Discounting refers to the way in which the value of an outcome depends on the delay until it is obtained. If an organism's discount function is known, then its rate of discounting at any delay can be found. If the function is not known, the normalised area under an estimate of the discount function has been used as a measure that summarises the strength of discounting over a range of delays. We propose a new measure of the strength of discounting: the overall discount rate W, which is the drop in value from the start to the end of the value curve divided by the area under this curve. We show that our measure has various advantages over the normalised area, namely it can be linked to the instantaneous rate of discounting and it respects the special nature of exponential discounting. It does not give a unique value to each curve, but we prove that this is incompatible with the requirement that similar discount functions be assigned similar values, and so this is not a defect of the measure.
- Area under the curve