what is the huntington hill apportionment method

Huntington-Hill Method

• Determine how many people each representative should represent. ...
• Divide each state’s population by the divisor to determine how many representatives it should have. ...
• Cut off the decimal part of the quota to obtain the lower quota, which we’ll call n. ...

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Full Answer

When was the Huntington-Hill method of apportionment used?

They continued to use Webster’s method in 1931, but after a second report recommending Huntington-Hill, it was adopted in 1941 and is the current method of apportionment used in Congress. The Huntington-Hill Method is similar to Webster’s method, but attempts to minimize the percent differences of how many people each representative will represent.

What is Hill's method of apportionment?

The bill passed and Hill’s method has been used to apportion the seats in a 435 member House ever since. Differences exhibited between the Webster and Hill apportionments repeatedly appeared.

How are geometric means used in apportionment?

In this method, geometric means are used to round modified state quotas until the sum of the modified quotas equals the exact number of seats to be apportioned in the House of Representatives. While the definition of the method seems a bit convoluted, the calculations are quite simple. Think of it like a roller coaster.

Who invented the Huntington-Hill method of voting?

It is credited to Edward Vermilye Huntington and Joseph Adna Hill. In a legislative election under the Huntington–Hill method, after the votes have been tallied, the qualification value would be calculated.

What is apportionment principle method?

Mathematics of apportionment describes mathematical principles and algorithms for fair allocation of identical items among parties with different entitlements. Such principles are used to apportion seats in parliaments among federal states or political parties.

How do you find the geometric mean of the Huntington method?

0:418:02Apportionment: Huntington-Hill Method - YouTubeYouTubeStart of suggested clipEnd of suggested clipNext we compute the square root of n times the quantity n plus one which is the geometric mean ofMoreNext we compute the square root of n times the quantity n plus one which is the geometric mean of the lower quota. And one value higher. Step four if the quota is larger than the geometric.

Which apportionment method is used by the United States today?

the Method of Equal ProportionsThe current method used, the Method of Equal Proportions, was adopted by congress in 1941 following the census of 1940. This method assigns seats in the House of Representatives according to a "priority" value. The priority value is determined by multiplying the population of a state by a "multiplier."

What is the Hamilton apportionment method?

Hamilton's Method of apportionment says that apportionment must start by assigning each state with its Lower Quota. If there are seats left over, assign those seats one at a time based on the descending order of fractional parts of each state's Standard Quota.

How do you solve apportionment?

Determine how many people each representative should represent. Do this by dividing the total population of all the states by the total number of representatives. This answer is called the divisor. Divide each state's population by the divisor to determine how many representatives it should have.

How can I find out how many seats are apportioned?

An apportionment method is a systematic procedure that solves the apportionment problem. The standard divisor is obtained by dividing the total population by the house size. A state's quota is obtained by dividing its population by the average district population.

Which apportionment method favors small states?

Hill's method tends to favor the smaller states at the expense of the larger ones, since its rounding is based on the geometric mean. The geometric mean is less than the ordinary (arithmetic) mean, and since the difference between these is greater for smaller quotas, Hill favors those smaller quotas.

How are U.S. House seats apportioned?

— U.S. Constitution, Amendment XIV, section 2 The Constitution provides for proportional representation in the U.S. House of Representatives and the seats in the House are apportioned based on state population according to the constitutionally mandated Census.

Which method of apportionment rounds quotas up or down?

Jefferson's Method. Jefferson's method divides all populations by a modified divisor and then rounds the results down to the lower quota. Sometimes the total number of seats will be too large and other times it will be too small.

What is the Jefferson method?

0:3210:10Apportionment: Jefferson's Method - YouTubeYouTubeStart of suggested clipEnd of suggested clipAvailable. So the first three steps of jefferson's method is the same as hamilton's method step oneMoreAvailable. So the first three steps of jefferson's method is the same as hamilton's method step one determine how many people each representative should represent we do this by dividing the total

When was Hamilton's method used?

1792In 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. 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.

What is the Alabama paradox in apportionment?

In general the term Alabama paradox refers to any apportionment scenario where increasing the total number of items would decrease one of the shares.

How do you find the geometric least square mean?

After the mean for each cell is calculated, the least squares means are simply the average of these means. For treatment A, the LS mean is (3+7.5)/2 = 5.25; for treatment B, it is (5.5+5)/2=5.25. The LS Mean for both treatment groups are identical.

What is geometric mean ratio?

The geometric mean is used as a proportion in geometry (and is sometimes called the “mean proportional”). The mean proportional of two positive numbers a and b, is the positive number x, so that: When solving this proportion, x=√ a*b.

What is a least square geometric mean?

Least Squares Mean is a mean estimated from a linear model. Least squares means are adjusted for other terms in the model (like covariates), and are less sensitive to missing data. Theoretically, they are better estimates of the true population mean.

What is Webster's method for apportionment?

The Webster Method is a modified version of the Hamilton/Vinton method. 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. States with a quotient with a fraction below 0.5 have the fraction dropped.

What is Huntington Hill method of appropriation?

The Huntington-Hill Method of Apportionment involves rounding state quotas to match their seats in the House of Representatives using geometry. Learn more about this process and identify the use of calculations in it, including modified calculations. Updated: 10/31/2021

What is the step 3 of the quota?

Step 3 is simply identifying the upper and lower quotas (the UQ or LQ) for each standard quota. These are the next higher and lower whole numbers, respectively. In our example, the UQs and LQs for the states are: A - 73 and 72, B - 29 and 28, and C - 44 and 43. That is an easy, downhill portion of the method procedures.

When was the Huntington Hill method adopted?

The current method, known as the Huntington–Hill method or method of equal proportions, was adopted in 1941 for reapportionment based on the 1940 census and beyond. The revised method was necessary in the context of the cap on the number of Representatives set in the Reapportionment Act of 1929.

What was the first apportionment method?

The first used apportionment method was contained in Art. I, § 2, cl. 3 of the Constitution . Jefferson recommended apportioning the states sequentially so that the largest state got the first seat, but then had their population de-weighted by half, and then the sums recalculated, and the highest state again getting the next seat. After the first Census in 1790, Congress passed the Apportionment Act of 1792 and adopted the Jefferson method to apportion U.S. Representatives to the states based on population. The Jefferson method was used until the 1830 census.

How does Huntington Hill assign seats?

The Huntington–Hill method of apportionment assigns seats by finding a modified divisor D such that each constituency’s priority quotient (its population divided by D ), using the geometric mean of the lower and upper quota for the divisor, yields the correct number of seats that minimizes the percentage differences in the size of sub constituencies. When envisioned as a proportional electoral system, it is effectively a highest averages method of party-list proportional representation in which the divisors are given by , with n being the number of seats a state or party is currently allocated in the apportionment process (the lower quota) and n +1 is the number of seats the state or party would have if it is assigned to the party list (the upper quota).

When was the Hamilton method used?

The Hamilton (Yes, that Hamilton)/ Vinton ( largest remainder) method was used from 1850 until 1900. The Vinton or Hamilton method was shown to be susceptible to an apportionment paradox .The Apportionment Act of 1911, in addition to setting the number of U.S. Representatives at 435, returned to the Webster method, which was used following the 1910 and 1930 censuses (no reapportionment was done after the 1920 census).

Who proposed the Webster method?

The Webster method, proposed in 1832 by Daniel Webster and adopted for the 1840 Census, allocated an additional Representative to states with a fractional remainder greater than 0.5.

Who was the first person to debate proportional representation?

The history of US apportionment features debate between Alexander Hamilton and Thomas Jefferson over the most appropriate way for the seats to be allocated to the states. The Apportionment Act of 1792 was a political concoction initially approved in a North v. South split, favoring the Northern states, and resulting in 120 seats. This allocation did not have the described method but was politically viable to pass the house and senate. George Washington issued a presidential veto, describing it as unfair and unconstitutional.

How is the population of each state calculated?

The population of each state is calculated in the Census. The states are given a quotient equal to their population. The state with the largest quotient wins one seat, and its quotient is recalculated per the formula below. This is repeated until the required number of seats is filled.

What is the Huntington Hill method?

The Huntington-Hill Method is a modified version of the Webster method, but it uses a slightly different rounding method. While Webster's method rounds at 0.5, the Huntington-Hill method rounds at the geometric mean, which is described below. If a state's quotient is higher than its geometric mean, it will be allocated an additional seat. This method will almost always result in the desired number of seats.

How does Jefferson avoid the problem of an apportionment resulting in a surplus or a deficit of?

The Jefferson Method avoids the problem of an apportionment resulting in a surplus or a deficit of House seats by using a divisor that will result in the correct number of seats being apportioned. For example:

What is Webster method?

The Webster Method is a modified version of the Hamilton/Vinton method. 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. States with a quotient with a fraction below 0.5 have the fraction dropped. 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.

What happens if a state's quotient is higher than its geometric mean?

If a state's quotient is higher than its geometric mean, it will be allocated an additional seat. This method will almost always result in the desired number of seats. The geometric mean of two numbers is the square root of their product. If a country had 4 states, and a planned 20-seat House of Representatives...

Which method favors smaller states?

Hill’s method tends to favor the smaller states at the expense of the larger ones, since its rounding is based on the geometric mean. The geometric mean is less than the ordinary (arithmetic) mean, and since the difference between these is greater for smaller quotas, Hill favors those smaller quotas. On the other hand, the geometric mean is closer to the ordinary mean than the harmonic mean is, so the bias of Hill is not as pronounced as the bias of Dean. See the spreadsheet 1980 - 2000 Webster v. Hill for an illustration comparing the Webster and Hill methods for the last three apportionments.

How many states adopted Webster's method?

The new method differed from the currently adopted Webster’s method in six states. Where they differed it was the larger states that suffered under Hill, not a good sign when passage of the method depends on a vote count in the House.

What was the last apportionment in 1929?

What finally passed in 1929 was a bill requiring the President to send to the Congress apportionments based on Webster, on Hill, and on the method used in the previous apportionment. If Congress took no specific action, the method last used would automatically be employed again. In the 1930s, not only was Webster the last used, but Webster and Hill agreed. This good fortune did not extend to the 1940s.

What was the goal of Joseph Hill in the 1920s?

His goal was to keep the ratio of one state’s “people per Representative” to that of another as close to 1 as possible.

What is Huntington Hill Apportionment?

Huntington-Hill Apportionment Method. Huntington-Hill's method is the current method of seat apportionment used by the US Congress. It has been signed in law by President Roosevelt on November 15, 1941. (Bold numbers could be clicked upon. To increase the number, click to the right of its vertical center line.

What is the cutoff value of Webster's method?

With the regular rounding used in the Webster's method the cutoff value is midway between two successive integers. If A is between an integer L and the next integer L+1, then it is rounded down or up depending on whether A is less or greater than the average (L + (L+1))/2.

What is the cutoff value of equal proportions?

In the method of equal proportions, the cutoff value depends on the magnitude of L = [A] and is equal to the square root of L (L+1).

History

The Huntington–Hill method is a way of allocating seats proportionally for representative assemblies such as the United States House of Representatives. The method assigns seats by finding a modified divisor D such that each constituency's priority quotient (its population divided by D), using the geometric mean of the lower and upper quota for the divisor, yields the correct number of seats that minimizes the percentage differences in the size of subconstituencies. Wh…

The Jefferson/D’Hondt Method

The Webster Method

The Hamilton Method

The Huntington-Hill Method