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Primary law of the European Union demands that the allocation of the seats of the European Parliament between the Member States must obey the principle of degressive proportionality. The principle embodies the political aim that the more populous states agree to be underrepresented in order to allow the less populous states to be better represented. This paper reviews four allocation methods achieving this goal: the Cambridge Compromise, the Power Compromise, the Modified Cambridge Compromise, and the 0.5-DPL Method. After a year of committee deliberations, Parliament decreed on 7 February 2018 an allocation of seats for the 2019 elections that realises degressive proportionality, but otherwise lacks methodological grounding. The allocation emerged from haggling and bargaining behind closed doors. [ABSTRACT FROM AUTHOR]

Deals with a study which shows how a modification of ridge regression can be used generally to investigate second-order mixture surfaces with many ingredients, particularly when the experimental mixture space is itself limited by further linear equalities in addition to the mixture requirement. Ridge analysis with multiple linear restrictions, including applications to mixture experiments; Generalized ridge analysis of the experiment.

Provides a criterion that is easy to compute and invariant under design rotation. How rotatability is one of many desirable characteristics of a response-surface design; Assessment of a rotatable design; Measuring rotatability; Components of composite designs; Roquemore's designs; Repairing design rotatability.

Presents designs that performed well for several approaches simulataneously. Three approaches; Individual optimality; Optimal mixture designs; D-optimal constraint designs; Conclusions.

Discusses the slope rotatability over all directions (SROAD) concept in applied statistics. Description of SROADs; Two-dimensional SROAD designs; Three-dimensional SROAD designs.

Discusses the Gauss inequality and presents a streamlined proof of the Vysochanskii-Petunin inequality using elementary calculus. Three proofs of the Gauss inequality's bounding of probability for a deviation from a mode v; Replacement of center v mode by the Vysochanskii-Petunin inequality.

Focuses on the effects of intraclass correlation of data on weighted averages. Types of weighting systems; Suggestions on the extension to 2-way classifications; Comparison of variance of the weighted averages in each fixed effects model.

Focuses on mathematical statistics on induction. Normality and independence; Class of parametric functions; Type of one-parameter regular exponential family.