If an $n$-bit Boolean function $f$ satisfies $f(x \land y) = f(x) \land f(y)$ then it is either constant or an AND. Nehama showed that if this equation holds most of the time, then $f$ is close to a constant or an AND. However, his bounds deteriorate with $n$.
We give a bound which is independent of $n$. This can be seen as a one-sided version of linearity testing, that should perhaps be called oligarchy testing.