 
Summary: A Simple Population Protocol for
Fast Robust Approximate Majority
Dana Angluin1, James Aspnes1, , and David Eisenstat2,
1
Yale University, Department of Computer Science
{dana.angluin, james.aspnes}@yale.edu
2
Princeton University, Department of Computer Science
deisenst@cs.princeton.edu
Abstract. We describe and analyze a 3state oneway 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 nonblank, 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
nonblank initial value, provided it exceeds the minority by a sufficient margin.
We prove that with high probability n agents reach consensus in O(n log n) in
teractions and the value chosen is the majority provided that its initial margin
is at least (
n log n). This protocol has the additional property of tolerating
