An example of the apportionment paradox known as "the Alabama paradox" was discovered in the context of United States congressional apportionment in 1880, : 228–231 when census calculations found that if the total number of seats in the House of Representatives were hypothetically increased, this would decrease Alabama's seats from 8 to 7.
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What is the Alabama paradox?
What is a paradox in math?
What is Hamilton method of apportionment?
What are the three paradoxes in the House of Representatives?
How to find the standard quota of a school?
What is the New State Paradox?
What is the population paradox?
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Section 17.4: Apportionment Paradoxes - The Nature of Mathematics ...
17.4 Outline. Introduction; Alabama paradox; Population paradox; New states paradox; Balinski and Young’s impossibility theorem . 17.4 Essential Ideas. Alabama Paradox
Hamilton's Method, the Quota Rule, Alabama Paradox, the ... - Docest
Algorithm for Hamilton s method. Calculate the standard divisor. Calculate each state s standard quota. Step 2:ALLOCATE THE LOWER QUOTA. Apportion to each state (for the time being) its lower quota. In other words, round each state s quota down. Step 3:DISTRIBUTE THE SURPLUS.
7. Alabama Paradox | georgeszpiro
7. More Seats or Less? The Alabama Paradox The question: Seats in a parliament are allocated according to the population size of the voting districts.
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Jefferson Apportionment Method Quiz - Quizizz
Q. Populations are as listed: State A-1,500 State B-1,800 State C-2,200 State D-2,700 Find standard divisor if 150 seats are being apportioned
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After calculating the apportionment for all of the states, Alabama does not receive any of the surplus states, and remains with 7 seats.
Background Continued
In 1790, there was a call to apportion seats to the House of Representatives, and though there was debate among whether to use methods of Jefferson or Hamilton, Jefferson's method prevailed
The Hamilton Method Today
Upon further investigation, Seaton found that if the total amount of seats in the House of Representatives was 299, Alabama would receive 8 seats, but if the total was 300, then it would receive 7.
The 1870 Census
Webster's method was used until the mid-20th century, when it was replaced by a method proposed by a man named Edward Vermilye Huntington, which we know as the Hill-Huntington model
How far does Achilles run in the Paradox of Achilles and the Tortoise?
In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 feet. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 feet, bringing him to the tortoise’s starting point. During this time, the tortoise has run a much shorter distance, say, 10 feet. It will then take Achilles some further time to run that distanc
What happens if you replace birthdays with passwords?
If we replace our birthday persons with online passwords we get the basis for a type of hack known as the birthday attack. When you make a password for a website that password is crunched into a fixed length hash value that stores and identifies the combination of characters in the input. So like 12345 becomes 827 c c b 0 e e a 8 a 706 c 4 c 34 a 16891 f 84 e 7 b. When the MD5 message-digest algorithm was a standard for encryption, its 128-bit 32-hexadecimal hashes were vulnerable to a hack based on the birthday paradox. The goal was to find and force a collision when two hashes have the same exact value regardless of what that value is. So, if Mathematics.doc and Beacon.doc have the same hash value, say a 316 a f c 4 c 04 d 1 a 8 e l 93 f b 6 a 0 a 65, one could change information in one and affect the other. Or one can eventually use collisions like this to decode the encryption algorithm itself and learn how it works. And the best way to do this is a trial and error or brute-force attempt to guess a specific match in the 3.4 x 10 38 possible outcomes. It was putting the birthday paradox to use. Hackers developed an algorithm based on the math of the birthday paradox to cause hash collisions more quickly and ultimately crack one of the most widely used cryptographic algorithms of its time. So, probability surrounding birthdays helped the improvement of internet security.
What is the Alabama paradox?
The Alabama paradox was the first of the apportionment paradoxes to be discovered. The US House of Representatives is constitutionally required to allocate seats based on population counts, which are required every 10 years. The size of the House is set by statute.
How many seats did Alabama get with a house size of 299?
W. Seaton, chief clerk of the United States Census Bureau, computed apportionments for all House sizes between 275 and 350, and discovered that Alabama would get 8 seats with a House size of 299 but only 7 with a House size of 300. In general the term Alabama paradox refers to any apportionmen
What are some examples of the Abilene paradox?
There are plenty of examples of the Abilene paradox, probably, in your own life. Let’s say you and friends are very tired after a day of rafting, but it’s Saturday night. One of you might think everyone would perk up and feel better if you went out bar-hopping . . . actually, the Abilene scenarios are just too stupid; and I am going to stop here.
How many people share the same birthday?
The answer may seem surprisingly low. In a group of 23 people there’s a 53.73 % chance that two people will share the same birthday. The odds aren’t 23 365 ≈ 6 %. This seems impossible as we got so few people and so many possible birthdays. And if we have 50 persons the odds of a birthday match jump up to 97 % and at 75 it’s 99.97 %, making it a virtual certainty that if you get 75 persons together, two of them will share a birthday. But with 365 days in a year, how’s it possible that you need such a small group to get even odds of a shared birthday? This is known as the birthday paradox. The birthday paradox is a veridical paradox. It’s surprising and absurd sounding but we have the math to prove it’s true. How is it possible that so few persons can have such a high chance of sharing a birthday and how is it that despite 365 possibilities, we only need 1 6 th of that number to be pretty sure that there’s a match? Why is our intuition so wrong?
How many pairs of pairs are there in a group of 5?
A group of 5 people has 10 possible pairs. Each of the 5 people can be paired with any of the other 4. 1 2 of those combinations are redundant because pairing person A with person B is same as pairing B with A. So, we divide by 2. By the same reasoning a group of 10 people has 10 × 9 2 = 45 pairs and a group of 23 has 23 × 22 2 = 253. The number of pairs grows quadratically meaning it’s proportional to the square of the number of people in the group. Unfortunately, our brains are notoriously bad at intuitively grasping non-linear functions. So it seems improbable at first that 23 people will produce 253 possible pairs. Once our brains accept that, the birthday problem makes more sense. Every one of those 253 pairs is a chance of a birthday match. For the same reason in a group of 70 people there are 2415 possible pairs and the probability that two people have the same birthday is more than 99.9 %. The birthday problem is just one example where math can show that things that seem impossible, like the same person winning a lottery twice actually aren’t unlikely at all. Sometimes coincidences aren’t as coincidental as they seem.
What is the Alabama paradox?
Alabama paradox. The Alabama paradox was the first of the apportionment paradoxes to be discovered. The US House of Representatives is constitutionally required to allocate seats based on population counts, which are required every 10 years. The size of the House is set by statute.
What is the inverse correlation between income and population growth?
For inverse correlation between income and population growth, see income and fertility. An apportionment paradox exists when the rules for apportionment in a political system produce results which are unexpected or seem to violate common sense . To apportion is to divide into parts according to some rule, the rule typically being one of proportion.
How many seats did Oklahoma have in 1907?
In 1907, when Oklahoma became a state, it was given a fair share of seats and the total number of seats increased by that number. The House increased from 386 to 391 members. A recomputation of apportionment affected the number of seats because of other states: New York lost a seat while Maine gained one.
Why would a pre-existing state lose a seat in the House of Representatives?
Also, even if the number of members in the House of Representatives is increased by the number of Representatives in the new state, a pre-existing state could lose a seat because of how the particular apportionment rules deal with rounding methods.
How does adding a new state affect the number of representatives?
Given a fixed number of total representatives (as determined by the United States House of Representatives), adding a new state would in theory reduce the number of representatives for existing states, as under the United States Constitution each state is entitled to at least one representative regardless of its population. Also, even if the number of members in the House of Representatives is increased by the number of Representatives in the new state, a pre-existing state could lose a seat because of how the particular apportionment rules deal with rounding methods. In 1907, when Oklahoma became a state, it was given a fair share of seats and the total number of seats increased by that number. The House increased from 386 to 391 members. A recomputation of apportionment affected the number of seats because of other states: New York lost a seat while Maine gained one.
What is the population paradox?
Population paradox. 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.
How is fair share computed?
First, the fair share of each state is computed, i.e. the proportional share of seats that each state would get if fractional values were allowed. Second, each state receives as many seats as the whole number portion of its fair share.
What is the Alabama paradox?
The Alabama Paradox states that increasing the total number of available voting seats causes a state to lose seats overall. It is called the Alabama Paradox because it was found in 1880 by C.W. Seaton and related to the fact that Alabama would actually lose a seat if the number of total seats available were 300.
What is a paradox in math?
A paradox is when logical operations result in illogical results, like the three main paradoxes of House apportionment. Explore the Alabama, New State, and Population paradoxes, as evaluated with Hamilton method of apportionment. Updated: 10/28/2021
What is Hamilton method of apportionment?
The Hamilton method of apportionment states that each state should be assigned their lower quota of seats, then, any leftover seats should be assigned based on descending order of fractional quotas. To understand all these terms, it is easiest to just work through the calculations, pointing out the terms on the way. In this scenario, let's assume that you are building a local focus group to support your school system. You want 40 teachers representing the high school, middle school, and primary school to be on your board.
What are the three paradoxes in the House of Representatives?
In this lesson, we are going to talk about three famous paradoxes that impact the method of apportionment in the House of Representatives; they are the Alabama, New State, and Population Paradoxes. A paradox is a contradictory situation in which logical procedures seem to result in illogical outcomes - otherwise stated: logical steps leading to an illogical result; that's a paradox! A common paradox can be found in the substance dry-ice. It is so cold that it actually burns the skin. How can something cold burn? It's a paradox - a contradiction that exists in a special situation.
How to find the standard quota of a school?
This is a fractional number derived by dividing the individual population by the standard divisor, representing the raw number of seats the school should get. Here, the high school standard quota is 10,170 divided by 500, or 20.34. Using the same calculation, we get the middle school standard quota of 18.3, and the primary school gets 1.36 seats on the board.
What is the New State Paradox?
The New State Paradox states that adding a new entity to the population as well as a fair number of additional seats to accommodate the new entity can still impact the existing entities' numbers. This paradox was found in 1907 when Oklahoma was added to the Union. Even though five seats were added to the House of Representatives to accommodate Oklahoma's quota, the re-apportionment altered other states' total apportioned seats.
What is the population paradox?
The final paradox we will discuss is the Population Paradox, which states increasing population can cause an entity to lose voting seats. This actually happened to the state of Virginia around 1900. It was increasing in size rapidly, but when a new apportionment was calculated, Virginia lost a seat instead of gaining seats in proportion to its gained population.