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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 1: Tutorial: Stochastic Processes of Opinion Formation (joint session SOE/TUT)

SOE 1.1: Tutorium

Sonntag, 26. März 2023, 16:00–16:45, HSZ 02

Bounded Confidence Revisited: What We Overlooked, Underestimated, and Got Wrong — •Rainer Hegselmann — Frankfurt School of Finance & Management, 60322 Frankfurt, Adickesallee 32-34

The talk will discuss the so called bounded confidence model (BC-model, for short). The model is very simple: Period by period, all agents average over all opinions that are not further away from their actual opinion than a given distance Epsilon, their *bound of confidence*.

The simplicity of the model is deceptive. Two decades ago, Ulrich Krause and me published an analysis of the model in which we overlooked completely a decisive feature of our model: For increasing values of Epsilon, our analysis back then suggests smooth transitions in the model*s behavior. But in fact, the transitions are wild, chaotic, and non-monotonic.

In my talk I will present a new type of approach in which everything we overlooked at the time becomes directly obvious and, in a sense, unmissable. Key component of the new approach is an algorithm that identifies, exactly and exhaustively, all bounds of confidence, that make a difference. We get a list that, then, allows direct checks for wild behavior exhaustive of all possible cases. That is a good news. But it is accompanied by a bad one: The algorithm that does the work, requires an absolutely exact fractional arithmetic with integers of arbitrary length. As a consequence, we have to pay a price in terms of computational speed.