We initiate the study of incentive-compatible forecasting competitions in which multiple forecasters make predictions about one or more events and compete for a single prize. We have two objectives: (1) to incentivize forecasters to report truthfully and (2) to award the prize to the most accurate forecaster. Proper scoring rules incentivize truthful reporting if all forecasters are paid according to their scores. However, incentives become distorted if only the best-scoring forecaster wins a prize, since forecasters can often increase their probability of having the highest score by reporting more extreme beliefs. In this paper, we introduce two novel forecasting competition mechanisms. Our first mechanism is incentive compatible and guaranteed to select the most accurate forecaster with probability higher than any other forecaster. Moreover, we show that in the standard single-event, two-forecaster setting and under mild technical conditions, no other incentive-compatible mechanism selects the most accurate forecaster with higher probability. Our second mechanism is incentive compatible when forecasters' beliefs are such that information about one event does not lead to belief updates on other events, and it selects the best forecaster with probability approaching 1 as the number of events grows. Our notion of incentive compatibility is more general than previous definitions of dominant strategy incentive compatibility in that it allows for reports to be correlated with the event outcomes. Moreover, our mechanisms are easy to implement and can be generalized to the related problems of outputting a ranking over forecasters and hiring a forecaster with high accuracy on future events.
翻译:我们开始研究与奖励相容的预测竞争,让多个预测者对一个或多个事件作出预测并竞争单一奖项。我们有两个目标:(1) 激励预测者诚实报告,(2) 奖励最准确的预测者。 正确的评分规则激励所有预测者按其分数付款的诚实报告。然而,如果只有最有分数的预测者赢得奖励,那么奖励就会被扭曲,因为预测者往往可以通过报告更极端的信念而提高获得最高分的可能性。在本文中,我们引入两个新的预测竞争机制。我们的第一个机制是鼓励和保证激励者选择最准确的预测者,其概率比任何其他预测者高。此外,我们显示,在标准的单日记、两档预测者设置和在较温和的技术条件下,没有任何其他与奖励兼容的机制选择最准确的预测者,而预测者认为关于某一事件的信息不会导致对其它事件的信仰更新,因此,我们选择最准确的预测者选择最准确的预测者,而其概率比任何其他预测者更精确的预测者更接近于前一期的预测,因此,我们的总的预测结果的准确性是比前期的准确性报告更精确。