On the Construction of High Dimensional Simple Games

Voting is a commonly applied method for the aggregation of the preferences of multiple agents into a joint decision. If preferences are binary, i.e., "yes" and "no", every voting system can be described by a (monotone) Boolean function $\chi\colon\{0,1\}^n\rightarrow \{0,1\}$. However, its naive encoding needs $2^n$ bits. The subclass of threshold functions, which is sufficient for homogeneous agents, allows a more succinct representation using $n$ weights and one threshold. For heterogeneous agents, one can represent $\chi$ as an intersection of $k$ threshold functions. Taylor and Zwicker have constructed a sequence of examples requiring $k\ge 2^{\frac{n}{2}-1}$ and provided a construction guaranteeing $k\le {n\choose {\lfloor n/2\rfloor}}\in 2^{n-o(n)}$. The magnitude of the worst-case situation was thought to be determined by Elkind et al.~in 2008, but the analysis unfortunately turned out to be wrong. Here we uncover a relation to coding theory that allows the determination of the minimum number $k$ for a subclass of voting systems. As an application, we give a construction for $k\ge 2^{n-o(n)}$, i.e., there is no gain from a representation complexity point of view.Comment: 13 pages, 1 tabl

Dimension and codimension of simple games

This paper studies the complexity of computing a representation of a simple game as the intersection (union) of weighted majority games, as well as, the dimension or the codimension. We also present some examples with linear dimension and exponential codimension with respect to the number of players.Comment: 5 page

Contribution of patient registries to regulatory decision making on rare diseases medicinal products in Europe

Between 2000 and 2021, the European Medicines Agency (EMA) assigned the orphan designation to over 1,900 medicines. Due to their small target populations, leading to challenges regarding clinical trial recruitment, study design and little knowledge on the natural history of the disease, the overall clinical evidence submitted at the time of marketing authorisation application for these medicines is often limited. Patient registries have been recognised as important sources of data on healthcare practices, drug utilisation and clinical outcomes. They may help address these challenges by providing information on epidemiology, standards of care and treatment patterns of rare diseases. In this review, we illustrate the utility of patient registries across the different stages of development of medicinal products, including orphans, to provide evidence in the context of clinical studies and to generate post-authorisation long term data on their effectiveness and safety profiles. We present important initiatives leveraging the role of registries for orphan medicinal products' development and monitoring to ultimately improve patients' lives

Cognitive impairment, dementia and quality of life.

Peer reviewe