The classic example of the apportionment problem deals with the U.S. House of Representatives, but it also arises in other contexts as well. For example, in the allocation of course sections based on enrollments, and deciding how many buses to give to various lines based on ridership.
The applet below will calculate an apportionment based on the Hamilton, Jefferson, Webster and Hill-Huntington methods. For each problem enter the population for each group (e.g., bus route, state population, etc.), the total population N and h (i.e., the size or number of things to allocate). Click the Apportionment button to fill in the mini-spreadsheet.
Problem 1: A bus company has three lines and a total of 48,000 riders. Route 1 has 21,700 riders, route 2 has 17,200 and route 3 has 9,100. The company has 40 buses to allocate to the three lines.
Problem 2: After a period of time our bus company in Problem 1 increases its number of buses to 60, even though the number of riders remain at 48,000. There have been slight shifts in the number of riders on each line. Route 1 now has 21,100 riders daily, Route 2 has 16,700 and Route 3 has 10,200.
Problem 3: The city grows and our bus company adds two new lines. There are now 70,000 riders and 100 buses to distribute among the five lines. The number of riders per line is as follows: Route 1 - 21,600, Route 2 - 19,400, Route 3 - 15,200, Route 4 - 8,745, Route 5 - 5,055.
Problem 4: A certain country has a parliamentary system in which the 100 seats in the parliament are allocated proportionately to the voters a party obtains in an election. A total of 2,605,000 votes are cast, with Party 1 obtaining 1,150,000 votes, Party 2 has 944,000 votes, Party 3 420,000 votes, and Party 4 just 91,000 votes.