  In this work, we analyze the performance of a simple majority-rule protocol
solving a fundamental coordination problem in distributed systems -
\emph{binary majority consensus}, in the presence of probabilistic message
loss. Using probabilistic analysis for a large scale, fully-connected, network
of $2n$ agents, we prove that the Simple Majority Protocol (SMP) reaches
consensus in only three communication rounds with probability approaching $1$
as $n$ grows to infinity. Moreover, if the difference between the numbers of
agents that hold different opinions grows at a rate of $\sqrt{n}$, then the SMP
with only two communication rounds attains consensus on the majority opinion of
the network, and if this difference grows faster than $\sqrt{n}$, then the SMP
reaches consensus on the majority opinion of the network in a single round,
with probability converging to $1$ exponentially fast as $n \rightarrow
\infty$. We also provide some converse results, showing that these requirements
are not only sufficient, but also necessary.
