Dana Angluin, James Aspnes, and David Eisenstat.
A simple population protocol for fast robust approximate majority.
*Distributed Computing* 21(2):87–102, July 2008 (DISC 2007 special issue).
An earlier version appeared in
Distributed Computing, 21st International Symposium, DISC 2007, Lemesos, Cyprus, September 24–26, 2007, Proceedings, pp. 20–32.

We describe and analyze a 3-state one-way population protocol for approximate majority in the model in which pairs of agents are drawn uniformly at random to interact. Given an initial configuration of x's, y's and blanks that contains at least one non-blank, the goal is for the agents to reach consensus on one of the values x or y. Additionally, the value chosen should be the majority non-blank initial value, provided it exceeds the minority by a sufficient margin. We prove that with high probability the agents reach consensus in time O(log n) and the value chosen is the majority provided that its initial margin is at least ω(sqrt(n) log n). This protocol has the additional property of tolerating Byzantine behavior in o(sqrt(n)) of the agents, making it the first known population protocol that tolerates Byzantine agents.

- DISC 2007 proceedings version: PDF.
- DISC 2007 proceedings version with corrected figures: PDF.
- Journal version:
**PDF**. - David Eisenstat's DISC 2007 talk slides and Java demo.

@article{AngluinAE2008majority, author = {Dana Angluin and James Aspnes and David Eisenstat}, title = {A simple population protocol for fast robust approximate majority}, journal = {Distributed Computing}, volume=21, number=2, month = jul, year = 2008, pages= {87--102}, }

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