Consensus Formation in Social Networks through Bayesian Iterated Learning

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Transcript of Consensus Formation in Social Networks through Bayesian Iterated Learning

  • Voter Dynamics Opinion Formation as Bayesian Learning Model Simulations The Role of Priors for Innovation Model Simulations Arnim Bleier, Haiko Lietz and Markus Strohmaier Contact: [email protected] ChASM, 23.07.2014 Consensus Formation in Social Networks through Bayesian Iterated Learning Agenda: Background Research
  • Voter Dynamics p(xi = k | {xj}j2Fo(i), ) / nik + K ni. + Xi Fo(i) nik No recovery for extinct states, nor introduction of new states. *) Valid for degree-regular networks only. * F. Palombia, S. Toti: Stochastic Dynamics of the MultiState Voter Model over a Network based on Interacting Cliques and Zealot Candidates, 2014 Normalized frequency of voter i observing state k.
  • Opinion Formation as Bayesian Learning Xi Fo(i) i Dirichlet prior in form of pseudo counts before the states of neighbors are observed.nik p(xi = k | {xj}j2Fo(i), ) / nik + K ni. + No recovery for extinct states, nor introduction of new states.no R T. Griffiths, M. Kalish: Language evolution by iterated learning with Bayesian agents, 2007
  • Effects of the prior on the evolution of opinions in a fully connected network. = 1 = 2.5Prior density for different values of and two different states. Each panel shows the evolution of the proportion of voters being in state one in a single simulation. =.1 0 25 50 75 none all none noneall all Simulations
  • Simulations =.1 = 1 = 2.5Prior density for different values of and two different states. Each panel shows the evolution in the probability distribution of voters being in one of the two states, i.e. p(X = 1). Effects of the prior on the evolution of opinions in a fully connected network. none all none noneall all 0 10 20 30
  • The Role of Priors for Innovation Xi Fo(i) i Dirichlet Process prior probability of voting for a new state. nik p(xi = k | {xj}j2Fo(i), ) / nik + K ni. + p(xi = k | {xj}j2Fo(i), ) / 8 >< >: nik ni. + if xi = k ni. + if xi = knew No recovery for extinct states nor Introduction of new states. Allowing for an infinite number of possible states, of which only a finite number is realized by the voters. R. M. Neal: Markov Chain Sampling Methods for Dirichlet Process Mixture Models, 2000
  • Simulations 1 10 100 1000 100 200 300 400 K iterations - = .01 - = .02 Network: Politicians twitter follower network BTW13: nodes 856, 11136 reciprocal edges, average degree 26 and clustering coefficient 0.4. Left: Number of distinct states over iterations for = .01 and = .02 and different initializations. Right: Empirical distribution of the number of present states (K) for different settings of . 10 20 30 % = .02 10 20 30 % = .01 25 50 75 1 2 3 4 5 6 7 8 9 10 % K = .001 steps