Pareto Principles in Infinite Ethics Published: May 01, 2018
Recommended citation: Askell, Amanda. ‘Pareto Principles in Infinite Ethics.’ PhD thesis, New York University (2018). https://askell.io/files/Askell-PhD-Thesis.pdf
Summary: In this thesis I argue that ethical rankings of worlds that contain infinite levels of wellbeing ought to be consistent with the Pareto principle, which says that if two worlds contain the same agents and some agents are better off in the first world than they are in the second and no agents are worse off than they are in the second, then the first world is better than the second. I show that if we accept four axioms – the Pareto principle, transitivity, an axiom stating that populations of worlds can be permuted, and the claim that if the ‘at least as good as’ relation holds between two worlds then it holds between qualitative duplicates of this world pair – then we must conclude that there is ubiquitous incomparability between infinite worlds.
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Context
Amanda Askell’s thesis addresses a fundamental tension in population ethics: how to compare worlds with infinite populations or infinite welfare distributions. Classical utilitarian aggregation breaks down when summing infinite utilities, yet we still need principles to guide ethical decisions affecting potentially infinite futures. This matters for longtermism, existential risk prioritization, and any framework considering indefinitely large futures.
Key Insights
Incomparability as inevitable, not defective. Askell proves that accepting four seemingly minimal axioms—Pareto, transitivity, permutation invariance, and qualitative invariance—forces “ubiquitous incomparability” between infinite worlds. This isn’t a bug to be fixed through cleverer aggregation, but a structural feature of infinite ethics. The result parallels impossibility theorems in social choice: we cannot have all desirable properties simultaneously. Rather than abandoning comparability entirely, we must accept that some world-pairs lack ordinal rankings.
Pareto remains non-negotiable. Unlike other axioms that might be weakened, Askell defends Pareto as foundational: if world A is identical to world B except some individuals fare better in A and none fare worse, A must be better. Rejecting Pareto permits rankings that ignore individual welfare entirely—a violation of welfarism’s core commitment. This constrains which infinite-ethics frameworks remain viable; approaches that violate Pareto (like some overtaking criteria) lose moral standing even if they avoid incomparability.
Practical implications for decision-making. If incomparability is ubiquitous, how do we act? Askell’s framework suggests adopting permissibility frameworks rather than maximization: multiple infinite futures may be permissible if incomparable. This aligns with recent work on maximality in decision theory under incomplete preferences.
Open Questions
How should we prioritize between finite and infinite considerations when they conflict—does any finite welfare gain justify foregoing incomparably different infinite futures? Can bounded rationality constraints justify practically rejecting Pareto in infinite cases where verification is computationally infeasible?
无限伦理学中的帕累托原则 发表日期：2018年5月1日
推荐引用：Askell, Amanda. ‘Pareto Principles in Infinite Ethics.’ PhD thesis, New York University (2018). https://askell.io/files/Askell-PhD-Thesis.pdf
摘要：在这篇论文中，我论证了对包含无限福祉水平的世界的伦理排序应当与帕累托原则一致。帕累托原则认为，如果两个世界包含相同的主体，而在第一个世界中某些主体的境况优于第二个世界，且没有主体的境况劣于第二个世界，那么第一个世界优于第二个世界。我证明了如果我们接受四条公理——帕累托原则、传递性、一条关于世界人口可置换的公理、以及"至少同样好"关系在两个世界之间成立则它在该世界对的定性副本之间也成立——那么我们必须得出结论：无限世界之间存在普遍的不可比性。
以下内容由 LLM 生成，可能包含不准确之处。
背景
阿曼达·阿斯凯尔的论文论述了种群伦理学中的一个根本矛盾：如何比较具有无限人口或无限福利分布的世界。经典功利主义的聚合方法在对无限效用求和时会失效，然而我们仍然需要原则来指导可能影响无限未来的伦理决策。这对于长期主义、存在风险优先级排序以及任何考虑无限期宏大未来的框架都很重要。
核心洞察
不可比性是必然的，而非缺陷。 阿斯凯尔证明了接受四个看似最小化的公理——帕累托原则、传递性、排列不变性和定性不变性——会导致无限世界之间的"普遍不可比性"。这不是可以通过更巧妙的聚合方法来修复的bug，而是无限伦理学的结构特征。该结果与社会选择中的不可能性定理相似：我们不能同时具备所有理想属性。与其完全放弃可比性，我们必须接受某些世界对缺乏序数排名的事实。
帕累托原则不可协商。 与其他可能被削弱的公理不同，阿斯凯尔将帕累托原则视为基础性的：如果世界A与世界B相同，只是某些个体在A中状况更好，在B中没有人状况更差，那么A必定更优。拒绝帕累托原则会允许完全忽视个人福利的排名——这违反了福利主义的核心承诺。这限制了哪些无限伦理学框架仍然可行；违反帕累托原则的方法（如某些超越标准）即使避免了不可比性，也失去了道德上的立足点。
对决策的实际影响。 如果不可比性是普遍存在的，我们该如何行动？阿斯凯尔的框架建议采用许可性框架而非最大化：如果无限期未来是不可比的，多个可能是许可的。这与最近在不完全偏好下的最大性决策论研究相吻合。
开放问题
当有限和无限考量相冲突时，我们应如何在两者之间排序——任何有限福利收益是否都足以证明放弃无限期不可比未来的合理性？有界理性约束是否能够在无限情况下（其中验证在计算上不可行）为实际上拒绝帕累托原则辩护？