Counterfactual (CF) explanations, also known as contrastive explanations and
recourses, are popular for explaining machine learning model predictions in
high-stakes domains. For a subject that receives a negative model prediction
(e.g., mortgage application denial), they are similar instances but with
positive predictions, which informs the subject of ways to improve. Various
properties of CF explanations have been studied, such as validity, feasibility
and stability. In this paper, we contribute a novel aspect: their behaviors
under iterative partial fulfillment (IPF). Specifically, upon receiving a CF
explanation, the subject may only partially fulfills 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 first propose a mathematical formalization of IPF and then
demonstrate, both theoretically and empirically, that different CF algorithms
exhibit vastly different behaviors under IPF and hence different effects on the
subject's welfare, warranting this factor to be considered in the studies of CF
algorithms. We discuss implications of our observations and give several
directions for future work.

本文研究递归部分履行 (CF) 解释在迭代过程中的行为是否增加或减少了被试的总改进成本，我们提出了一个 IPF 的数学形式化，并理论和实验上证明了不同 CF 算法在 IPF 下表现出截然不同的行为，因此对 CF 算法的研究需要考虑这一因素。