BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Malin Rau (Universität Hamburg) DTSTART:20240311T121500Z DTEND:20240311T130000Z DTSTAMP:20260417T003358Z UID:cam/33 DESCRIPTION:Title: Asy nchronous Opinion Dynamics in Social Networks\nby Malin Rau (Universit ät Hamburg) as part of CAM seminar\n\nLecture held in MV:L14.\n\nAbstract \nOpinion spreading in society decides the fate of elections\, the success of products\, and the impact of political or social movements.\nA promine nt model to study opinion formation processes is due to Hegselmann and Kra use. It has the distinguishing feature that stable states do not necessari ly show consensus\, i.e.\, the population of agents might not agree on the same opinion.\n\nWe focus on the social variant of the Hegselmann-Krause model. There are $n$ agents\, which are connected by a social network. The ir opinions evolve in an iterative\, asynchronous process in which agents are activated one after another at random. When activated\, an agent adopt s the average of the opinions of its neighbors having a similar opinion (w here similarity of opinions is defined using a parameter $\\varepsilon$). Thus\, the set of influencing neighbors of an agent may change over time. To the best of our knowledge\, social Hegselmann-Krause systems with async hronous opinion updates have only been studied with the complete graph as social network.\n\nWe show that such opinion dynamics are guaranteed to co nverge for any social network. We provide an upper bound of $\\mathcal{O}( n|E|^2 (\\varepsilon/\\delta)^2)$ on the expected number of opinion update s until convergence to a stable state\, where $|E|$ is the number of edges of the social network\, and $\\delta$ is a parameter of the stability con cept. For the complete social network\, we show a bound of $\\mathcal{O}(n ^3(n^2 + (\\varepsilon/\\delta)^2))$ that represents a major improvement o ver the previously best upper bound of $\\mathcal{O}(n^9 (\\varepsilon/\\d elta)^2)$.\n LOCATION:https://researchseminars.org/talk/cam/33/ END:VEVENT END:VCALENDAR