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Thus, the set of influencing neighbors of an agent may change over time. We show that such opinion dynamics are guaranteed to converge for any social network. We provide an upper bound of$${\\text {O}}(n|E|^2 (\\varepsilon \/\\delta )^2)$$<\/jats:tex-math>O<\/mml:mtext>(<\/mml:mo>n<\/mml:mi>|<\/mml:mo>E<\/mml:mi>|<\/mml:mo>2<\/mml:mn><\/mml:msup>(<\/mml:mo>\u03b5<\/mml:mi>\/<\/mml:mo>\u03b4<\/mml:mi>)<\/mml:mo><\/mml:mrow>2<\/mml:mn><\/mml:msup>)<\/mml:mo><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>on the expected number of opinion updates until convergence to a stable state, where$$|E|$$<\/jats:tex-math>|<\/mml:mo>E<\/mml:mi>|<\/mml:mo><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>is the number of edges of the social network, and$$\\delta $$<\/jats:tex-math>\u03b4<\/mml:mi><\/mml:math><\/jats:alternatives><\/jats:inline-formula>is a parameter of the stability concept. For the complete social network we show a bound of$${\\text {O}}(n^3(n^2 + (\\varepsilon \/\\delta )^2))$$<\/jats:tex-math>O<\/mml:mtext>(<\/mml:mo>n<\/mml:mi>3<\/mml:mn><\/mml:msup>(<\/mml:mo>n<\/mml:mi>2<\/mml:mn><\/mml:msup>+<\/mml:mo>(<\/mml:mo>\u03b5<\/mml:mi>\/<\/mml:mo>\u03b4<\/mml:mi>)<\/mml:mo><\/mml:mrow>2<\/mml:mn><\/mml:msup>)<\/mml:mo><\/mml:mrow>)<\/mml:mo><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>that represents a major improvement over the previously best upper bound of$${\\text {O}}(n^9 (\\varepsilon \/\\delta )^2)$$<\/jats:tex-math>O<\/mml:mtext>(<\/mml:mo>n<\/mml:mi>9<\/mml:mn><\/mml:msup>(<\/mml:mo>\u03b5<\/mml:mi>\/<\/mml:mo>\u03b4<\/mml:mi>)<\/mml:mo><\/mml:mrow>2<\/mml:mn><\/mml:msup>)<\/mml:mo><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>.<\/jats:p>","DOI":"10.1007\/s00446-024-00467-3","type":"journal-article","created":{"date-parts":[[2024,4,26]],"date-time":"2024-04-26T06:01:52Z","timestamp":1714111312000},"page":"207-224","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Asynchronous opinion dynamics in social networks"],"prefix":"10.1007","volume":"37","author":[{"given":"Petra","family":"Berenbrink","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martin","family":"Hoefer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dominik","family":"Kaaser","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pascal","family":"Lenzner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Malin","family":"Rau","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daniel","family":"Schmand","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,4,26]]},"reference":[{"issue":"1","key":"467_CR1","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1086\/267152","volume":"27","author":"R Abelson","year":"1963","unstructured":"Abelson, R., Bernstein, A.: A computer simulation model of community referendum controversies. 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