Picture yourself in a committee numerically evaluating a scientific proposal that you find worth funding: A rating of "0" means "easily achievable but not at all innovative", whereas "1" means "very innovative but totally unachievable". In both cases, funding is not recommended. In contrast, "1/2" means "innovative and achievable", in other words: worth funding. All intermediate values are possible. Any rating that is closer to "1/2" than to "1/4" and "3/4" is considered a vote for funding. The proposal passes if 50% of the members support funding, i.e., rate the proposal between "1/2 - 1/8" and "1/2 + 1/8". Now, there are 10 meetings ahead of you. You have an idea how the opinions of the committee members develop. How should your statements look like in the meetings one through ten if you want to have eventually as many supporters of the proposal as possible? This is an instance of the "Optimal Diplomacy Problem" (ODP), introduced by Hegselmann, König, Kurz, Niemann, and Rambau in 2010, published in 2015. How do opinions interact? How is the dynamics of opinions modeled mathematically? What does it mean to "influence others" in this dynamical system? How difficult is it to find optimal diplomacies? How can one compute or at least narrow down optimal diplomacies? What happens if not all informations about committee members are known to the diplomat? In this talk we will discuss our findings, techniques, and open questions based on the arguably most influential model: the Bounded-Confidence model by Hegselmann and Krause. We draw on joint work with Andreas Deuerling, Rainer Hegselmann, Stefan König, Julia Kinkel, Sascha Kurz, and Christoph Niemann.
Nov 19, 2018 | 02:15 PM
Technische Universität Berlin Institut für Mathematik Straße des 17. Juni 136 10623 Berlin Room MA 041 (Ground Floor)