用因果模型统一决策理论,明确区分主观与客观,让不同理论可比较。
A causal modeling perspective on decision theory
- 基于非参数结构方程模型构建统一决策框架,明确定义因果与反事实。
- 提出个人决策理论,主张最大化自身反事实效用,且在假设下最优。
- 以吸烟病灶和纽康问题为例,为决策理论提供可量化的评估标准。
决策理论为不确定性下的选择提供了形式化框架,融合了哲学、概率与因果思想。尽管已有进展,但该领域仍缺乏统一建模语言,关键概念如主观与客观的区分,或决策理论表现良好的含义常被隐含。这使得不同理论难以评估与比较,尤其在争议性案例中。本文通过引入非参数结构方程模型(NPSEMs)——因果推断中的成熟工具——构建决策理论的正式框架。NPSEMs统一表示代理、反事实与因果关系,从而可清晰定义预期效用理论(EDT)与因果决策理论(CDT)。在此基础上,我们提出一种新理论——个人决策理论,指导代理最大化其自身反事实效用的主观模型。我们进一步提出一个基于假设干预的性能度量:若通过教育或政策使整个群体遵循某一决策理论,该理论的表现如何。在某些假设下,个人决策理论在此度量下是最优的。全文以吸烟病灶问题为贯穿例证,并对纽康问题进行形式分析。目标是为决策理论提供更清晰的建模语言和更坚实的评价基础,促进理论间的严格比较与概念进展。
原文摘要 · Abstract (English)
Decision theory provides a formal framework for how agents should make choices under uncertainty, drawing on ideas from philosophy, probability, and causality. Despite significant progress, the field still lacks a unified modeling language, and key concepts - such as the distinction between subjective and objective elements, or what it means for a decision theory to perform well - are often left implicit. This can make it difficult to evaluate and compare competing theories, particularly in controversial cases. In this paper, we address these issues by introducing a formal framework for decision theory based on nonparametric structural equation models (NPSEMs), a well-established tool in causal inference. NPSEMs provide a unified foundation for representing agents, counterfactuals, and causal relationships, allowing for unambiguous definitions of EDT and CDT. Building on this foundation, we propose a novel decision theory - personal decision theory - which instructs agents to maximize a subjective model of their own counterfactual utility. We introduce a formal performance metric based on hypothetical interventions that enforce a given decision theory across a population - such as might be achieved through education or policy -- and show that, under certain assumptions, personal decision theory is optimal with respect to this metric. Throughout, we use the smoking lesion problem as a running example and conclude with a formal analysis of Newcomb's problem. Our aim is to provide decision theory with a clearer modeling language and firmer evaluative ground, thereby enabling more rigorous comparisons and facilitating conceptual progress in the field.
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