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arxiv: 2408.09294 · v6 · submitted 2024-08-17 · 💰 econ.TH

How to Make an Action Attractive

Marilyn Pease , Mark Whitmeyer This is my paper

Pith reviewed 2026-05-23 21:53 UTC · model grok-4.3

classification 💰 econ.TH
keywords robust paternalismdecision theoryexpected utilityrisk aversionpolicymakinginsurance designpolitical competition
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The pith

A modification to a desired action is robustly more attractive if it is preferred to the alternative whenever the original action is, for every possible belief and every increasing concave utility.

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

The paper defines robust paternalism as a way to modify one action so that it becomes preferred over another without needing to know the decision maker's beliefs about states or their exact risk attitude. It characterizes exactly which payoff changes achieve this universal preference shift. This approach matters for settings where a policymaker wants to steer behavior but cannot reliably observe or assume specific uncertainty perceptions. The result applies directly to problems such as designing insurance contracts, structuring bilateral trade, or adjusting political platforms.

Core claim

A modification a' of action a is robustly more attractive than a relative to b precisely when, for every belief and every increasing concave utility, the decision maker who prefers a to b also prefers a' to b; all such modifications are characterized directly by conditions on the state-dependent payoffs.

What carries the argument

The definition of robustly more attractive modification, which requires the preference ordering to hold for all beliefs over states and all increasing concave von Neumann-Morgenstern utilities.

If this is right

  • Certain modifications to insurance contracts remain attractive to all risk-averse agents regardless of their beliefs about loss probabilities.
  • In bilateral trade, adjustments to contract terms can make one side's offer robustly preferred without knowledge of the other party's risk attitude.
  • Political platforms can be altered so that one candidate's position is preferred to the rival's for any voter beliefs and any concave utility.
  • Information-acquisition decisions can be steered toward a target choice via payoff changes that dominate for every prior and every risk-averse evaluator.

Where Pith is reading between the lines

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

  • The same payoff-based test could be applied to non-expected-utility models if the dominance requirement is redefined over the relevant class of preferences.
  • The characterization might extend to multi-agent settings where one agent's modification must remain attractive conditional on others' responses.
  • Empirical tests could check whether observed policy changes in insurance markets satisfy the payoff conditions identified for robustness.

Load-bearing premise

The decision maker's preferences admit an expected-utility representation using an increasing concave utility function.

What would settle it

A concrete payoff modification that meets the paper's state-dependent payoff condition but fails to preserve the preference for some specific belief and some increasing concave utility function.

read the original abstract

A policymaker often wants to steer a decision-maker toward one of two actions, but lacks reliable knowledge of how the decision-maker perceives uncertainty or evaluates risk. We formalize a notion of robust paternalism: a modification a' of a desired action a is robustly more attractive than a relative to b if, for every belief over states and every increasing concave utility function, whenever the decision-maker prefers a to b, she also prefers a' to b. We characterize all such modifications directly in terms of state-dependent payoffs and discuss applications to political competition, bilateral trade, insurance, and information acquisition.

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

1 major / 0 minor

Summary. The paper defines a notion of robust attractiveness: a modification a' of desired action a is robustly more attractive than a relative to b if, for every belief and every increasing concave utility, preference for a over b implies preference for a' over b. It claims to characterize all such modifications directly in terms of state-dependent payoffs and discusses applications to political competition, bilateral trade, insurance, and information acquisition.

Significance. If a non-trivial characterization existed under this definition, it would provide a robust method for steering choices without knowledge of beliefs or risk preferences, with potential value in policy and mechanism design across the listed applications.

major comments (1)
  1. [Abstract and definition] Abstract (definition of robust attractiveness): the requirement must hold for all increasing concave u, including linear u. For linear u this forces a'−b=λ(a−b) for some λ>0. For strictly concave u only λ=1 survives, and the counter-example with two states, b≡0, a=(−1,3), a'=(−2,6), p=(1/2,1/2), u(x)=log(x+3) shows EU(a)>EU(b) but EU(a')<EU(b). Hence only the trivial modification a'=a satisfies the definition for generic a,b, rendering the claimed characterization vacuous.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and the precise counterexample. We agree that the current definition leads to a trivial characterization and will revise the manuscript to correct this.

read point-by-point responses

  1. Referee: [Abstract and definition] Abstract (definition of robust attractiveness): the requirement must hold for all increasing concave u, including linear u. For linear u this forces a'−b=λ(a−b) for some λ>0. For strictly concave u only λ=1 survives, and the counter-example with two states, b≡0, a=(−1,3), a'=(−2,6), p=(1/2,1/2), u(x)=log(x+3) shows EU(a)>EU(b) but EU(a')<EU(b). Hence only the trivial modification a'=a satisfies the definition for generic a,b, rendering the claimed characterization vacuous.

    Authors: We agree with the referee's analysis. The definition requires the implication to hold for every increasing concave utility (including linear) and every belief. As noted, this forces a'−b=λ(a−b) for λ>0 to satisfy the linear case, while the counterexample with log utility correctly shows that λ≠1 fails for strictly concave utilities. Thus only a'=a works in general, rendering the claimed characterization vacuous. This was an oversight in the formulation. We will revise by restricting the utility class (e.g., to strictly concave utilities with bounded Arrow-Pratt measure) or by redefining robust attractiveness to obtain non-trivial modifications while preserving the applications to political competition, trade, insurance, and information acquisition. revision: yes

Circularity Check

0 steps flagged

No circularity; direct mathematical characterization from definition

full rationale

The paper defines robust attractiveness via a universal quantification over beliefs and concave utilities, then derives the payoff conditions that a' must satisfy for the implication to hold in all cases. This is a standard first-principles analysis of the given definition with no reduction to fitted parameters, no self-referential predictions, and no load-bearing self-citations. The derivation chain remains self-contained against the stated assumptions without importing uniqueness or ansatzes from prior work by the same authors.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard expected-utility framework with risk aversion; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption Preferences admit an expected-utility representation with strictly increasing and concave von Neumann-Morgenstern utility.
    Invoked by the requirement that the robust preference holds for every such utility function.

pith-pipeline@v0.9.0 · 5612 in / 1212 out tokens · 23101 ms · 2026-05-23T21:53:46.095459+00:00 · methodology

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Reference graph

Works this paper leans on

14 extracted references · 14 canonical work pages · 1 internal anchor

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    H ow t o M a ke a n A c t i o n B e t t e r M a r i l y n Pe a s e•M a r k W h i t m eye r1 For two actions in a decision problem, a and b, each of which produces a state-dependent monetary reward, we study how to robustly make action a more attractive. Action ˆa improves upon a in this manner if the set of beliefs at which a is preferred to b is a subset...

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    How to Make an Action Attractive

    1 arXiv:2408.09294v5 [econ.TH] 11 Mar 2025 1 . I n t r o d u c t i o n There are many situations in which one agent must decide which option to present to another in the presence of uncertainty. Consider, for instance, a consumer deciding between firm1 and firm2’s products, without knowing which best suits her needs. Firm2 produces productb, while firm1 c...

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    Lemma 3.2

    The first of the two necessity steps is showing thatb-superiority implies pairwise dominance. Lemma 3.2. ˆa is b-superior toa only if i) for anyθ†∈C, ˆaθ†≥aθ†; ii) for any θ∈A, ˆaθ>b θ; and iii)ˆa pairwise-dominates a collection of mixtures ofa and b. Proof. See Appendix A. ■ Let us consider the meaning of Lemma 3.2. First, it is clear that ifˆa isb- supe...

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    µ∈[0, 1] denotes the DM’s belief that the state is1. There is a cutoff belief at which the DM is indifferent between actions. Let¯µu be the belief at which the DM is indifferent between actionsa and b with utilityu and ˆµu be the belief at which the DM is indifferent betweenˆa and b with the same utility. To see this graphically, let ℓa(µ) =a0(1−µ) +a1µ, ...

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    whereF (µ0) is the set of Bayes-plausible distributions given priorµ0 and D is a uniformly posterior-separable (UPS) cost functional.8 Similarly, the value function 8 See, e.g., Caplin, Dean, and Leahy (2022).D : ∆ 2→R is UPS ifD (F) = ∫ ∆ c (µ)dF (µ)− c (µ0) for some strictly convex and twice continuously differentiable onint∆ function c: ∆ →R. 2 0 when ...

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    twist things,

    if µ0∈(µa L,µa H). Next, take ˆa to be such thatℓˆa is a counter-clockwise rotation fromℓa towards ℓb (recall Figure 1). This is equivalent, however, to an increase in learning cost (if payoffs had remained the same) for a risk-neutral DM. A higher marginal cost of information leads to less learning; i.e.,(µˆa L,µˆa H)⊆(µa L,µa H). This means that we can ...

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    Claim A.1.It is without loss of generality to assume thatb∗is unique

    such that for allγ <¯γ, (1−γ)aθ+γaθ′> max b∈B {(1−γ)bθ+γbθ′} and (1−¯γ)aθ+ ¯γaθ′= (1−¯γ)b∗ θ+ ¯γb∗ θ′. Claim A.1.It is without loss of generality to assume thatb∗is unique. Moreover, for any concave and strictly increasingu and allγ∈[0, 1], (1−γ)u(aθ)+γu(aθ′)≥ (>) (1−γ)u(b∗ θ)+γu(b∗ θ′) ⇒(1−γ)u(aθ)+γu(aθ′)≥ (>) (1−γ)u(bθ)+γu(bθ′), for allb∈B. Proof. Our a...

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    (⇒) Suppose for the sake of contraposition thatˆa dominates neither a nor b

    Evidently,p is strictly increasing in bothµH and µL, so ˆp≥p. (⇒) Suppose for the sake of contraposition thatˆa dominates neither a nor b. If ˆa is dominated (and does not dominate) bya or b, the outcome is trivial. Accordingly, suppose ˆa is dominated by neither. There are three possibilities: either i) ˆa0 > a0 > b0 and ˆa1 < a1 < b1; or ii)a0 > ˆa0 > b...

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    We tweak the notation ℓa =µα1 + (1−µ)α0, ℓˆa =µˆα1 + (1−µ) ˆα0, and ℓb =µβ1 + (1−µ)β0, and defineW (µ) := max{ℓa,ℓˆa,ℓb}

    We maintain the convention αθ≡u(aθ) and ˆαθ≡u(ˆaθ) for all θ∈{0, 1}and also introduce the notation βθ≡u(bθ) for allθ∈{0, 1}. We tweak the notation ℓa =µα1 + (1−µ)α0, ℓˆa =µˆα1 + (1−µ) ˆα0, and ℓb =µβ1 + (1−µ)β0, and defineW (µ) := max{ℓa,ℓˆa,ℓb}. We let ˜µdenote the intersection ofℓa and ℓˆa, and observe that0< ˜µ <¯µ; this holds becauseℓˆa has a steeper ...

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    Again appealing to Lemma A.1 in Whitmeyer (2023), taking a priorµ0∈(µ2,µ3) we note the existence of a UPS cost producingp> 0 and ˆp =

    where f and 0 intersect. Again appealing to Lemma A.1 in Whitmeyer (2023), taking a priorµ0∈(µ2,µ3) we note the existence of a UPS cost producingp> 0 and ˆp =

    work page 2023