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.
