A Prediction Tournament Paradox
A Prediction Tournament Paradox
复制标题
预测锦标赛悖论
作者：
D. Aldous
在预测比赛中，参赛者通过断言100个未来现实世界事件中的每个事件的数值概率来“预测”。评分系统是这样设计的（不管未知的真实概率如何），更准确的预测者可能会得到更好的分数。这对于选手之间的一对一比较来说是正确的。但考虑一下现实规模的比赛，有很多选手，准确度也有一定范围。似乎不言自明的是，获胜者很可能是预测最准确的人之一。但是，在范围扩展到非常精确的预报员的情况下，模拟表明，在一个看似合理的模型中，这在数学上是错误的。即使在此之外，获胜者也不太可能像直觉所暗示的那样，成为少数几个最佳预测者之一。虽然在最近的技术论文中暗示了这一矛盾，但显然以前没有明确指出，虽然很容易解释。这可能会对正在进行的由iarpa赞助的有关预测的研究项目产生影响。
Abstract 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.