English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In several real \emph{Multi-Agent Systems} (MAS), it has been observed thatonly weaker forms of\emph{metastable consensus} are achieved, in which a largemajority of agents agree on some opinion while other opinions continue to besupported by a (small) minority of agents. In this work, we take a step towardsthe investigation of metastable consensus for complex (non-linear)\emph{opinion dynamics} by considering the famous \undecided dynamics in thebinary setting, which is known to reach consensus exponentially faster than the\voter dynamics. We propose a simple form of uniform noise in which eachmessage can change to another one with probability $p$ and we prove that thepersistence of a \emph{metastable consensus} undergoes a \emph{phasetransition} for $p=\frac 16$. In detail, below this threshold, we prove thesystem reaches with high probability a metastable regime where a large majorityof agents keeps supporting the same opinion for polynomial time. Moreover, thisopinion turns out to be the initial majority opinion, whenever the initial biasis slightly larger than its standard deviation.On the contrary, above thethreshold, we show that the information about the initial majority opinion is"lost" within logarithmic time even when the initial bias ismaximum.Interestingly, using a simple coupling argument, we show theequivalence between our noisy model above and the model where a subset ofagents behave in a \emph{stubborn} way.

Phase Transition of a Non-Linear Opinion Dynamics with Noisy Interactions