A bi-proportional method applied to the Spanish Congress

Abstract

A bi-proportional divisor method is applied to allocate the seats of the 2004 Spanish Congress, thus achieving proportionality relative to the population counts in the fifty-two provinces, as well as proportionality relative to the vote counts for the political parties. Also, advantages and disadvantages of the method are discussed.

Biproportional scaling of matrices and the iterative proportional fitting procedure

“…In 2003, the Swiss Canton of Zurich adopted a doubly proportional system, the biproportional divisor method with standard rounding, see Schuhmacher (2004, 2011), and Balinski and Pukelsheim (2006). The method may be attractive also for other countries as studied by Pennisi (2006) for Italy, Zachariassen and Zachariasen (2006) for the Faroe Islands, Ramírez et al (2008) for Spain, and Oelbermann and Pukelsheim (2011) for the European Union. A computer program for the calculations is provided at www.uni-augsburg.de/bazi, see Pukelsheim (2004), Joas (2005), Maier (2009).…”

Parametric maximum flow methods for minimax approximation of target quotas in biproportional apportionment

“…This software was successfully used in the 2006 elections of the Zurich Canton (Pukelsheim [26]) and more recently (2009) in those of the Aargau and the Schaffhausen Cantons. Several authors have advocated the use of sound biproportional apportionment algorithms to distribute seats to parties within districts in countries such as Mexico (Balinski and Ramırez [7]), France (Balinski [2]), Switzerland (Pukelsheim and Schuhmacher [27], Pukelsheim [26], Balinski and Pukelsheim [5, 6]), Italy (Pennisi et al [23]), Spain (Ramırez et al [29]), Faroe Islands (Zachariasen [33]). Balinski ([2] p. 215) discusses also the application of such algorithms to the election of French representatives in the European Parliament.…”