PaReSoGo: Dataset on party representation of social groups for 25 countries, 2002–2016

Whereas social scientists have devised various ways to measure representation gaps between the political elite and the masses across nations and time, few datasets can be used to measure this gap for particular social groups. Minding the gap between what parties social groups vote for and what parties actually attain seats in parliament can reveal the position of social groups in the political power structure. We help to fill this gap with a new publicly available dataset, Party Representation of Social Groups (PaReSoGo), consisting of 25 countries and 150 country-years, and a method for its construction. We used the European Social Survey 2002–2016 and ParlGov data for this time span to create a Dissimilarity Index. To demonstrate the utility and flexibility in the combination of cross-national surveys and administrative data, we chose social groups of gender, age, and education, as well as intersectional groups based on gender and age, and attitudinal groups. We conclude this research note with empirical illustrations of PaReSoGo’s use.

On atom-swarming and Luce’s theorem for probabilistic beliefs

For qualitative probability spaces, monotone continuity and third-order atom-swarming are together sufficient for a unique countably additive probability measure representation that may have atoms (Mackenzie in Theor Econ 14:709–778, 2019). We provide a new proof by appealing to a theorem of Luce (Ann Math Stat 38:780–786, 1967), highlighting the usefulness of extensive measurement theory (Krantz et al. in Foundations of Measurement Volume I: Additive and Polynomial Representations. Academic Press, New York, 1971) for economists.

Gabriel–Roiter Measure, Representation Dimension and Rejective Chains

The Gabriel–Roiter measure is used to give an alternative proof of the finiteness of the representation dimension for Artin algebras, a result established by Iyama in 2002. The concept of Gabriel–Roiter measure can be extended to abelian length categories and every such category has multiple Gabriel–Roiter measures. Using this notion, we prove the following broader statement: given any object $X$ and any Gabriel–Roiter measure $\mu$ in an abelian length category $\mathcal{A}$, there exists an object $X^{\prime}$ that depends on $X$ and $\mu$, such that $\Gamma =\operatorname{End}_{\mathcal{A}}(X\oplus X^{\prime})$ has finite global dimension. Analogously to Iyama’s original results, our construction yields quasihereditary rings and fits into the theory of rejective chains.

A foundation for probabilistic beliefs with or without atoms

We propose two novel axioms for qualitative probability spaces: (i) unlikely atoms, which requires that there is an event containing no atoms that is at least as likely as its complement; and (ii) third‐order atom‐swarming, which requires that for each atom, there is a countable pairwise‐disjoint collection of less‐likely events that can be partitioned into three groups, each with union at least as likely as the given atom. We prove that under monotone continuity, each of these axioms is sufficient to guarantee a unique countably‐additive probability measure representation, generalizing work by Villegas to allow atoms. Unlike previous contributions that allow atoms, we impose no cancellation or solvability axiom.

KESULITAN MAHASISWA CALON GURU FISIKA DALAM MEREPRESENTASIKAN KONSEP LISTRIK MAGNET

Communication in science is multimodal (verbal and visual). Representation skills are one of the communication skills in science. A physics teacher is required to have representation skills so that the students more easily to acsess the concept that they have to lean and the teacher communicate physics concepts more easily to his students. This study examines the representation skills of preservice physics teacher. Three aspects of representation skills, that examined are: 1) the skill of making a single mode representation, 2) the skills of translation between representation modes and 3) multi-representation skills. The instrument used to measure representation skills has been validated and used to measure representation skills of preservice physics teacher in Listrik-Magnet courses. The results showed that the preservive physics student have difficulty in making all of the aspect of representation. It is occured because there has never been learning related to representation or assessment skills that specifically test their representation skills

Convex and Radially Concave Contoured Distributions

Integral representations of the locally defined star-generalized surface content measures on star spheres are derived for boundary spheres of balls being convex or radially concave with respect to a fan inRn. As a result, the general geometric measure representation of star-shaped probability distributions and the general stochastic representation of the corresponding random vectors allow additional specific interpretations in the two mentioned cases. Applications to estimating and testing hypotheses on scaling parameters are presented, and two-dimensional sample clouds are simulated.

Relations Between Hidden Regular Variation and the Tail Order of Copulas

We study the relations between the tail order of copulas and hidden regular variation (HRV) on subcones generated by order statistics. Multivariate regular variation (MRV) and HRV deal with extremal dependence of random vectors with Pareto-like univariate margins. Alternatively, if one uses a copula to model the dependence structure of a random vector then the upper exponent and tail order functions can be used to capture the extremal dependence structure. After defining upper exponent functions on a series of subcones, we establish the relation between the tail order of a copula and the tail indexes for MRV and HRV. We show that upper exponent functions of a copula and intensity measures of MRV/HRV can be represented by each other, and the upper exponent function on subcones can be expressed by a Pickands-type integral representation. Finally, a mixture model is given with the mixing random vector leading to the finite-directional measure in a product-measure representation of HRV intensity measures.