Apportionment Essay

regularitys of parcelling ar numeral techniques phthisisd to every last(predicate)ocate resources such(prenominal) as police officers in a certain city or sexual relationional seating atomic fare 18a. These techniques ar kinda confused and are based on several variables depending on which order nonpareilnessness is choosing to use. Two of the close famous methods for firmness storage allocation problems are cognize as The Hamilton Method and The Huntington-Hill ruler. In this paper we leave start by discussion the Hamilton Method by pretending that 10 different acress are to be appoint speed of light congressional lay by apply apportioning. The Hamilton Method of ApportionmentThe Hamilton Method is a common sense method that Alexander Hamilton used to apportion the very first United earths congress. With that macrocosm said, hotshot could pretend that they have to divide or apportion 100 congressional seats among 10 supposes of the Union. To do this use The Hamilton Method the tribe for each of the 10 severalizes would have to be k straight offn. Then the world for each 10 enjoins would need to be fulled. erstwhile this make out is have, so the add together world leave need to be divided into each private distinguishs community. For example, secern 1 has a world of 1500 and area 2 has a universe of discourse of 2000 for a state total of 3500 (Pir non, n.d.). 1500/3500 = 0.42857143 (state 1)2000/3500 = 0.57142857 (state 2)Next the decimal places in the add up above go forth need to be moved 2 places to the right and round to the nearest hundred if necessary. This should give the answers 42.86 for state 1 and 57.14 for state 2. These poetry are k right awayn as your Hamilton numbers. this instant in The Hamilton Method the numbers before thedecimal are known as the Integers and they represent how many seats each state charms, and the decimal numbers are known as the waist-length numbers secure who wil l get the remaining seats, if at that place are any. The remaining seats are given to the states that have the colossalst fragmentary numbers first and work their vogue raze. Therefore, assuming there are a 100 seats to be apporti unmatchabled, then 42 seats will go to state one and 57 seats will go to state 2. However, we must r each(prenominal)y that there are 100 seats to apportion. 42+57 = 99, whence there is 1 remaining seat to be apportioned. Since state 1 has a fractional instigate of .86 and state 2 has a fractional part of 14, state 1 receives the extra seat because it has the large fractional number (Pirnot, n.d.).Now let us get back to the master key problem of 10 states apportioning 100 seats. Seeing how this is a rather large problem with large numbers one might fatality to use a calculator or spread sheet to determine how many seats are assigned to each start. By using a spread sheet one can construe that the seats are assigned as followedPopulationHamil tonAssign AdditionalStateInsert Below% RepresentationNumbersInteger Partfractional PartMembers ManuallyThe scruple now becomes, are these seats all apportioned fairly? To find issue we need to know the average Constituency of each state. The Average Constituency mea positive(predicate)s the fairness of an parcelling (Pirnot, n.d. pg. 534). To find the Average Constituency one would take the population of a state and divide it by the assigned seats, and the compare them to determine fairness. Giving an example from the calculations above, one can take heed that state 1 has a population of 15475 and state 2 has a population of 35644. State 1 has 3 assigned seats and state 2 has 7 (Pirnot, n.d.). 15457/3 = 5158Constituents35644/7 = 5092 ConstituentsIn comparison, just by looking at the number of constituent verses the number of seats one would assume that the states are not really stand for fairly, because state one has more(prenominal) constituents and fewer representatives than state 2. Below is the average constituency of all 10 states in the given problem above (Pirnot, n.d.).Having these numbers to compare helps us get a better understanding of how poorly some state can be represented. One would like to think that having the same summation of constituents in each state would be the sure-fire answer to solving that problem, but according to (Pirnot, n.d., pg. 535), it is usually not possible to achieve this nonsuch when making and actual tryst. Therefore we should at least try to sop up average constituencies as correspond as possible. One can truly measure this by using what is called Absolute dark (Pirnot, n.d.).Absolute immoralityAbsolute shabbiness is defined as being the difference in average constituencies (Pirnot, n.d). To find the secure unrighteousness of 2 of the states given above, we should use this simple formula. (averageconstituencies of state A) (average constituencies of state B) =Now to use this formula to fill if any of the states in our problem has any commanding unfairness, we will fragmentise states 3 and 2 to use as a comparison. (state 3) 5486 (state 2) 5092 = 394 Absolute UnfairnessOne can now see that the overbearing unfairness of constituencies surrounded by states 3 & 2 is 394. Therefore, according to absolute unfairness these ii states are not compeerly represented. The constituencies would have to have been the same in some(prenominal) states in order for the states to be equally represented, and this is rarely the case. With that being said, absolute unfairness is not what one would want to use to measure the unfairness of two apportionments, because it really show the imbalance of an apportionment of two states. In other words, absolute unfairness might give some plenty the wrong conclusion ab extinct the imbalance. Meaning, just because there is a large absolute unfairness doe not predict a salienter imbalance. In all actuality, the sized of the state needs to be interpreted into consideration as well, when measuring unfairness. For example, in a state with a larger amount of voters like Texas, if a politician loses by 100,000 to 1,500,000 votes, it is considered a close race, in a small town election where the votes sum as 100 to 30 then the difference is considered to be quite large. This is why it is important to measure the congener unfairness (Pirnot, n.d).Relative UnfairnessRelative unfairness considers the size of constituencies in a calculating absolute unfairness (Pirnot, n.d. pg. 356). To calculate the relative unfairness of apportioned seats surrounded by two states one would use this formula. absolute unfairness of apportionment / littler average constituency of the two states =So, using the two states were given to figure out the absolute unfairness we can distinguish that 0.08 is the relative unfairness of the two states. 394 (absolute unfairness) / 5092 (state 2) = 0.07737628(rounded to the nearest hundred) = 0.08 relative unfairness To get a comparison we will use two other states. State 1 has 5158 average constituencies, and state 4 has 5196 for a total of 38 absolute unfairness. Remember to reckon the state with the smallest amount of constituencies from the larger states constituencies to get the absolute unfairness. To find the relative unfairness, take the absolute unfairness and divide it by the state with the lowest constituency number which was state 1. 38/5158 = 0.007367197(rounded to the nearest hundred) = 0.007 relative unfairnessThe relative unfairness of states 1 and 4 is 0.007. Therefore in comparison with states 2 and 3s larger relative unfairness of 0.08, it tells us that there is more of an unfair apportionment for states 2 and 3 than the states of 1 and 4. In other words, when comparing relative unfairness the larger number in comparison means its apportioned more unfairly. However, due to the fact that all of these calculations were based on The Hamilton Method all of the information could p ossibly change if there were a sudden population change due to growth. This is called a population paradox (Pirnot, n.d.).Population conundrumA population paradox occurs when one state grows in population faster than the other, and the state with the faster growth loses a seat or representative to the other state (Pirnot, n.d.). For example, state 6 has a population of 85663 and state 8 has a population of 84311 for a total population of 169974. Now we want to assign these two states 100 seats of congress using The Hamilton Method. First take the total population and divide by 100 seats to get our monetary standard divisor (Pirnot, n.d.). 169976/100 = 1699.74 (standard divisor)Now divide each state by 1699.74 to get your Hamilton Number. 85663/1699.74 = 50.4 (state 6)84311/1699.74 = 49.6 (state 8)Hamilton Numbers reduce Quota (Integer) Fractional Part Assigned Seats state 6 50.6 50 0.4 50 state 8 49.6 49 0.6 50 = 100seats ( flyer that the total for the integer or lower quota is 9 9, so therefore there was one extra seat to assign and it went to the state with the highest fractional part which was state 8.)Now if we outgrowth state 6s population by 1000 and state 8s population by 100 you will get a population paradox. To find out how this happens you will need to make the same calculations by using The Hamilton Methods, demur you will need to increase the population of both states to get the modernistic totals, integers, fractional parts, and assigned seats (Pirnot, n.d.). (state 6) 85663 + 1000 = 86663 (new population)(state 8) 84311 + 100 = 84411 (new population)86663 + 84411 = 171074 (total population)171074/100 = 1710.74 (standard divisor)86663/ 1710.74 = 50.66 (Hamilton number)84411 / 1710.74 = 49.34 (Hamilton number)Notice that the fractional part has changed for the two states Hamilton numbers. Therefore since state 6 now has the larger fractional part due to the population change it will take the extra seat from state 8 for a total of 100 seats. St ate 6 will have 51 and state 8 will have 49. To find out which state received the greatest amount of growth we simply divide the growth by the original population (Pirnot, n.d.). 1000/85663 = 1.16% (state 6) and 100/84311 (state 8) = 1.19% One can now see that this is a population paradox that occurs when using The Hamilton Method, because the state that had the most growth in population lost a seat to the state with the least of amount of growth due to how the fractional part of the Hamilton numbers changed. However, a population paradox is not the only paradox associated with The Hamilton Method. The aluminum Paradox has also shown its ugly face when using The Hamilton Method of apportionment (Pirnot, n.d.).Alabama ParadoxIn 1870, after the census, the Alabama paradox surfaced. This occurred when a house of 270 members increased to 280 members of the fireside of Representatives causing Rhode Island to lose one of its 2 seats. Later on after the census a man by the name of C.W. S eaton calculated theapportionments for all House sizes that ranged from 275 to 350 members. According to (ua.edu, n.d.), He then wrote a letter to Congress pointing out that if the House of Representatives had 299 seats, Alabama would get 8 seats but if the House of Representatives had ccc seats, Alabama would only get 7 seats. This became known as the Alabama paradox. It is simply when the total number of seats to be apportioned increases, and in turn causes a state to lose a seat. There is a method called the Huntington-Hill Principle that helps avoid the Alabama paradox. This method only apportions the new seats when the House of Representatives increases in size. This is what avoids the Alabama paradox. To apply the Huntington-Hill Principle we would use this simple algebraic formula below for each of the states for comparison that are in question of gaining the extra seat (Pirnot, n.d.). (population of y)2 / y * (y + 1)Let us say that Y has a population of 400 and let Y equal 5, and lets say that X has a population of 300 and let X equal 2. Now let us see which one of these gets the extra seat. (400)2 / 5 * (5 + 1) and (300)2 / 2 * (2 + 1)160,000 / 5 * 6 = 90,000 / 2 * 3 == 160,000 / 30 = 90,000 / 6= 5333.33 = 15,000By using the Huntington-Hill Principle method of apportionment we can now compare the two states to see which one will get the extra seat. Notice that state X with the Huntington -Hill number of 15,000 is great than that of state Y, therefore state X should get the extra seat. With this being said, if I were to use apportionment as my way of assigning seats to the House of Representatives, I would definitely pick to use The Huntington-Hill Principle method of apportionment (Pirnot, n.d.).Apportionment is a great way to achieve fair representation as long as we are not using the Hamilton Method. The Hamilton Method has the possibility of cause threesome types of paradoxes the Alabama paradox, the population paradox, and the new states parado x. Even though the Hamilton Method does not violate the quota rule, avoiding these paradoxes are more important whentrying to give equal representation to each state of the Union. There are other apportionment methods that are equally as great as The Huntington-Hill Principle, such as Websters method (Pirnot, n.d.).Websters Method of apportionmentWhat really sets Websters method apart from Huntington-Hill is that Webster uses limited divisor instead of a standard divisor to calculate what is called a modified quota or Integer. A modified divisor is a divisor that is smaller than the standard divisor. A modified quota is a quota that is larger than the standard quota. One would basically pick a number smaller than the standard divisor and work their way down until they end up with one that will give them and modified quota. Once that quota or Integer is found then it will need to be rounded either up or down depending on the number (the standard way of rounding) to determine who wil l get the allotted seats. Websters method is actually exactly like Huntington-Hill except for the rounding part, and it was the apportionment method used until it was replaced by Huntington-Hill (Pirnot, n.d.)ConclusionApportionment methods are a great way to equally divide certain numbers of substances among vary numbers, as long as one stays away from the Hamilton Method. certainly the Hamilton Method is quite simple to use, but causes many problems such as paradoxes. The Alabama paradox, the population paradox, and the new state paradox are among the ones that the Hamilton Method can cause. This causes states to lose seats due to new Representatives, new population growth and even a new border or state joining the Union. Thankfully there were some people out there that were smart enough to come up with new methods of apportionment that eliminated the issues of the paradoxes, such as the Huntington-Hill method and Websters method. Both of these methods are the best apportionment methods out there to help make sure that states are represented equally by congress. , and considering the fact that I live in a very poor, poverty stricken state, I want to make sure that our state gets the best representation possible, so that maybe our representatives will be able to listen to all of their constituents and do something to help boost our economy, increase employment rates, and bring people out of poverty.ReferencesApportionment Paradoxes. Alabama Paradox. Retreived from http//www.ctl.ua.edu/math103/apportionment/paradoxs.htmIllustrating the Alabama Paradox Pirnot, T. Mathematics All Around, Fourth Addition. Apportionment. 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