Counterfactual explanations are the de facto standard when tasked with interpreting decisions of (opaque) predictive models. Their generation is often subject to algorithmic and domain-specific constraints -- such as density-based feasibility for the former and attribute (im)mutability or directionality of change for the latter -- that aim to maximise their real-life utility. In addition to desiderata with respect to the counterfactual instance itself, the existence of a viable path connecting it with the factual data point, known as algorithmic recourse, has become an important technical consideration. While both of these requirements ensure that the steps of the journey as well as its destination are admissible, current literature neglects the multiplicity of such counterfactual paths. To address this shortcoming we introduce the novel concept of explanatory multiverse that encompasses all the possible counterfactual journeys and shows how to navigate, reason about and compare the geometry of these paths -- their affinity, branching, divergence and possible future convergence -- with two methods: vector spaces and graphs. Implementing this (interactive) explanatory process grants explainees more agency by allowing them to select counterfactuals based on the properties of the journey leading to them in addition to their absolute differences.

翻译：反事实解释是解释（不透明）预测模型决策的事实标准。其生成通常受制于算法与领域特定约束——前者如基于密度的可行性，后者如属性（不可）变异性或变化方向性——旨在最大化其实际效用。除对反事实实例本身的期望外，连接反事实与事实数据点的可行路径存在性（即算法可逆性）已成为重要技术考量。尽管这两项要求确保了旅程步骤与目的地均具有可接受性，当前文献忽视了反事实路径的多样性问题。为弥补这一不足，我们引入"解释性多元宇宙"这一新颖概念，涵盖所有可能反事实旅程，并提出两种方法——向量空间与图——来导航、推理并比较这些路径的几何特性（亲和性、分支、发散及未来潜在收敛）。实施这一（交互式）解释过程使被解释者得以依据通往反事实的旅程属性（而非仅绝对差异）选择反事实，从而增强其自主性。