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arxiv: 2403.17641 · v2 · submitted 2024-03-26 · 💰 econ.TH

A Dominance Argument Against Incompleteness

Christian Tarsney , Harvey Lederman , Dean Spears This is my paper

Pith reviewed 2026-05-24 03:10 UTC · model grok-4.3

classification 💰 econ.TH
keywords value incompletenessnegative dominanceex ante Paretoprudential rankingmoral rankingslotteriesoutcomesdominance principles
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The pith

Two dominance principles rule out incompleteness in prudential and moral value rankings.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper argues that a weak negative dominance principle and a weak ex ante Pareto principle, together with modest auxiliary assumptions, eliminate incompleteness from the ranking of individual lives and many moral evaluations of outcomes and lotteries. Incompleteness occurs when options cannot be judged better, worse, or equally good. The argument matters because it challenges the idea that value can be incomplete, which is used in philosophy to handle cases where comparisons seem impossible. If correct, it forces more complete rankings in ethics and decision theory under uncertainty.

Core claim

Given modest auxiliary assumptions, the weak negative dominance principle and the weak form of ex ante Pareto rule out incompleteness in the prudential ranking of individual lives, and many forms of incompleteness in the moral rankings of outcomes and lotteries.

What carries the argument

The weak negative dominance principle, stating that Lottery 1 is better than Lottery 2 only if some possible outcome of Lottery 1 is better than some possible outcome of Lottery 2, working together with a weak ex ante Pareto principle.

If this is right

  • Incompleteness is ruled out for the prudential ranking of individual lives.
  • Many forms of incompleteness are ruled out for moral rankings of outcomes.
  • Many forms of incompleteness are ruled out for moral rankings of lotteries.
  • The principles apply under modest auxiliary assumptions about value.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This could extend to ruling out incompleteness in other areas of value theory like social welfare.
  • It suggests that dominance-based arguments can resolve long-standing debates on incomparability.
  • Future work might explore whether stronger versions of these principles have even broader implications.
  • These principles might be tested by seeing if they conflict with intuitive cases of incompleteness in real-world decisions.

Load-bearing premise

The weak negative dominance principle holds, meaning one lottery is better than another only if some outcome of the first is better than some outcome of the second.

What would settle it

A concrete scenario with lotteries where the two principles are satisfied but incompleteness remains in the prudential or moral ranking would show the argument fails.

read the original abstract

This article presents a new argument against many forms of moral and prudential value incompleteness. The argument relies on two central principles: (i) a weak "negative dominance" principle, to the effect that Lottery 1 is better than Lottery 2 only if some possible outcome of Lottery 1 is better than some possible outcome of Lottery 2, and (ii) a weak form of ex ante Pareto, to the effect that, if Lottery 1 gives an unambiguously better (stochastically dominant) prospect to some individuals than Lottery 2, and equally good prospects to everyone else, then Lottery 1 is better than Lottery 2. Given modest auxiliary assumptions, these two principles rule out incompleteness in the prudential ranking of individual lives, and many forms of incompleteness in the moral rankings of outcomes and lotteries.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The manuscript argues that a weak negative dominance principle (Lottery 1 is better than Lottery 2 only if some possible outcome of 1 is better than some possible outcome of 2) together with a weak ex ante Pareto principle (if one lottery stochastically dominates another for some individuals and is equal for all others, then the first is better), plus modest auxiliary assumptions, entail completeness of the prudential ranking of individual lives and rule out many forms of incompleteness in the moral ranking of outcomes and lotteries.

Significance. If the derivation holds, the result supplies a new dominance-based route to completeness that relies only on comparatively weak necessary conditions rather than stronger dominance or Pareto axioms; this could narrow the space of admissible incompleteness views in decision theory and ethics while preserving the standard tools of the field.

minor comments (3)
  1. [Abstract / §2] The abstract states that the argument relies on 'modest auxiliary assumptions' but does not list them; §2 or §3 should enumerate these assumptions explicitly (e.g., transitivity of betterness, existence of lotteries with given supports) so that readers can verify they do not covertly presuppose completeness.
  2. [§3] The negative dominance principle is introduced as a 'weak necessary condition'; the manuscript should clarify whether this principle is intended to be a conceptual truth about betterness or a substantive axiom, and whether it is compatible with all standard incompleteness examples in the literature (e.g., the 'small improvement' cases).
  3. [Figure 1] Figure 1 (or the corresponding diagram in the prudential argument) uses arrows for 'better than' and 'incomparable'; the caption should explicitly state whether the diagram assumes or illustrates the target conclusion.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their accurate summary of the manuscript, positive assessment of its significance, and recommendation of minor revision. No specific major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper's central derivation relies on two explicitly stated normative principles (weak negative dominance and weak ex ante Pareto) plus modest auxiliary assumptions to entail completeness results. These principles are introduced as independent premises rather than being defined in terms of the target notion of incompleteness, and the argument contains no fitted parameters, statistical predictions, self-citation chains, or ansatzes smuggled via prior work. The structure is a straightforward deductive entailment from the stated premises, making the derivation self-contained against external benchmarks with no reduction by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the two principles stated in the abstract together with modest auxiliary assumptions whose content is not specified here.

axioms (2)
  • domain assumption Weak negative dominance: Lottery 1 is better than Lottery 2 only if some possible outcome of Lottery 1 is better than some possible outcome of Lottery 2.
    One of the two load-bearing principles invoked to derive the result against incompleteness.
  • domain assumption Weak ex ante Pareto: If Lottery 1 gives an unambiguously better (stochastically dominant) prospect to some individuals than Lottery 2, and equally good prospects to everyone else, then Lottery 1 is better than Lottery 2.
    Second load-bearing principle invoked to derive the result against incompleteness.

pith-pipeline@v0.9.0 · 5663 in / 1387 out tokens · 42407 ms · 2026-05-24T03:10:15.660757+00:00 · methodology

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Reference graph

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