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Statistical analysis of the departure from proportionality in the 1991 election in Poland

Bondarczuk Z., Ciok A., Szczęsny W.

Matematyka Stosowana : matematyka dla społeczeństwa

1993

Nr 36

115--128

New statistical measures of departure from proportional representation, introduced in Bondarczuk, Kowalczyk, Pleszczyńska and Szczęsny (1992), are applied to the results of the 1991 election to the Polish Parliament. A pair of indices is used to evaluate departures from proportionality between number of votes and number of elects. One index indicates general strength of the departures, the other one indicates to which extent they are due to overrepresentation increasing (or decreasing) with number of votes. The indices are corrected in order to eliminate the influence of the distribution of votes, number of votes and size of representation. The correction is based on intensive computer simulation. The analysis of the election data showed significant overrepresent ation of six parties (or group of parties forming election committees) with maximal numbers of votes. On the other hand, in the subpopulation of voters formed by these six parties only, the departure from proportionality is very small.