Apportionment: world population and hamilton method essay apportionment maranda jackson instructor: terry vannoy general education mathematics argosy university 2/26/2014 methods of apportionment are mathematical techniques used to allocate resources such as police officers in a certain. Some in the congress were so displeased with the state of affairs that a bill was introduced to enshrine a permanent apportionment method the house, while the other allowed the census bureau to continue to count overseas military and civilian personnel and their families toward the populations of their home states. The jefferson method of apportionment is just one of many different methods of apportionment in this lesson, we will review the jefferson method. In the 1830s, john quincy adams believed that the method of apportionment being used by congress was biased in this lesson, we hamilton's method of apportionment in politics experiments vs standard divisor (sd) is the total population divided by number of seats, used to divide state populations standard quota. The state of delaware has three counties: kent, new castle, and sussex the delaware state house of representatives has 41 members 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 the populations of the. After the 1790 census, rival methods emerged for how to apportion the house of representatives, using what today have come to be called hamilton's method and 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.
Administrative region, ie\ the number of seats its entitled to based on its population, is not more common around the world (see table 1) indeed table 2: a comparison of apportionment methods quota house population venice monotonicity monotonicity hamilton both no no no jefferson/d'hondt. Elsewhere in the world jefferson s method (proposed by jefferson s method let m denote the number of seats in the house step 1 find a modified divisor d such that the states modified quotas state s population modified quota = d president washington vetoed hamilton s method (the first presidential veto in us. Methods george washington exercised the first presidential veto in history by rejecting hamilton's method of apportionment in this article, i will discuss the table 3: a comparison of the apportionment methods state population quota jefferson adams webster hill hamilton state a 1,908,578 40705.
Jefferson asserted that the correct approach was to choose a common divisor, divide it into each state's population, and drop the fractional part of the resulting quotient the “trick” is to to apportion 22 seats, hamilton's method would round two states up and one down (even though all remainders exceed 05) since the. Hill: (state population)/√ × where l is the lower quota and u is the upper quota hamilton's method we first saw hamilton's method in the congressional apportionment debates based on the census of 1790 the original congressional bill, which president george washington vetoed, was based on house. Tion whether alternative apportionment methods are more appropriate in the dutch case 1 figure 1: apportionment of the cattle using hamilton's method and jefferson's method equivalent points historical examples concerning states and population figures illustrate a point particularly well in those.
Tioning legislative seats by population moreover, they laud it as the best method not just out of these six, but in a global sense, against all of the infinitely many possible algorithms however, their notion of “fair” is based on the house delegation only because this apportionment is also put to use in the electoral college. What is the problem the above figures are from the 2000 census, and the official apportionment is a small example rounding does not work the extra seat should go to the state with the smallest population pi largest remainder ri = qi - qi largest relative remainder ri / pi hamilton's method give to each state the. Let p=∑k pk be the total population start with sk = ⌊pk s/p⌋ (rounding every ratio down) then if the total number of seats is too small, start awarding extra seats to the states pre-sorted in decreasing order by rounded-off fractional parts, until the correct total number of seats is achieved hamilton's method has a very. The hamilton/vinton method sets the divisor as the proportion of the total population per house seat after each state's population is divided by the divisor, the whole number of the quotient is kept and the fraction dropped this will result in surplus house seats the first surplus seat is assigned to the state.
The population paradox is a counterintuitive result of some procedures for apportionment when two states have populations increasing at different rates, a small state with rapid growth can lose a legislative seat to a big state with slower growth some of the earlier congressional apportionment methods, such as hamilton,. 3 calculate the absolute and relative unfairness of this apportionment absolute from math mat109 at argosy university one method to resolving unfairness is to redistribute the boundaries of the states, which would allocate equal population altering the percentages in column 3 shown in the table above would alter the.
1 chapter 14: apportionment lesson plan for all practical purposes the apportionment problem the hamilton method divisor methods the jefferson method the webster method the hill-huntington method which divisor method is best mathematical literacy in today's world, 7th ed 1 © 2006, wh freeman and.
Lecture on mathematics of voting and apportionment ernesto diaz assistant professor of mathematics department of natural sciences and mathematics residues represent as a percent of the state's population in so doing, hamilton's method creates a systematic bias in favor of larger states over smaller ones. Paradox for the hare/hamilton method and show that other popular election methods come with their very own paradoxa 1 introduction practically all democratic countries are faced with the problem of selecting members of their legislative bodies according to votes of their population the method by which.