Fair apportionment of voting districts in Hungary?

One of the aims of the new electoral law of Hungary has been to define a fairer apportionment into voting districts. This is ensured by a set of rules slightly more premissive than those laid out in the Code of Good Practice in Electoral Matters of the Venice Commission. These rules fix the average size of the voting districts, require voting districts not to split smaller towns and villages and not to cross county borders. We show that such an apportionment is mathematically impossible. We make suggestions both to the theoretical approach to resolve this problem, study the properties of our approach and using our efficient algorithm and the data of the 2010 national elections we determine the optimal apportionment. We also study the expected effect of demographic changes and formulate recommendations to adhere to the rules over the long term: increase the number of voting districts to about 130, allow the number of voting districts to change flexibly at each revision of the districts and base the districts on regions rather than counties.