Taleb's criticism was that the chance it rains four months from now shouldn't reliably vary about a mean (say from 30% to 70% to 30% to 70% etc) in the four mon

Taleb's criticism was that the chance it rains four months from now shouldn't reliably vary about a mean (say from 30% to 70% to 30% to 70% etc) in the four months leading up to that day. Because if it does, I can make risk-free money by betting it won't rain on days the payout for not-rain is high, and betting it will rain on days the payout for rain is high. If a time-smoothed average of your predictions is a better prediction of the outcome than your current prediction, then your current prediction is wrong. The idea that someone can improve on your current prediction by averaging your last 10 predictions is a sign that your methodology for generating "current predictions" is deeply suboptimal.