Robust Naïve Learning in Social Networks

33 Pages Posted: 25 Mar 2021 Last revised: 1 Sep 2021

See all articles by Gideon Amir

Gideon Amir

Bar Ilan University

Itai Arieli

Technion-Israel Institute of Technology

Galit Ashkenazi-Golan

Tel Aviv University

Ron Peretz

Bar Ilan University

Date Written: February 23, 2021

Abstract

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 that under DeGroot \cite{degroot1974reaching} dynamics 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 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.

Keywords: DeGroot dynamics, Robust Learning

Suggested Citation

Amir, Gideon and Arieli, Itai and Ashkenazi-Golan, Galit and Peretz, Ron, Robust Naïve Learning in Social Networks (February 23, 2021). Available at SSRN: https://ssrn.com/abstract=3791413 or http://dx.doi.org/10.2139/ssrn.3791413

Gideon Amir

Bar Ilan University ( email )

Israel

Itai Arieli (Contact Author)

Technion-Israel Institute of Technology ( email )

Technion City
Haifa 32000, Haifa 32000
Israel

Galit Ashkenazi-Golan

Tel Aviv University ( email )

Ramat Aviv
Tel-Aviv, 6997801
Israel

Ron Peretz

Bar Ilan University ( email )

Ramat Gan
5290002
Israel

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