Biproportional apportionment

Condorcet methods Positional voting Cardinal voting Quota-remainder methods Approval-based committees Fractional social choice Semi-proportional representation By ballot type Pathological response Strategic voting Paradoxes of majority rule Positive results Biproportional apportionment is a proportional representation method to allocate seats in proportion to two separate characteristics.

Analogically, the same highest averages method is used to determine how many of all seats each region deserves.

Effectively, the objective of the iterative process is to modify the regional divisors and party divisors so that The following two correction steps are executed until this objective is satisfied: Using the Sainte-Laguë method, this iterative process is guaranteed to terminate with appropriate seat numbers for each regional party list.

Suppose there are three parties A, B and C and three regions I, II and III and that there are 20 seats are to be distributed and that the Sainte-Laguë method is used.

The final seat numbers are: A method of biproportional appointment that was proposed in 2003 by German mathematician Friedrich Pukelsheim[1] is now used for cantonal and municipal elections in some cantons of Switzerland, i.e. Zurich (since 2006), Aargau and Schaffhausen (since 2008), Nidwalden, Zug (since 2013), Schwyz (since 2015) and Valais (since 2017).

It was proposed in 2008 by Michel Balinski (who also invented the single-winner voting system called majority judgment) as a way to eliminate the power of gerrymandering, especially in the United States.