We develop a design-based framework for causal inference that accommodates random potential outcomes without introducing outcome models, thereby extending the classical Neyman--Rubin paradigm in which outcomes are treated as fixed. By modelling potential outcomes as random functions driven by a latent stochastic environment, causal estimands are defined as expectations over this mechanism rather than as functionals of a single realised potential-outcome schedule. We show that under local dependence, cross-sectional averaging exhibits an ergodic property that links a single realised experiment to the underlying stochastic mechanism, providing a fundamental justification for using classical design-based statistics to conduct inference on expectation-based causal estimands. We establish consistency, asymptotic normality, and feasible variance estimation for aggregate estimators under general dependency graphs. Our results clarify the conditions under which design-based inference extends beyond realised potential-outcome schedules and remains valid for mechanism-level causal targets.

翻译：我们发展了一个基于设计的因果推断框架，该框架在无需引入结果模型的情况下容纳随机潜在结果，从而扩展了将结果视为固定量的经典Neyman-Rubin范式。通过将潜在结果建模为由潜在随机环境驱动的随机函数，因果估计量被定义为对该机制的期望，而非单一已实现潜在结果表上的泛函。我们证明在局部依赖性条件下，截面平均具有遍历性质，能将单次已实现实验与底层随机机制联系起来，这为使用经典基于设计的统计量对基于期望的因果估计量进行推断提供了根本依据。我们在一般依赖图下建立了聚合估计量的一致性、渐近正态性及可行方差估计方法。我们的结果明确了基于设计的推断能够超越已实现潜在结果表，并对机制层面的因果目标保持有效的条件。