The article presents the electoral formulae used in systems of proportional representation and it analyses the degree of proportionality in the division of mandates among political parties. Proportionality is a key factor in determining the political consequences of the formulae used and at the same time it is an indicator of the distortion of party representation. The research the article draws on was based on the Monte Carlo method. Eight indexes of proportionality were used to compare the qualities of electoral formulae. The results of their measurements differed significantly. A more detailed analysis is made of two main approaches to proportionality, represented by the two most important indexes: the Loosemore-Hanby index and the RR index. Using them electoral formulae are classified into two types of scales according to the degree of disproportionality (on a proportionality - disproportionality continuum) and the direction of disproportionality ('to the advantage of small parties - to the advantage of large parties' continuum). These scales relativise some of the conclusions formulated to date in literature in this field. The article also suggests a scale of formulae constructed on the basis of a third, compromise approach, as the weighted average of the Loosemore-Hanby and the RR indexes.
The article exposes the problems connected with defining and measuring the proportionality of election results. It presents current and predominant methods used to measure proportionality and points to some possible alternative approaches to understanding and measuring proportionality. Current discourse gives priority to measuring proportionality using one of two basic methods for determining the proportional division of seats: quotas and largest remainders. Proportionality measured using these formulae is based on the principle of summing up the absolute differences between the share of votes and the share of seats. These measurement methods are known for their ability to best assess election results attained with the aid of the Hare quota and the largest remainders method. The article therefore presents an alternative approach in the 'real quota theory', which provides the theoretical bases for constructing a new RR index and its derivatives the ARR and the SRR indices. This approach to measurement is tied to the principle of dividing seats using the highest averages method, that is, the d'Hondt divisor. These new indices are defined as alternatives to traditional indices of proportionality.