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Comput."],"published-print":{"date-parts":[[2025,12,31]]},"abstract":"<jats:p>\n                    We study information aggregation in networks when agents interact to learn a binary state of the world. Initially each agent privately observes an independent signal which is\n                    <jats:italic toggle=\"yes\">correct<\/jats:italic>\n                    with probability\n                    <jats:inline-formula content-type=\"math\/tex\">\n                      <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\(\\frac{1}{2}+\\delta\\)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    for some \u03b4 &gt; 0. At each round, a node is selected uniformly at random to update their public opinion to match the majority of their neighbours (breaking ties in favour of their initial private signal). Our main result shows that for sparse and connected binomial random graphs\n                    <jats:inline-formula content-type=\"math\/tex\">\n                      <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\({\\mathcal {G}}(n,p)\\)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    the process stabilizes in a\n                    <jats:italic toggle=\"yes\">correct<\/jats:italic>\n                    consensus in\n                    <jats:inline-formula content-type=\"math\/tex\">\n                      <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\(\\mathcal {O}(n\\log ^2 n\/\\log \\log n)\\)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    steps with high probability. In fact, when\n                    <jats:inline-formula content-type=\"math\/tex\">\n                      <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\(\\log n\/n \\ll p = o(1)\\)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    the process terminates at time\n                    <jats:inline-formula content-type=\"math\/tex\">\n                      <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\(\\hat{T} = (1+o(1))n\\log n\\)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    , where\n                    <jats:inline-formula content-type=\"math\/tex\">\n                      <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\(\\hat{T}\\)<\/jats:tex-math>\n                    <\/jats:inline-formula>\n                    is the first time when all nodes have been selected at least once. However, in dense binomial random graphs with\n                    <jats:italic toggle=\"yes\">p<\/jats:italic>\n                    = \u03a9 (1), there is an information cascade where the process terminates in the\n                    <jats:italic toggle=\"yes\">incorrect<\/jats:italic>\n                    consensus with probability bounded away from zero.\n                  <\/jats:p>","DOI":"10.1145\/3771091","type":"journal-article","created":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T11:28:38Z","timestamp":1759922918000},"page":"1-26","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Asynchronous Majority Dynamics on Binomial Random Graphs"],"prefix":"10.1145","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8671-5714","authenticated-orcid":false,"given":"Divyarthi","family":"Mohan","sequence":"first","affiliation":[{"name":"School of Computer Science, Tel Aviv University","place":["Tel Aviv, Israel"]},{"name":"Faculty of Computing and Data Sciences, Boston University","place":["Tel Aviv, Israel"]}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9176-8493","authenticated-orcid":false,"given":"Pawel","family":"Pralat","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Toronto Metropolitan University","place":["Toronto, Canada"]}]}],"member":"320","published-online":{"date-parts":[[2025,11,12]]},"reference":[{"key":"e_1_3_4_2_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.dam.2014.07.026","article-title":"Global majority consensus by local majority polling on graphs of a given degree sequence","volume":"180","author":"Abdullah Mohammed Amin","year":"2015","unstructured":"Mohammed Amin Abdullah and Moez Draief. 2015. 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