Counterfactual (CF) explanations, also known as contrastive explanations and algorithmic recourses, are popular for explaining machine learning models in high-stakes domains. For a subject that receives a negative model prediction (e.g., mortgage application denial), the CF explanations are similar instances but with positive predictions, which informs the subject of ways to improve. While their various properties have been studied, such as validity and stability, we contribute a novel one: their behaviors under iterative partial fulfillment (IPF). Specifically, upon receiving a CF explanation, the subject may only partially fulfill it before requesting a new prediction with a new explanation, and repeat until the prediction is positive. Such partial fulfillment could be due to the subject's limited capability (e.g., can only pay down two out of four credit card accounts at this moment) or an attempt to take the chance (e.g., betting that a monthly salary increase of \800 is enough even though \1,000 is recommended). Does such iterative partial fulfillment increase or decrease the total cost of improvement incurred by the subject? We mathematically formalize IPF and demonstrate, both theoretically and empirically, that different CF algorithms exhibit vastly different behaviors under IPF. We discuss implications of our observations, advocate for this factor to be carefully considered in the development and study of CF algorithms, and give several directions for future work.
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