Ch. \text { Sussex } & 197,145 \\ 3. Since he was interested in the question of Congressional representation, we’ll use the language of states and representatives, so he determines how many representatives each state should get. (A similar incident happened ten years earlier involving the state of Rhode Island, but the paradox is named after Alabama.) If Delaware wants to divide this representation along county lines (which is not required, but let’s pretend they do), let’s use Hamilton’s method to apportion them. Watch the recordings here on Youtube! The Quota Rule states that every sample in the population for which items are to be apportioned, should be apportioned either its lower quota or its upper quota. This will result in surplus house seats. The methods below go under a surprisingly large number of names, partly because the methods were independently discovered for a variety of reasons. Hamilton's Method is fair until the surplus allocation, and then some states get preferential treatment. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. The Alabama Paradox is named for an incident that happened during the apportionment that took place after the 1880 census. 1. The Webster Method is a modified version of the Hamilton/Vinton method. \text { Providence } & 626,667 & 44.6528 & 44 & 45 \\ \text { Sussex } & 197,145 & 9.0017 & 9\\ Question 1 Using Hamilton’s method, the state of Alabama would be entitled to 8 representatives in a House having 299 members, but in a House having 300 members it would only receive 7 representatives – loss of house monotone property. We need 41 representatives and this only gives 40. Webster’s method was later chosen to be used in 1842 but Adams’s method was never used. But Virginia ended up losing a representative to Maine. 1. Goals Info sheet Overview Begin Lesson 9.1- Apportionment Hamilton Method Adjusting a list HW Guide Discrete vs. \text { Newport } & 82,888 & 5.9061 & 5 & 6 \\ The remaining one goes to the county with the largest decimal part, which is New Castle: \(\begin{array}{lrrcc} Hamilton’s Method looks at absolute fraction. \text { Kent } & 166,158 & 11.8395\\ Apportionment Using the Hamilton Method Using the Hamilton method of apportionment, determine the number of seats each state should receive. Apportionment methods are used to translate a set of positive natu- ral numbers into a set of smaller natural numbers while keeping the proportions between the numbers very similar. That meant that the apportionment would need to be done again, still using Hamilton’s method and the same 1880 census numbers, but with more representatives. Note that even though Bristol County’s decimal part is greater than .5, it isn’t big enough to get an additional representative, because three other counties have greater decimal parts. Legal. The Hamilton/Vinton Method sets the divisor as the proportion of the total population per house seat. \text { Kent } & 166,158\\ Step 2: Round the standard quota’s down and give to each state its lower quota. Watch the associated video lesson, Hamilton's Method of Apportionment in Politics, to further expose yourself to information concerning the following: Definition of apportionment Low Quota Hamilton’s method obeys something called the Quota Rule. Modified Divisor A Modified Divisor (MD) is a divisor (relatively near the Standard Divisor) chosen in an attempt to make the "Rounded Quotas" exactly equal to the number of seats to be apportioned. History of Hamilton’s Method -The apportionment method was suggested by Alexander Hamilton was approved by Congress in 1791. These are called the. Modified Divisor A Modified Divisor (MD) is a divisor (relatively near the Standard Divisor) chosen in an attempt to make the "Rounded Quotas" exactly equal to the number of seats to be apportioned. This answer is called the, Divide each state’s population by the divisor to determine how many representatives it should have. Lowndes’s Method Same as Hamilton’s Method until the step of apportioning the surplus seats. After the population for each of the 10 states has been divided by the divisor (5,321.9), the whole number of … The Hamilton Apportion Method (also “Hamilton/Vinton Method”, US Census Bureau, 2014) sets the divisor as the proportion of the total population per house seat. Solution for Hamilton's Method of apportionment changes (adjusts) the standard devisor. The first surplus seat is assigned to the state with the largest fraction after the original division. You can use the arrow keys to move from cell to cell. Hamilton's Method is fair until the surplus allocation, and then some states get preferential treatment. Hamilton method Many of the Founding fathers came up with their own methods for apportionment. The Quota Rule says that the final number of representatives a state gets should be within one of that state’s quota. (4 + 5) ⁄ 2 = 4.5, The geometric mean is 4.47: the proportional share of seats … \hline Assign the excess seats in priority order according to the decimal part if each fair share. 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Explain your decision making process for allocating the remaining seats. \text { Sussex } & 197,145 & 9.0017 & 9 & 9 \\ Countries like Costa Rica and Sweden use Hamilton’s Method (see the historic notes on apportionment in the text). The paradox is that Alabama ended up losing a representative in the process, even though no populations were changed and the total number of representatives increased. Lowndes’s Method Same as Hamilton’s Method until the step of apportioning the surplus seats. \text { Washington } & 126,979\\ It was later adopted in 1852 and used through 1911. \text { County } & \text { Population } & \text{ Quota } & \text{ Initial }\\ The methods are used to allocate seats in a It is named after Alexander Hamilton, who invented the largest-remainder method in 1792. Find the apportionment for the Boxwood district. That meant that the apportionment would need to be done again, still using Hamilton’s method and the same Using the Hamilton method of apportionment, determine the number of seats each state should receive. The apportionment method suggested by future president Thomas Jefferson as a competitor to Hamilton's method. 4.2 Hamilton’s Method In 1792 Alexander Hamilton proposed the following simple method as a way to apportion the US House of Representatives. His method was approved by Congress in 1791, but was vetoed by President Washington. You can use the arrow keys to move from cell to cell. The apportionment method suggested by future president Thomas Jefferson as a competitor to Hamilton's method. APPORTIONMENT is a FORTRAN90 program which demonstrates some of the methods used to apportion seats in the United States House of Representatives.. Methods that have been proposed include: Alexander Hamilton's method; Thomas Jefferson's method; John Adam's method; Apportionment: Jefferson's method. number. There are 10 seats on the county council that need to be apportioned, using the Hamilton method. Apportionments based on Hamilton’s method were calculated for all House sizes from 350 through 400. The Constitution does not specify a certain method of apportionment. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Agenda. In the spring of 1792 they passed a bill to apportion the House, using a method proposed by Alexander Hamilton and now known as Hamilton’s method. This answer is called the, Cut off all the decimal parts of all the quotas (but don’t forget what the decimals were). The state of Delaware has three counties: Kent, New Castle, and Sussex. B. (Bold numbers could be clicked upon. The Hamilton/Vinton Method sets the divisor as the proportion of the total population per house seat. Hamilton’s Method Hamilton’s Method was used between 1852 and 1901 to apportion the House of Representatives. The Jefferson method of apportionment can display the population paradox. \textbf{ Total } & \bf{ 897,934 } & & \bf{ 40 } & \bf { 41 } \end{array}\). Hamilton’s Method looks at absolute fraction. NCTM states DM is the study of mathematical properties of sets and systems that have only a finite number of elements. \hline \text { Bristol } & 49,875 & 3.5538 & 3 & 3 \\ Webster’s method and Hamilton’s method often give the same result. Click in the cells in the population column of the table and enter or edit the population value in the "State/Pop" field. Methods Hamilton method Many of the Founding fathers came up with their own methods for apportionment. - Hamilton Method o This method is based on standard divisor and standard quota of the population. The Delaware state House of Representatives has 41 members. The LibreTexts libraries are Powered by MindTouch® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. \text { County } & \text { Population } \\ 3. Then it was decided that because of the country’s growing population, the House of Representatives should be made larger. 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. 4 - Building Inspectors A city apportions 34 building... Ch. 2. The apportionment methods are Jefferson’s method, Hamilton’s method, Webster’s method, Hill’s method, Dean’s method, and Adams’s method. \text { Washington } & 126,979 & 9.0478\\ Enter the house size in the text field at the top right. Congress passed a bill that kept Hamilton's method but changed the House size to 325 so that Hamilton's method gave the same apportionment as Webster's. Discovery: If Hamilton's Method is used to apportion a House of 299 seats, Alabama gets 8 seats. Removing the decimal parts of the quotas gives: \(\begin{array}{lrrc} The Alabama Paradox In 1882 — different apportionment methods were being debated for the House of Representatives. Almost as soon as the first census was completed in 1790, political thinkers, including Alexander Hamilton and Thomas Jefferson, began suggesting their own methods. Hamilton's Method of apportionment says that apportionment must start by assigning each state with its Lower Quota. Using the Hamilton method of apportionment, determine the number of seats each state should receive. Explain your decision making process for allocating the remaining seats. Example: 250 seats are being apportioned among 6 states. Using the numbers you just calculated from applying the Hamilton method, determine the average constituency for each state. Record this answer to several decimal places. 12 Questions Show answers. A different method proposed by Thomas Jefferson was used instead for the next 50 years. Apportionment Systems . Cake Cutting Methods. Missed the LibreFest? Rules. Describe the 4 methods of apportionment. apportionment had been completed, using Hamilton’s method and the new population numbers from the census. Lowndes’s Method looks at relative fraction. 1. State B has 6,936,000 people and State E has 685,000 people. Few, if any, source apportionment methods can be rated highly in all respects, and it can be expected that regulatory decisions will be based on imperfect models. \text { Kent } & 162,310 \\ 4 - Is the Jefferson apportionment method susceptible... Ch. There are several different methods of apportionment, listed below, each of which allocates seats in a slightly different way. Cut and choose detailed examples. 4. Alexander Hamilton proposed the first apportionment method to be approved by Congress. Step 3 of Hamilton Method. A local department store has budgeted for 120 eight-hour retail shifts to be staffed every week. The Population Paradox happened between the apportionments after the census of 1900 and of 1910. \hline \hline Treasury Secretary Hamilton proposed to compute the exact proportionate number for each state, and then reduce each to a whole number. That meant that the apportionment would need to be done again, still using Hamilton’s method and the same It was later adopted in 1852 and used through 1911. Using the numbers you just calculated from applying the Hamilton method, determine the average constituency for each state. Now we determine each county’s quota by dividing the county’s population by the divisor: \(\begin{array}{lr} Select the apportionment method to use by clicking the tabs at the top of the panel. \text { Providence } & 626,667\\ The geometric mean of two numbers is the square root of their product. In this video, we learn how to use Hamilton's Method to solve apportionment problems. The problem is that Hamilton’s method is subject to several paradoxes. \text { County } & \text { Population } & \text{ Quota }\\ Remove the decimal part of each quota: \(\begin{array}{lrrc} Virginia started with more people, grew at a faster rate, grew by more people, and ended up with more people than Maine. It was first adopted to apportion the U.S. House of Representatives every ten years between 1852 and 1900. You decide that apportionment (chapter 11, sections 1-4 in your textbook) is the best approach to solving this problem, but need to compare several methods and then determine which is actually fair. He begins by determining, to several decimal places, … 4 - Automobile Sales Consider the apportionment of 27... Ch. Alexander Hamilton The apportionment method suggested by Alexander Hamilton was approved by Congress in 1791, but was subsequently vetoed by president Washington - in the very first exercise of the veto power by President of the United States. That happened, but another thing also happened: Maine gained a representative (from New York). Have questions or comments? \hline \text { Bristol } & 49,875 & 3.5538 & 3 \\ \text { Newport } & 82,888 & 5.9061 & 5 \\ 4 - Music Company MusicGalore.biz has offices in Los... Ch. Three of them happened, on separate occasions, when Hamilton’s method was used to apportion the United States House of Representatives. They just stay the same and dont get another seat, and dont lose one either. Enter the house size in the text field at the top right. The Hamilton method of apportionment is actually a largest-remainder method which uses the Hare Quota. Using the Hamilton method of apportionment, determine the number of seats each state should receive. \text { Kent } & 162,310 & 7.4111 & 7\\  … Unfortunately for Hamilton, President Washington vetoed its selection. The Quota Rule isn’t a law of any sort, but just an idea that some people, including Hamilton, think is a good one. True False Alexander Hamilton proposed the method that now bears his name. State B has 6,936,000 people and State E has 685,000 people. These methods are some of the most frequently used apportionment methods, although readers might know them by different names. Alexander Hamilton The apportionment method suggested by Alexander Hamilton was approved by Congress in 1791, but was subsequently vetoed by president Washington - in the very first exercise of the veto power by President of the United States. \textbf{ Total } & \bf{ 1,052,567 }\end{array}\), 1. A local department store has budgeted for 120 eight-hour retail shifts to be staffed every week. The apportionment method suggested by Alexander Hamilton was approved by Congress in 1791, but was subsequently vetoed by president Washington ­ in the very first exercise of the veto power by President of the United States. The next is assigned to the state with the second-largest fraction and so on.For example: If a country had 4 states, and a 20-seat House of Representative… The Jefferson method is also known as the greatest divisor Using the numbers you just calculated from applying the Hamilton method, determine the average constituency for each state. \textbf{ Total } & \bf{ 897,934 }\end{array}\), 1. Hamilton Method calculator; Jefferson Method calculator; Adams Method calculator; Webster Method calculator; Huntington-Hill Method calculator. (Remember that fractions are not allowed.) \text { New Castle } & 538,479 & 24.5872 & 24\\ \text { Kent } & 162,310 & 7.4111 \\ After each state's population is divided by the divisor, the whole number of the quotient is kept and the fraction dropped. Answers are integers and/or decimals only. Lowndes’s Method looks at relative fraction. The number of shifts staffed on a single day of the week is apportioned based on the total number of … Standard Divisor (SD) = P/A, where P is the total population and A is the required allocation or the number of items to be distributed among the groups. His method was approved by Congress in 1791, but was vetoed by President Washington. 1901 — The Census Bureau gave Congress tables showing apportionments based on Hamilton’s method … Decimals, Fractions, Percents. So, what is the Quota Rule? We need 75 representatives and we only have 72, so we assign the remaining three, one each, to the three counties with the largest decimal parts, which are Newport, Kent, and Providence: \(\begin{array}{lrrcc}  This will result in surplus house seats. The Droop quota is the integer part of Hamilton's Method of apportionment says that apportionment must start by assigning each state with its Lower Quota. If Hamilton's Method is used to apportion a House of 300 seats, Alabama gets 7 seats. First, we determine the divisor: \(897,934/41 = 21,900.82927\). This method will almost always result in the desired number of seats. 4.2 Hamilton’s Method In 1792 Alexander Hamilton proposed the following simple method as a way to apportion the US House of Representatives. The next is assigned to the state with the second-largest fraction and so on.For example: If a country had 4 states, and a 20-seat House of Representatives... 2560 + 3315 + 995 + 5012 = 11882 Please NOTE: Enter only the sample sizes of the samples. The Huntington-Hill Method is a modified version of the Webster method, but it uses a slightly different rounding method. Congress passed a bill that kept Hamilton’s method but changed the House size to 325 so that Hamilton’s method gave the same apportionment as Webster’s. Oklahoma had enough population to qualify for five representatives in Congress. Take advantage of them, and keep several decimal places. Hamilton’s Method Step 1: Calculate each state’s lower quota. \text { Kent } & 166,158 & 11.8395 & 11 \\ Hamilton's method was adopted by the US Congress in 1852 and was Those five representatives would need to come from somewhere, though, so five states, presumably, would lose one representative each. c. Use Hamilton's Method to find the apportionment for the given number of seats, M. 3. \text { Kent } & 166,158 & 11.8395 & 11 & 12 \\ Here is a table of equivalency for these names. The divisor is \(1,052,567/75 = 14,034.22667\). The number of shifts staffed on a single day of the week is apportioned based on the total number of shoppers who visit the store during the day. \textbf{ Total } & \bf{ 897,934 } & & \bf{ 40 }\end{array}\). Government The conflict that took shape in the 1790s between Hamilton and Jefferson viewed government and how to better it, to move it forward in different ways. Here is the procedure: The divisor “ D ” in the method is the ratio of all U.S. residents to Representatives; it came out to a bit over 30,000 in this case. 1901 — The Census Bureau gave Congress tables showing apportionments based on Hamilton’s method … Use Hamilton's Method to find the apportionment for the given number of seats, M. 3. To play this quiz, please finish editing it. \text { County } & \text { Population } & \text{ Quota } & \text{ Initial } & \text{ Final } \\ 2. Note on rounding: Today we have technological advantages that Hamilton (and the others) couldn’t even have imagined. Hamilton’s Method Step 1: Calculate each state’s lower quota. apportionment had been completed, using Hamilton’s method and the new population numbers from the census. The method for apportionment used during this period, originally put forth by Alexander Hamilton, but vetoed by George Washington and not adopted until 1852, was as follows: First, the fair share of each state is computed, i.e. showing the apportionment produced by Hamilton’s method for all sizes of the House between 275 and 350 seats. The assumption was that some states would gain another representative and others would stay with the same number they already had (since there weren’t enough new representatives being added to give one more to every state). \text { New Castle } & 538,479 & 24.5872 & 24 & 25 \\ Standard Quotas: B:138.72 E: 13.70 History of Hamilton’s Method -The apportionment method was suggested by Alexander Hamilton was approved by Congress in 1791. Example: 250 seats are being apportioned among 6 states. The Webster method of apportionment can display the population paradox. 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