Alabama paradox

Alabama paradox means adding seats may cause some list  lose a seat,It is a kind of “relative fairness” as a standard distribution method in the share of paradox.

History

The Alabama  paradox was discovered in 1880, when it was found that increasing the total number of seats would decrease Alabama’s share from 8 to 7. There was more to come—in the 1900s, Virginia  lost a seat to Maine as a result of its population growing faster  than Maine’s. When Oklahoma became a state in 1907, a recomputation of apportionment showed that the number of seats due to other states would be affected even though Oklahoma would be given a fair share of seats and the total number of seats increased by that number.

The method for apportionment used during this period, originally put forth by Alexander Hamilton but not adopted until 1852, was as follows. First, the fair share of each state, i.e. the proportional share of seats that each state would get if fractional values were allowed, is computed. Next, the fair shares are rounded down to whole numbers, resulting in unallocated “leftover” seats. These seats are allocated, one each, to the states whose fair share exceeds the rounded-down number by the highest amount.

One might expect that the abundance of paradoxes is perhaps due to some deficiency of Hamilton’s method. Indeed, a number of schemes have been proposed and four different methods were signed into law (five counting repetitions). Amusingly, this vacillation has had less to do with mathematical than political considerations, such as the total number of seats that each party would be allotted by a given method. No method, however, has been found perfectly satisfactory in practice.

Background knowledge

In 1881 while considering reapportionment the united states congress wiscovered that by using the then current system.Alabama would be entitled to 8 representatives in a House with 299 members,but would receive only 7 representatives in a 300 member house.Wihtout any change in population  Alabama would receive fewer representatives in a larger house.This came to be known as the Alabama paradox.

Here we will take a simpler example in which the same situation arises .
A college has three main departments:Arts,science and engineering.There are 235 students in the ATS department,333 students in the science department and 432 in engineering,a total of 1000 students.The college has a 10 member student council to look after student affairs.

Other introduce

The Alabama paradox was the first of the apportionment paradoxes to be discovered. After the 1880 census, C. W. Seaton, chief clerk of the U. S. Census Office, 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 apportionment scenario where increasing the total number of items would decrease one of the shares

Maybe you are interested in Game Theory