Suppose there are two populations, optimists and pessimists. Optimists are more optimistic about the future economy and pessimists are more pessimistic. There are equal number of optimists and pessimists, I draw their forecasts from them and consider the median forecasts. Suppose there are news and their forecasts (the distributions of forecasts) change. Under what conditions that new forecasts will be more volatile from old forecasts (i.e. the variance of the median is larger)?
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