A New Method for Defining Electoral Units in Croatia

  • Kristian Sabo Odjel za matematiku, Sveučilište Josipa Jurja Strossmayera u Osiijeku
  • Rudolf Scitovski Fakultet primijenjene matematike i informatike, Sveučilište Josipa Jurja Strossmayera u Osijeku
Keywords: elections, electoral units, weight of the electoral votes, apportionment methods, clustering


The paper shows how it is possible to configure electoral units in such a way as to preserve the borders of the counties, while at the same time keeping the relative differences in the weights of voters’ votes within the predetermined accuracy (i.e. 5%). When creating a proposal for the configuration of electoral units, it is
necessary to define the number of electoral units and the maximum relative difference in the weights of electoral votes. After the proposal is made, it should be evaluated and compared with other proposals in terms of the indicated indices, and the one that shows the best properties should be taken as the final solution. Two proposals providing for six constituencies and two proposals providing for ten constituencies are presented. The proposals are chosen from a set of solutions provided by an algorithm based on its own method. As a result, the algorithm gives possible configurations for which the maximum absolute relative deviation of the weight of a voter’s vote by electoral unit from the average weight of a voter’s vote is less than the predetermined accuracy, which we set at 5%. A quantitative comparison of the index of the proposals of NOVI–6a and NOVI–6b with six constituencies with the proposals by GONG and SDP shows that the proposals
of NOVI–6a and NOVI–6b have slightly better properties. Also, the proposals of NOVI–10a and NOVI–10b with ten constituencies, in terms of the indices, are slightly worse than the configurations with six constituencies. On the other hand, since the division into ten constituencies in Croatia has been in force for more than two decades, the aforementioned proposals could also be taken into account. The deviations in the weight of a voter’s vote in the case of a proposal in which the constituencies coincide with the counties amount to over 60%, and in this sense such a proposal is not appropriate. Finally, the latest proposal by the Government from 2023: (1) does not respect the borders of counties, (2) based on the population census, the weights of voters’ votes by electoral unit differ by more than 13%, and (3) the index values are higher compared to all proposals.