Understanding Alabama Paradox Testing
An Alabama paradox calculator studies a surprising apportionment problem. A group may lose a seat after the total number of seats grows. That result feels unfair because more seats should usually help, or at least not hurt, any participant. The effect is linked to Hamilton apportionment. This method uses quotas, lower quotas, and fractional remainders.
Why The Paradox Matters
Apportionment appears in legislatures, committees, budget shares, school boards, districts, and weighted representation plans. A small rounding rule can change final seats. The Alabama paradox shows why a simple largest remainder method can behave in an unexpected way. It does not mean the arithmetic is wrong. It means the rule has a weakness when the house size changes.
What The Calculator Checks
This tool compares two Hamilton allocations. The first allocation uses the original seat total. The second allocation uses a larger total. For each group, the calculator lists population, quota, lower quota, remainder, seat count, and change. A paradox warning appears when a group has fewer seats in the larger allocation.
How The Numbers Move
When total seats increase, every quota increases. However, fractional remainders do not rise evenly. One group may move from a strong remainder rank to a weaker rank. Another group may pass it. Since leftover seats are assigned by remainder rank, the final distribution can shift sharply. That shift can remove a seat from a smaller or middle group.
Good Data Practices
Use current population figures. Keep group names clear. Check totals before sharing results. Try nearby seat counts to see whether the outcome is stable. Review tie settings when remainders are equal. Export the result for audit records. The table helps explain every step. It also helps readers see why a paradox was detected.