In this paper we analyze the consequences of the fairness recommendation of the Venice Commission in allocating voting districts among larger administrative regions. This recommendation requires the size of any constituency not to differ from the average constituency size by more than a fixed limit. We show that this minimum difference constraint, while attractive per definition, is not compatible with monotonicity and Harequota properties, two standard requirements of apportionment rules. We present an algorithm that efficiently finds an allotment such that the differences from the average district size are lexicographically minimized. This apportionment rule is a welldefined allocation mechanism compatible with and derived from the recommendation of the Venice Commission. Finally, we compare this apportionment rule with mainstream mechanisms using real data from Hungary and the United States.
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