Maybe I've made an error no-one else made. Maybe everyone else made an error I didn't make. (I have personally experienced this. I knew what error everyone else was making and stuck to my answer, which in the end turned out to be right.) The thing to do is to find out why the discrepancy happened; then I will know what to do about it.

In some situations this will not be possible. Then I will have to just make an optimal Bayesian calculation based on limited information, i.e. guess. But "optimal" no more implies "accurate" than "statistically significant" implies "important".