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arxiv: 2606.29779 · v1 · pith:BOHNEOSOnew · submitted 2026-06-29 · 💰 econ.TH

Discounted Expected Utility: A Revealed Preference Analysis

Wei Ma This is my paper

Pith reviewed 2026-06-30 04:08 UTC · model grok-4.3

classification 💰 econ.TH
keywords revealed preferencediscounted expected utilitynonparametric testconcave utilityintertemporal choicerisk
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The pith

The discounted expected utility model with concave utility admits a revealed preference characterization that supplies a nonparametric test.

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

The paper derives conditions on observed choices that are necessary and sufficient for those choices to arise from maximization of discounted expected utility with a concave utility function. These conditions form the basis for a direct, nonparametric test that requires no assumed functional forms for utility or discounting. When the test is applied to an existing experimental dataset, the conditions are violated in nearly every case. The violations remain even when attention is restricted to choices in which every payment is subject to risk. The result supplies a concrete way to check whether standard discounted expected utility can rationalize observed behavior over time and uncertainty.

Core claim

We present a revealed preference characterization of the discounted expected utility model with a concave utility function. The characterization offers a nonparametric test of the model. We apply the test to an experimental data set in the literature and find that the model is almost always rejected even when all payments involved are subject to risk.

What carries the argument

The revealed preference characterization: a collection of conditions on choice data that must hold if and only if the data are generated by discounted expected utility with concave utility.

If this is right

  • The model can be tested directly on choice data without parametric assumptions.
  • The test rejects the model in almost all observations from the experimental dataset.
  • Rejection continues to hold when the data are limited to risky payments.
  • The same conditions can be checked on any other suitable choice dataset.

Where Pith is reading between the lines

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

  • Similar characterizations could be derived for alternative discounting or risk models to enable comparable nonparametric tests.
  • Persistent rejections point toward the need for models that relax concavity or separability between time and risk.
  • Experiments could be designed around choices that are borderline with respect to the derived conditions to sharpen the test.

Load-bearing premise

The experimental data set is appropriate for direct application of the nonparametric test, with all payments subject to risk as described.

What would settle it

Deriving a set of choices that satisfy discounted expected utility with concave utility yet violate one of the stated conditions would falsify the characterization; finding a dataset in which every observed choice satisfies the conditions would support its empirical usefulness.

read the original abstract

We present a revealed preference characterization of the discounted expected utility model with a concave utility function. The characterization offers a nonparametric test of the model. We apply the test to an experimental data set in the literature and find that the model is almost always rejected even when all payments involved are subject to risk.

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 manuscript presents a revealed preference characterization of the discounted expected utility (DEU) model with concave utility. This yields a nonparametric test of the model, which is applied to an experimental dataset from the literature; the test rejects the model in almost all cases, even when all payments are subject to risk.

Significance. A correct revealed-preference characterization of DEU with concave u would supply a parameter-free test for a core model in decision theory under risk and time, which is a substantive contribution. The reported rejection on existing data would then constitute a falsifiable empirical claim with direct implications for the descriptive validity of DEU.

major comments (1)
  1. The abstract states that a characterization and nonparametric test are derived, yet no axioms, theorem statement, or derivation is supplied in the provided text. Without these, it is impossible to verify whether the test is indeed nonparametric or whether it correctly characterizes DEU with concave utility.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the report. We address the single major comment below.

read point-by-point responses

  1. Referee: The abstract states that a characterization and nonparametric test are derived, yet no axioms, theorem statement, or derivation is supplied in the provided text. Without these, it is impossible to verify whether the test is indeed nonparametric or whether it correctly characterizes DEU with concave utility.

    Authors: We agree that the version of the manuscript provided to the referee contains only the abstract and does not include any axioms, theorem statement, or derivation. This omission means the referee cannot assess the claimed characterization. In the revised manuscript we will add the full set of axioms, the precise theorem statement characterizing discounted expected utility with concave utility, and the derivation of the resulting nonparametric test. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper states a revealed-preference characterization of discounted expected utility (with concave u) together with a nonparametric test. No equations, axioms, or self-citations are supplied in the provided text that would reduce the characterization to a fitted parameter, a self-referential definition, or a load-bearing self-citation. The test is reported to reject the model on existing data, which is consistent with an independent, falsifiable statement rather than a tautology. This is the normal case for an axiomatic revealed-preference result; the derivation chain is self-contained against external data.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract; full details on assumptions, parameters, or entities are unavailable.

axioms (1)
  • domain assumption The utility function is concave
    Explicitly included in the model description in the abstract.

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discussion (0)

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