Abstract The Venice Commission in its Code of Good Practice in Electoral Matters specifies that (single-seat) constituencies should be drawn so that the size difference of a constituency’s size from the average should not exceed a fixed limit while its borders must not cross the borders of administrative regions, such as states or counties. Assuming that constituencies are of equal size within each of the administrative regions, the problem is equivalent to the apportionment problem, that is, the proportional allocation of voting districts among the administrative regions. We show that the principle of maximum admissible departure is incompatible with common apportionment properties, such as monotonicity and Hare-quota. When multiple apportionments satisfy the smallest maximum admissible departure property we find a unique apportionment by the repeated application of the property. The allotment such that the differences from the average district size are lexicographically minimized can be found using an efficient algorithm. This apportionment rule is a well-defined allocation mechanism compatible with and derived from the recommendation of the Venice Commission. Finally, we compare this apportionment rule with mainstream mechanisms using data from Hungary, Germany and the United States
