure that every party gets a seat. It might seem like going in circles as you choose a divisor, run the calculations, get a result, and head back to the start to choose another divisor. It is easy to remember if you think about the word 'portion' in ap'PORTION'ment; it means to divide. 491). Thus, we have given away exactly 25 seats as required. Example \(\PageIndex{3}\): Webster’s Method. Here, we have 22 + 18 + 34 = 74, which is not 75. Apportionments based on Hamilton’s method were calculated for all House sizes from 350 through 400. Create your account. Hamilton’s Method looks at absolute fraction. Next, we have Step 4, which is to add the quota figures together and compare the sum to the total seats to be assigned. Rounding down always results in the lower quota. Standard Quotas: B:138.72 E: 13.70 (Bold numbers could be clicked upon. How to use apportionment … To make things easier to see, we'll start with establishing a pretend country of 1517 people and three states named State A, State B, and State C. Their populations are 453 for A, 367 for B, and C has 697 people. Adams' method works by always rounding up. Not only that, it proposed scrapping Jefferson’s method in favor of that of Webster. Adams' method works by always rounding up. could divide by to obtain the same apportionment of 25 seats. Thus, we have given away exactly 25 seats as required. << /Type /Font /Subtype /Type1 /BaseFont /Courier /Encoding /WinAnsiEncoding >> This shows a difference from our standard calculations. Parador's Congress: Webster's Apportionment 50,000) 1,646000 32.92 154,000 3.08 138.72 139 Standard quota (SD = Nearest integer Modified quota (D Nearest integer 4.6 Webster's Method Daniel Webster (1782 1852) Law,'er, Statesman, Senator from Massachusetts Method used in 1842, 1901, 1911, 1931 Basically a compromise between Jefferson and Adams Attachments Hamilton's Method of Apportionment Anyone can earn ! After Washington vetoed Hamilton’s method, Jefferson’s method was adopted, and used in Congress from 1791 through 1842. The apportionment method suggested by Alexander Hamilton was approved by Congress in 1791, but ... in use through 1911 when it was replaced by Webster's method. [�E�곲|�8 a5 �A��)S.vprJA31N����&Lh�R�$-�� cf�HŅ%``�A� P�%�� ���"�0D�2�e� 0hAA��;P��! `Ŭ�{�h�|j�g�H���d@�"�5���4C`�?�7�$ݥ��aÄ�M��Tm�jY��0�pRi�@�qeX�n����܆dp�ؐpᇤA�C��Ϡ�d�7ݰ�' �k�Ȁ'a�A�X�w!z� ��_��!�I��:�!��o$r8��m�ӆ����=���p�iko�k]'�V�A�2����K{I��7u������ qK��-'��6�u�����rQ[z�[z}+��/W� ��!��~���ҶC/�@�\�_��/����_���A�]'ﮭo��=S���t���߄ӯ�uou��߿��������W�W2���?���޻ߥ�M��k��������1 In comparison to majority vote, seats in proportional representation elections are allocated and calculated according to the d’Hondt method, Hare-Niemeyer method or the Webster method. This apportionment is known as the Jefferson apportionment, and in this example the results are the same as what we got by using Webster's method. Webster proposed the method in United States Congress in 1832 for proportional allocation of seats in United States congressional apportionment. But after the census of 1900, new “numbers games” surfaced. In fact, you might even say that the desire for fair representation caused the birth of the country. An apportionment method is in principal a function which maps each pos-apportionment method with given a and M.) =. Services. ��i�V��oT�&�an����v&* '�U�M��A�uTյ�wP�կ���ޚ ?�O�i��5���a+[_!�=���ӆ ���0�$�aA�׆ � {{courseNav.course.topics.length}} chapters | ePU��}U�(&�:w;w�pl8rLB,#�NM�S�M̔�������t�G�'O$�]�:�=�]'�z��d���{�x'��_�������k��׭���=��CN��������������߭��"4�B����D�-d ��D`C��� ‘A�w5�ۛ�"&0DUc @@�}�@P�0A�� >K���D�yA��PDA�`�!%�@� �c �>A���A�a�Z�,!y���A��A�&M4Ol ��4�&;�z�[���8M> =9�� To conduct this method required the use of standard calculations. These calculations were: If the standard calculations do not result in rounded quotas that sum to the desired number, then you must repeat the steps using a chosen modified divisor until the rounded modified quotas do sum to the exact number of seats being assigned. I'll just jump right to the one that worked and show you the calculations. Objective: To become familiar with the Jefferson, Adams, and Webster Methods of apportionment. How Long Does IT Take To Get A PhD IN Nursing? What Is the Rest Cure in The Yellow Wallpaper? Hamilton's Method worked out for our 6­state Congress Example. Step 2. In the 1850s it was Hamilton’s method, the one vetoed by Washington, that was adopted. << /Type /XObject /Subtype /Image /Width 4872 /Height 6614 /BitsPerComponent 1 /ColorSpace /DeviceGray /Filter [/CCITTFaxDecode] /DecodeParms [<< /Columns 4872 /Rows 6614 /K -1 >>] /Length 200751 >> The proposal passed. After the state populations are divided by the divisor, those with quotients that have fractions of 0.5 or above are awarded an extra seat. Apportionment definition is - an act or result of apportioning; especially : the apportioning of representatives or taxes among the states according to U.S. law. Step 3: Assign each state either its upper or lower quota based on traditional rounding. 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