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Opinions are influenced by neighbors, with varying degrees of emphasis basedon their connections. Some may value more connected neighbors' views due toauthority respect, while others might lean towards grassroots perspectives. Theemergence of ChatGPT could signify a new ``opinion leader'' whose views peopleput a lot of weight on. This study introduces a degree-weighted DeGrootlearning model to examine the effects of such belief updates on learningoutcomes, especially the speed of belief convergence. We find that greaterrespect for authority doesn't guarantee faster convergence. The influence ofauthority respect is non-monotonic. The convergence speed, influenced byincreased authority-respect or grassroots dissent, hinges on the unity of eliteand grassroots factions. This research sheds light on the growing skepticismtowards public figures and the ensuing dissonance in public debate.

From Authority-Respect to Grassroots-Dissent: Degree-Weighted Social Learning and Convergence Speed