  Via extensive Monte Carlo simulations along with systematic analyses of
corrections to scaling, we estimate the order parameter critical exponent
$\beta$ of absorbing phase transitions in systems with two symmetric absorbing
states. The value of $\beta$ was conjectured to be $\frac{13}{14}\approx 0.93$
and Monte Carlo simulation studies in the literature have repeatedly reproduced
values consistent with the conjecture. In this paper, we systematically
estimate $\beta$ by analyzing the effective exponent after finding how strong
corrections to scaling are. We show that the widely accepted numerical value of
$\beta$ is not correct. Rather, we obtain $\beta = 1.020(5)$ from different
models with two symmetric absorbing states.
