A Dynamic Method of the Representatives Apportionment

All the federal unions, like the United States of America or the European Union face the issue of finding the right allocation of seats to their member states. There has been a lot of debates in the United States of America since two centuries in order to find the right mechanism to round off the number of representatives per state proportionally to their populations. This problem is now well documented. The existing methods of the representative apportionment actually are based on the max-utility rule, but they just satisfy one or two Fair Apportionment Axioms. To answer this question, we consider to present a dynamic apportionment method which satisfies the three axioms 1, 3 and 4. The calculable program is also presented.