On Conditions for Convergence to Consensus

A new theorem on conditions for convergence to consensus of a multiagent time-dependent time-discrete dynamical system is presented. The theorem is build up on the notion of averaging maps. We compare this theorem to results by Moreau (IEEE Transactions on Automatic Control, vol. 50, no. 2, 2005) about set-valued Lyapunov theory and convergence under switching communication topologies. We give examples that point out differences of approaches including examples where Moreau's theorem is not applicable but ours is. Further on, we give examples that demonstrate that the theory of convergence to consensus is still not complete.Comment: 5 pages, 2 columns, example adde

On Elo based prediction models for the FIFA Worldcup 2018

We propose an approach for the analysis and prediction of a football championship. It is based on Poisson regression models that include the Elo points of the teams as covariates and incorporates differences of team-specific effects. These models for the prediction of the FIFA World Cup 2018 are fitted on all football games on neutral ground of the participating teams since 2010. Based on the model estimates for single matches Monte-Carlo simulations are used to estimate probabilities for reaching the different stages in the FIFA World Cup 2018 for all teams. We propose two score functions for ordinal random variables that serve together with the rank probability score for the validation of our models with the results of the FIFA World Cups 2010 and 2014. All models favor Germany as the new FIFA World Champion. All possible courses of the tournament and their probabilities are visualized using a single Sankey diagram.Comment: 22 pages, 7 figure