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Several multi-winner systems that use approval voting have been developed butthey each suffer from various problems. Six of these methods are discussed inthis paper. They are Satisfaction Approval Voting, Minimax Approval Voting,Proportional Approval Voting, Monroe's Fully Proportional Representation,Chamberlin-Courant's Rule, and Ebert's method. They all fail at least one ofProportional Representation (PR), strong PR, monotonicity or positive support.However, the new method described in this paper - Proportional Approval Methodusing Squared loads, Approval removal and Coin-flip approval transformation(PAMSAC) - passes them all. PAMSAC uses the squared loads of Ebert's method,but removes non-beneficial approvals to restore monotonicity. It also uses theCoin-Flip Approval Transformation (CFAT), where voters are "split" into two foreach candidate they approve, and where one half of this split voter approvesand the other half does not approve each candidate approved on the ballot. Thisrestores positive support, and also makes the method equivalent to the D'Hondtparty-list method for party voting. PAMSAC reduces to simple approval voting inthe single-winner case. A score voting version is described that also reducesto simple score voting in the single-winner case.

Proportional Approval Method using Squared loads, Approval removal and  Coin-flip approval transformation (PAMSAC) - a new system of proportional  representation using approval voting