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In this article we propose a new conceptualization of the crucial party system characteristics: disproportionality, electoral volatility, territorial heterogeneity and inter-election incongruence. We argue that these characteristics can be studied as dissimilarities between vectors of votes or seats. We present different specifications of vectors in order to address various research questions important for students of parties and party systems. Subsequently, developing the analyses of Monroe (1994) and Taagepera and Grofman (2003), we present nine measures of vectors’ dissimilarity: index of dissimilarity, Gallagher’s least squares measure and its transformations, cosine measure, Gini coefficient, Kullback-Leibler divergence (relative entropy), weighted variance and weighted standard deviation of ratios. We discuss their utility in empirical studies of main party system characteristics, using several dimensions of comparison, based on the formal postulates. We also add two new postulates concerning measure’s decomposability: horizontal (sumtype) and vertical (variance-type).

The disproportionality is one of the main problems of political representation. Nonetheless, the empirical research on disproportionality in local councils occurs only as an exception. In our paper we demonstrate how disproportionality can be studied at the local level. Following van Puyenbroeck (2008), we distinguish the postulates of “equally treated voters” and “equally treated parties” which are the basis for the assessment of disproportionality. Using the results of recent Polish local elections (2010), we demonstrate how the disproportionality varies between the municipalities of different size, using different electoral formulae, how it is affected by the electoral districting, seat apportionment and local differences in turnout. Moreover, as a preparation for the empirical study of the electoral reform, effective in 2014 (November) elections, we formulate several hypotheses on how the introduction of single-member districts would affect political representation at the local level.

Welzel et al. (2021) claim that non-invariance of instruments is inconclusive and inconsequential in the field for cross-cultural value measurement. In this response, we contend that several key arguments on which Welzel et al. (2021) base their critique of invariance testing are conceptually and statistically incorrect. First, Welzel et al. (2021) claim that value measurement follows a formative rather than reflective logic. Yet they do not provide sufficient theoretical arguments for this conceptualization, nor do they discuss the disadvantages of this approach for validation of instruments. Second, their claim that strong inter-item correlations cannot be retrieved when means are close to the endpoint of scales ignores the existence of factor-analytic approaches for ordered-categorical indicators. Third, Welzel et al. (2021) propose that rather than of relying on invariance tests, comparability can be assessed by studying the connection with theoretically related constructs. However, their proposal ignores that external validation through nomological linkages hinges on the assumption of comparability. By means of two examples, we illustrate that violating the assumptions of measurement invariance can distort conclusions substantially. Following the advice of Welzel et al. (2021) implies discarding a tool that has proven to be very useful for comparativists.