2021/02/23 by Amir, Gideon, Arieli, Itai, Ashkenazi-Golan, Galit +1
#60C05 #91D30 #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Physics and Society (physics.soc-ph) #Probability (math.PR) #Social and Information Networks (cs.SI)
paper · doi:10.48550/arxiv.2102.11768
We study a model of opinion exchange in social networks where a state of the world is realized and every agent receives a zero-mean noisy signal of the realized state. It is known from [Golub and Jackson 2010] that under DeGroot dynamics [DeGroot 1974] agents reach a consensus that is close to the state of the world when the network is large. The DeGroot dynamics, however, is highly non-robust and the presence of a single ``stubborn agent'' that does not adhere to the updating rule can sway the public consensus to any other value. We introduce a variant of DeGroot dynamics that we call \emph (1)/(m)-DeGroot. (1)/(m)-DeGroot dynamics approximates standard DeGroot dynamics to the nearest rational number with m as its denominator and like the DeGroot dynamics it is Markovian and stationary. We show that in contrast to standard DeGroot dynamics, (1)/(m)-DeGroot dynamics is highly robust both to the presence of stubborn agents and to certain types of misspecifications.