  In a prediction tournament, contestants "forecast" by asserting a numerical
probability for each of (say) 100 future real-world events. The scoring system
is designed so that (regardless of the unknown true probabilities) more
accurate forecasters will likely score better. This is true for one-on-one
comparisons between contestants. But consider a realistic-size tournament with
many contestants, with a range of accuracies. It may seem self-evident that the
winner will likely be one of the most accurate forecasters. But, in the setting
where the range extends to very accurate forecasters, simulations show this is
mathematically false, within a somewhat plausible model. Even outside that
setting the winner is less likely than intuition suggests to be one of the
handful of best forecasters. Though implicit in recent technical papers, this
paradox has apparently not been explicitly pointed out before, though is easily
explained. It perhaps has implications for the ongoing IARPA-sponsored research
programs involving forecasting.
