We consider constructing probability forecasts from a parametric binary choice model under a large family of loss functions (“scoring rules”). Scoring rules are weighted averages over the utilities that heterogeneous decision makers derive from a publicly announced forecast (Schervish, 1989). Using analytical and numerical examples, we illustrate howdifferent scoring rules yield asymptotically identical results if the model is correctly specified. Under misspecification, the choice of scoring rule may be inconsequential under restrictive symmetry conditions on the data-generating process. If these conditions are violated, typically the choice of a scoring rule favors some decision makers over others.

中文翻译：

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预测错误规格下的二进制结果的条件概率

我们考虑在大量损失函数（“评分规则”）下，根据参数二元选择模型构建概率预测。计分规则是异构决策者从公开宣布的预测中得出的效用的加权平均值（Schervish，1989）。使用分析和数值示例，我们说明了如果正确指定了模型，则不同的评分规则将如何产生渐近相同的结果。在错误指定的情况下，在数据生成过程中的限制性对称条件下，评分规则的选择可能无关紧要。如果违反了这些条件，通常选择计分规则会使某些决策者胜于其他决策者。