Consensus Dynamics on Networks of Biased Agents

The consensus problem for a network of distributed agents is defined as follows: each node in the network holds some opinion or belief and interacts with its neighbours according to some specific rule to reach a state of consensus where all nodes adopt the same opinion or belief. The interaction rules which lead to consensus are called consensus protocols or algorithms. Recently, there has been considerable interest in the analysis of consensus protocols due to the wide applicability of consensus protocols to a range of areas including social networks, distributed computing, biological networks, and statistical physics. While the classical consensus problem assigns the same value to all opinions/beliefs, in real-world networks, the agents often exhibit some form of bias/preference towards intrinsically superior alternatives (e.g., a newer technology or a better political opponent).

In this talk, I shall focus on the effect of bias on consensus dynamics. Specifically, I shall describe how different forms of bias (strong and weak) can affect the speed at which the network reaches consensus. We shall show that the effect of bias on the network dynamics depends on several factors including the consensus protocol being used, the initial distribution of the opinions/beliefs and the connectivity among the agents. I shall present some recent results which analytically characterise the effect of these factors on the speed of consensus. The talks will be based on the following papers:

1. A. Mukhopadhyay, R. R. Mazumdar, R. Roy, "Voter and Majority Dynamics with Biased and Stubborn Agents", Journal of Statistical Physics, 2020.
2. A. Mukhopadhyay, "Phase Transitions in Biased Opinion Dynamics with 2-choices Rule", Probability in Engineering and Informational Sciences, 2022

Dr. Arpan Mukhopadhyay received the B.E. degree in electronics and telecommunication engineering from Jadavpur University, India, in 2009, the M.E. degree in telecommunications from the Indian Institute of Science, India, in 2011, and the Ph.D. degree in electrical and computer engineering from the University of Waterloo, Canada, in 2016. He is currently an Assistant Professor at the Department of Computer Science, University of Warwick, U.K. His research interests include performance analysis of computer and communication networks, distributed network algorithms and theoretical machine learning. He has received Best Paper Awards at IFIP Performance 2015 and the International Teletraffic Congress (ITC) 2015. He was also awarded the Rising Scholar Award at the International Teletraffic Congress 2018 for his contributions to mean-field analysis of large heterogeneous networks.

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