A Central Limit Theorem for intransitive dice

Intransive dice $D^{(1)}, \ldots, D^{(\ell)}$ are dice such that $D^{(1)}$ has advantage with respect to $D^{(2)}$, dice $D^{(2)}$ has advantage with respect to $D^{(3)}$ and so on, up to $D^{(\ell)}$, which has advantage over $D^{(1)}$. In this twofold work, we present: first, (deterministic) results on existence of general intransitive dice. Second and mainly, a central limit theorem for the vector of normalized victories of a die against the next one in the list when the faces of a die are i.i.d.\ random variables and all dice are independent, but different dice may have distinct distributions associated to, as well as they may have distinct number of faces. From this central limit theorem we derive a criteria to assure that the asymptotic probability of observing intransitive dice is null, which applies for many cases, including all continuous distributions and many discrete ones.Comment: 37 pages, 3 figure

Quantifying garnet-melt trace element partitioning using lattice-strain theory: New crystal-chemical and thermodynamic constraints

Many geochemical models of major igneous differentiation events on the Earth, the Moon, and Mars invoke the presence of garnet or its high-pressure majoritic equivalent as a residual phase, based on its ability to fractionate critical trace element pairs (Lu/Hf, U/Th, heavy REE/light REE). As a result, quantitative descriptions of mid-ocean ridge and hot spot magmatism, and lunar, martian, and terrestrial magma oceans require knowledge of garnet-melt partition coefficients over a wide range of conditions. In this contribution, we present new crystal-chemical and thermodynamic constraints on the partitioning of rare earth elements (REE), Y and Sc between garnet and anhydrous silicate melt as a function of pressure (P), temperature (T), and composition (X). Our approach is based on the interpretation of experimentally determined values of partition coefficients D using lattice-strain theory. In this and a companion paper (Draper and van Westrenen this issue) we derive new predictive equations for the ideal ionic radius of the dodecahedral garnet X-site,

Measuring collective action intention toward gender equality across cultures

Collective action is a powerful tool for social change and is fundamental to women and girls’ empowerment on a societal level. Collective action towards gender equality could be understood as intentional and conscious civic behaviors focused on social transformation, questioning power relations, and promoting gender equality through collective efforts. Various instruments to measure collective action intentions have been developed, but to our knowledge none of the published measures were subject to invariance testing. We introduce the gender equality collective action intention (GECAI) scale and examine its psychometric isomorphism and measurement invariance, using data from 60 countries (N = 31,686). Our findings indicate that partial scalar measurement invariance of the GECAI scale permits conditional comparisons of latent mean GECAI scores across countries. Moreover, this metric psychometric isomorphism of the GECAI means we can interpret scores at the country-level (i.e., as a group attribute) conceptually similar to individual attributes. Therefore, our findings add to the growing body of literature on gender based collective action by introducing a methodologically sound tool to measure collective action intentions towards gender equality across cultures

Measuring collective action intention toward gender equality across cultures

Collective action is a powerful tool for social change and is fundamental to women and girls’ empowerment on a societal level. Collective action towards gender equality could be understood as intentional and conscious civic behaviors focused on social transformation, questioning power relations, and promoting gender equality through collective efforts. Various instruments to measure collective action intentions have been developed, but to our knowledge none of the published measures were subject to invariance testing. We introduce the gender equality collective action intention (GECAI) scale and examine its psychometric isomorphism and measurement invariance, using data from 60 countries (N = 31,686). Our findings indicate that partial scalar measurement invariance of the GECAI scale permits conditional comparisons of latent mean GECAI scores across countries. Moreover, this metric psychometric isomorphism of the GECAI means we can interpret scores at the country-level (i.e., as a group attribute) conceptually similar to individual attributes. Therefore, our findings add to the growing body of literature on gender based collective action by introducing a methodologically sound tool to measure collective action intentions towards gender equality across cultures.info:eu-repo/semantics/acceptedVersio

Gendered self-views across 62 countries: a test of competing models

Social role theory posits that binary gender gaps in agency and communion should be larger in less egalitarian countries, reflecting these countries’ more pronounced sex-based power divisions. Conversely, evolutionary and self-construal theorists suggest that gender gaps in agency and communion should be larger in more egalitarian countries, reflecting the greater autonomy support and flexible self-construction processes present in these countries. Using data from 62 countries (N = 28,640), we examine binary gender gaps in agentic and communal self-views as a function of country-level objective gender equality (the Global Gender Gap Index) and subjective distributions of social power (the Power Distance Index). Findings show that in more egalitarian countries, gender gaps in agency are smaller and gender gaps in communality are larger. These patterns are driven primarily by cross-country differences in men’s self-views and by the Power Distance Index (PDI) more robustly than the Global Gender Gap Index (GGGI). We consider possible causes and implications of these findings

Measuring collective action intention toward gender equality across cultures

Collective action is a powerful tool for social change and is fundamental to women and girls’ empowerment on a societal level. Collective action towards gender equality could be understood as intentional and conscious civic behaviors focused on social transformation, questioning power relations, and promoting gender equality through collective efforts. Various instruments to measure collective action intentions have been developed, but to our knowledge none of the published measures were subject to invariance testing. We introduce the gender equality collective action intention (GECAI) scale and examine its psychometric isomorphism and measurement invariance, using data from 60 countries (N = 31,686). Our findings indicate that partial scalar measurement invariance of the GECAI scale permits conditional comparisons of latent mean GECAI scores across countries. Moreover, this metric psychometric isomorphism of the GECAI means we can interpret scores at the country-level (i.e., as a group attribute) conceptually similar to individual attributes. Therefore, our findings add to the growing body of literature on gender based collective action by introducing a methodologically sound tool to measure collective action intentions towards gender equality across cultures