Apportionment Math: Hamilton, Jefferson, Webster & Huntington–Hill

What you'll build

What you will be able to do

Each lab ends with a concrete result that you build yourself and the checker confirms, cell by cell.

• Calculate the standard divisor and each state's exact quota of the 40 seats, round the quotas down and count the seats that are still left to hand out.
• Rank the fractional parts of the quotas and give the leftover seats to the states with the largest remainders, exactly as Hamilton's method (largest remainder method) does.
• Apportion the 40 seats with Jefferson's method using a modified divisor, check that exactly 40 seats are handed out and find the divisor at which the next seat would go to another state.
• Round the standard quotas normally, see that the seats do not add up, fix it with a modified divisor and compare Webster's seats with Hamilton's.
• Round each modified quota at the geometric mean of its two neighbouring whole numbers, see why the smallest state gains a seat, and use priority values to find who would get seat 41.
• Put the four apportionments side by side, measure how far Jefferson moves away from the quota, count the states that gain under Jefferson, compare representation per seat and chart the four methods.
• Rerun Hamilton's method with 41 seats and watch Dunmoor lose a seat when the House grows, then show that Dunmoor also loses a seat to a slower-growing state after a new census.
• Build the quotient tables for D'Hondt and Sainte-Laguë, find the 15th-largest quotient with LARGE and count each party's seats with COUNTIF.