Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
169 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

On a Voter Model with Context-Dependent Opinion Adoption (2305.07377v2)

Published 12 May 2023 in cs.MA and cs.DC

Abstract: Opinion diffusion is a crucial phenomenon in social networks, often underlying the way in which a collective of agents develops a consensus on relevant decisions. The voter model is a well-known theoretical model to study opinion spreading in social networks and structured populations. Its simplest version assumes that an updating agent will adopt the opinion of a neighboring agent chosen at random. The model allows us to study, for example, the probability that a certain opinion will fixate into a consensus opinion, as well as the expected time it takes for a consensus opinion to emerge. Standard voter models are oblivious to the opinions held by the agents involved in the opinion adoption process. We propose and study a context-dependent opinion spreading process on an arbitrary social graph, in which the probability that an agent abandons opinion $a$ in favor of opinion $b$ depends on both $a$ and $b$. We discuss the relations of the model with existing voter models and then derive theoretical results for both the fixation probability and the expected consensus time for two opinions, for both the synchronous and the asynchronous update models.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (31)
  1. Reversible markov chains and random walks on graphs. https://www.stat.berkeley.edu/~aldous/RWG/book.pdf, 2002.
  2. Biased opinion dynamics: when the devil is in the details. Information Sciences, 593:49–63, 2022.
  3. Chalee Asavathiratham. The Influence Model: A Tractable Representation for the Dynamics of Networked Markov Chains. PhD thesis, Massachussets Institute of Technology, 2000.
  4. Metastability and anomalous fixation in evolutionary games on scale-free networks. Physical review letters, 109(18):188701, 2012.
  5. Fixation and consensus times on a network: A unified approach. Physical Review Letters, 101(25):258701, December 2008.
  6. Bounds on the voter model in dynamic networks. In Ioannis Chatzigiannakis, Michael Mitzenmacher, Yuval Rabani, and Davide Sangiorgi, editors, 43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016, July 11-15, 2016, Rome, Italy, volume 55 of LIPIcs, pages 146:1–146:15. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2016.
  7. Discordant voting processes on finite graphs. SIAM Journal on Discrete Mathematics, 32(4):2398–2420, 2018.
  8. Coalescing Random Walks and Voting on Connected Graphs. SIAM Journal on Discrete Mathematics, 27(4):1748–1758, January 2013. Publisher: Society for Industrial and Applied Mathematics.
  9. Phase transitions of the k-majority dynamics in a biased communication model. In ICDCN ’21: International Conference on Distributed Computing and Networking, Virtual Event, Nara, Japan, January 5-8, 2021, pages 146–155. ACM, 2021.
  10. Absorption time of the Moran process. Random Structures & Algorithms, 49(1):137–159, 2016.
  11. Finite particle systems and infection models. Mathematical Proceedings of the Cambridge Philosophical Society, 94(1):167–182, July 1983. Publisher: Cambridge University Press.
  12. Invasion dynamics in the biased voter process. In Luc De Raedt, editor, Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence, IJCAI 2022, Vienna, Austria, 23-29 July 2022, pages 265–271. ijcai.org, 2022.
  13. Warren Ewens. Mathematical Population Genetics I: Theoretical Introduction. Springer, 2012.
  14. J. Glaz. Probabilities and moments for absorption in finite homogeneous birth-death processes. Biometrics, 35(4):813–816, 1979.
  15. Distributed probabilistic polling and applications to proportionate agreement. Inf. Comput., 171(2):248–268, 2001.
  16. Counterintuitive properties of the fixation time in network-structured populations. Journal of The Royal Society Interface, 11(99):20140606, 2014.
  17. On coalescence time in graphs: When is coalescing as fast as meeting?: Extended Abstract. In Proceedings of the 2019 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Proceedings, pages 956–965. Society for Industrial and Applied Mathematics, January 2019.
  18. Motoo Kimura. On the probability of fixation of mutant genes in a population. Genetics, 47(6):713–719, 1962.
  19. Drift analysis and evolutionary algorithms revisited. Combinatorics, Probability and Computing, 27(4):643–666, July 2018.
  20. Biased majority opinion dynamics: Exploiting graph k-domination. In Luc De Raedt, editor, Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence, IJCAI 2022, Vienna, Austria, 23-29 July 2022, pages 377–383. ijcai.org, 2022.
  21. Markov Chains and Mixing Times. American Mathematical Society, 2009.
  22. Evolutionary dynamics on graphs. Nature, 433:312–316, 2005.
  23. Thomas M. Liggett. Interacting Particle Systems. Springer New York, 1985.
  24. The spread of innovations in social networks. Proceedings of the National Academy of Sciences, 107(47):20196–20201, 2010.
  25. P. A. P. Moran. Random processes in genetics. Mathematical Proceedings of the Cambridge Philosophical Society, 54(1):60–71, January 1958.
  26. Martin A. Nowak. Evolutionary Dynamics. Harvard University Press, 2006.
  27. Random walks on graphs: new bounds on hitting, meeting, coalescing and returning. In 2019 Proceedings of the Sixteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO), pages 119–126. SIAM, 2019.
  28. Effect of algorithmic bias and network structure on coexistence, consensus, and polarization of opinions. Physical Review E, 104(4):044312, 2021.
  29. Consensus of interacting particle systems on erdös-rényi graphs. In Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 1945–1964. SIAM, 2018.
  30. Quasi-majority functional voting on expander graphs. arXiv preprint arXiv:2002.07411, 2020.
  31. Voter models on heterogeneous networks. Physical Review E, 77(4):041121, April 2008.
Citations (1)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now