Fair apportionment in the view of the Venice Commission’s recommendation

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 equivelent 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

Apportionment and districting by Sum of Ranking Differences

“…Optimization methods compose the third branch of apportionment methods. The Burt-Harris method [24,25] minimizes the maximum disparity in representation between any two states, while the Leximin method [26], lexicographically minimizes the maximum departure, that is, the difference between the population of any constituency and the average constituency size.…”

“…But this only applies within state. Across states there seems to be no restrictions-this is why currently the voters of Rhode Island have 88% more influence than the voters of Montana [26]. Table 3 summarizes the correspondence between apportionment methods and properties.…”

“…This is quite common in apportionment, see other examples in refs. [26] or [23]. Given that the apportionment may significantly affect the outcome of the election even small differences matter.…”

Applications of Compter Vision: Skyline Extraction and Congressional Districting [védés előtt] = A gépi látás alkalmazásai: skyline-kiemelés és választókerület-szabdalás

“…After we determined the number of citizens belonging to one district, the boundaries have to be drawn, which is critical from the perspective of proportional representation of the voters. More details on apportionment methods can be found in Kóczy et al [37] and [38]. Districting problems were examined by, for instance, Ricca et al [59], Kalcsics [35], Chambers [16], Oehrlein and Haunert [52], Tasnádi [69], and Puppe and Tasnádi [55].…”

Igazságosság és rangsorolás: Alkalmazások a közgazdaságtan és sport területéről

“…Hazai szerzők is foglalkoztak ezzel a problémával, Tasnádi (2008) eredménye szerint az 1990 és 2010 közötti magyar országgyűlési választásokon egy pártkoalíció számára hátrányossá válhatott a tagjaira leadott több szavazat. Biró et al (2012) és Biró et al (2015) a Velencei Bizottság választási kódexével összhangban a lexmin módszer használatát javasolja a körzetkiosztási probléma megoldására.…”