  The initial majority identification task is a fundamental test problem in
cellular automaton research. To pass the test, an automaton must evolve to a
uniform configuration consisting of the state that was in the majority for any
initial configuration, employing only its internal, local dynamics. It is known
that no two-state automaton can perform the majority task perfectly. Thus, it
is a matter of continuing interest to identify and analyze new automata with
improved majority identification capability. Here, we show that a coarsened
version of one of the best majority identifiers can out-perform its parent
automaton while simultaneously reducing the associated computational costs.
