A Family of Strictly Proper Scoring Rules Which Are Sensitive to Distance

Abstract
An assessment which is “further away” from the “true” event than another assessment should receive a lower score. A definition of distance (from the true event) is considered as well as the sensitivity of scoring rules to distance. A family of scoring rules for n × n cost-loss ratio decision situations with incomplete knowledge is defined and is shown to be strictly proper. These scoring rules are modified to give a family of strictly proper scoring rules which are also sensitive to distance.

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