Scholars study representative international surveys to understand cross-cultural differences in mentality patterns, which are measured via complex multi-item constructs. Methodologists in this field insist with increasing vigor that detecting “non-invariance” in how a construct’s items associate with each other in different national samples is an infallible sign of encultured in-equivalences in how respondents understand the items. Questioning this claim, we demonstrate that a main source of non-invariance is the arithmetic of closed-ended scales in the presence of sample mean disparity. Since arithmetic principles are culture-unspecific, the non-invariance that these principles enforce in statistical terms is inconclusive of encultured in-equivalences in semantic terms. Because of this inconclusiveness, our evidence reveals furthermore that non-invariance is inconsequential for the cross-cultural functioning of multi-item constructs as concerns their nomological linkages to other variables of interest. We discuss the implications of these insights for measurement validation in cross-cultural settings with large sample mean disparity.

with almost ten staff, and a project team across the world with four Principal Investigators, fifteen Project Managers (PMs), 30+ Regional Managers, 170 Country Coordinators, Research Assistants, and 2,500 Country Experts, the V-Dem project is one of the largest ever social science research-oriented data collection programs.

Our original 2021 SMR article “Non-Invariance? An Overstated Problem with Misconceived Causes” disputes the conclusiveness of non-invariance diagnostics in diverse cross-cultural settings. Our critique targets the increasingly fashionable use of Multi-Group Confirmatory Factor Analysis (MGCFA), especially in its mainstream version. We document—both by mathematical proof and an empirical illustration—that non-invariance is an arithmetic artifact of group mean disparity on closed-ended scales. Precisely this arti-factualness renders standard non-invariance markers inconclusive of measurement inequivalence under group-mean diversity. Using the Emancipative Values Index (EVI), OA-Section 3 of our original article demonstrates that such artifactual non-invariance is inconsequential for multi-item constructs’ cross-cultural performance in nomological terms, that is, explanatory power and predictive quality. Given these limitations of standard non-invariance diagnostics, we challenge the unquestioned authority of invariance tests as a tool of measurement validation. Our critique provoked two teams of authors to launch counter-critiques. We are grateful to the two comments because they give us a welcome opportunity to restate our position in greater clarity. Before addressing the comments one by one, we reformulate our key propositions more succinctly.

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Many non-democratic countries anchor the word “democracy” in their national constitutions and everyday rhetoric, while ignoring the conceptual roots of democracy and its scholarly-defined procedural standards. This article argues that governments intentionally “oversell” democracy to their people, in order to exploit the legitimizing effect that the word embodies. This can, however, only succeed if the receiving side is susceptible to such claims to legitimacy. Accordingly, this study investigates how effective “overselling” attempts are in light of individuals' liberal vs. illiberal notions of democracy. Building on congruence theory, it juxtaposes the, at times blatant, “overselling” with individual-level notions of democracy and, thus, investigates whether governments' attempts to claim democratic-procedural legitimacy are contingent on citizens' understanding of the concept. Using multilevel moderation analyses, it shows that illiberal, authoritarian notions of democracy can convert “overselling” into positive evaluations of a regime, whereas prevailing liberal notions unmask “overselling” governments and create additional criticality. The conclusion argues that notions of democracy function as a filter, which matches true and false demand and supply of democracy. The findings help to understand why and how democratization movements can unfold and why some citizens see their country as democratic even though it is not.