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Majority Dynamics and the Retention of Information

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Abstract

We consider a group of agents connected by a social network who participate in majority dynamics: each agent starts with an opinion in {−1, +1} and repeatedly updates it to match the opinion of the majority of its neighbors.

We assume that one of {−1, +1} is the “correct” opinion S, and consider a setting in which the initial opinions are independent conditioned on S, and biased towards it. They hence contain enough information to reconstruct S with high probability. We ask whether it is still possible to reconstruct S from the agents’ opinions after many rounds of updates.

While this is not the case in general, we show that indeed, for a large family of bounded degree graphs, information on S is retained by the process of majority dynamics.

Our proof technique yields novel combinatorial results on majority dynamics on both finite and infinite graphs, with applications to zero temperature Ising models.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, Rehovot, 76100, Israel

    Omer Tamuz

  2. Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Givat Ram, Jerusalem, 91904, Israel

    Ran J. Tessler

Authors
  1. Omer Tamuz
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  2. Ran J. Tessler
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Corresponding author

Correspondence to Omer Tamuz.

Additional information

Omer Tamuz is supported by ISF grant 1300/08, and is a recipient of the Google Europe Fellowship in Social Computing, and this research is supported in part by this Google Fellowship.

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Tamuz, O., Tessler, R.J. Majority Dynamics and the Retention of Information. Isr. J. Math. 206, 483–507 (2015). https://doi.org/10.1007/s11856-014-1148-2

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  • DOI: https://doi.org/10.1007/s11856-014-1148-2

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