engleski

Over- and Underrepresentation in Proportional Electoral Systems -- an Empirical Study

We consider the proportional electoral seat allocation methods, with respect to the problem of fair seat distributions or a fair representation. Let n be the total number of parties, s=(s_1, ..., s_n) be the vector of seats assigned to corresponding parties and let v=(v_1, ..., v_n) be the vector of votes each party receives. In general, since there exists the integer constraint on the number of seats, s_i integers for all i=1, ..., n, over- and underrepresentation of the parties appear. With respect to the quality of the representation, one can define a representation vector y=(y_1, ..., y_n$, where y_i=s_i / v_i is a seat-to-vote ratio (seat density per vote) of the party i, i=1, ..., n. In relation to the representation vector y, we look at the so-called Lorenz curve and Gini concentration index, as well as the concept of majorization, as the measure of fair seat distributions, which have their origin in the measurement of fair income distributions in welfare economics. We apply several traditional quotient (largest remainders) methods and divisor methods to certain historical data. By an empirical study and simulation experiments we compare various methods from the viewpoint of the representation quality.

proportional electoral systems; over- and underrepresentation; quotient and divisor methods

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