Theory and Model Craft (jru-theory-model)

When to trigger

• The paper proposes or adopts a preference representation (utility + probability weighting, an ambiguity functional) but its axiomatic foundation or behavioral content is unclear
• A functional form is asserted (CRRA + Prelec weighting, α-MEU, smooth ambiguity) without saying what it rules out
• A referee asks "what does your model predict that EU does not?" and the draft has no crisp answer
• The model is being used to interpret experimental or empirical results but its parameters are not behaviorally interpretable

The JRU theory bar

JRU is the home of decision theory under risk and uncertainty, so a model is judged on three things at once: an axiomatic basis (what preference conditions characterize the representation), a functional form that is tractable and identifiable, and behavioral content (the model must forbid some observable choices — a representation that fits everything explains nothing). Theory here is rarely art-for-art's-sake; even an axiomatization is expected to connect to measurable behavior, because JRU's readership lives at the theory–experiment–empirics interface.

Representation discipline

• State the primitive and the domain. Are choices over lotteries (risk, known probabilities) or acts (uncertainty, subjective/unknown probabilities)? The Ellsberg-relevant distinction governs which family is admissible.
• Tie axioms to the functional form. If you adopt cumulative prospect theory, the axioms are rank-dependence + sign-dependence; for α-MEU, the relevant conditions concern the set of priors and the ambiguity index. Do not present a functional form as if it fell from the sky.
• Name the behavioral content. State at least one choice pattern the model predicts and one it forbids. "It can match Allais and Ellsberg" is content; "it has free parameters" is not.
• Separate the structural parameter from the nuisance. Curvature of utility (u) vs. probability weighting (w) are often confounded in EU; a JRU model must say how they are separately interpretable.

Common representations and what each commits you to

From representation to testable content

A JRU model is only as valuable as the predictions it exports to the experiment or the data:

• Derive comparative statics, not just existence. State how the object of interest moves with a parameter (how takeup moves with ambiguity, how the certainty equivalent moves with probability weighting) — these are what the empirical sections test.
• Map each parameter to an observable. For every structural parameter, name the choice or moment that will pin it (this is the bridge to jru-identification).
• Show the EU nesting. State the parameter restriction under which your model collapses to expected utility; the contribution is what happens away from that restriction.
• Keep the model minimal. Add structure only where it earns a prediction; referees punish free parameters that buy fit without content.

Checklist

• Domain stated: risk (lotteries) vs. uncertainty (acts) — and the family matches
• The functional form is tied to its characterizing axioms, not asserted
• At least one prediction the model forbids is named (falsifiable content)
• Utility curvature and probability weighting (or risk vs. ambiguity attitude) are separately interpretable
• The reference point / prior set is pinned down a priori, not fit after seeing choices
• Comparative statics that the experiment or data can test are derived explicitly
• Any proof of a key result is in the main text, not exiled to an appendix

Anti-patterns

• A representation flexible enough to rationalize any choice — JRU referees test for falsifiable content
• Letting the reference point or the set of priors be a free parameter chosen to fit the data
• Conflating utility curvature with probability weighting and calling the bundle "risk aversion"
• Presenting a functional form with no axiomatic story (or an axiomatization with no behavioral implication)
• Claiming an α-MEU model "explains ambiguity aversion" without identifying α apart from u

Risk vs. uncertainty: pick the right object

The single most consequential modeling choice is whether the primitive is risk (objective, known probabilities — lotteries) or uncertainty (subjective or unknown probabilities — acts). Getting this wrong invites a fast referee objection.

• If probabilities are given to the agent, model risk: EU, RDU, or CPT over lotteries.
• If probabilities are unknown or the source is ambiguous, model uncertainty: maxmin, α-MEU, smooth ambiguity, or variational preferences over acts.
• If the paper studies how behavior changes as probabilities become known, the model must span both and the Ellsberg-style distinction is itself the object of study.

State which world the agent inhabits before writing a single axiom; the admissible representations follow from it.

Worked vignette (illustrative)

A paper models insurance under ambiguity with smooth ambiguity (KMM). A referee asks what distinguishes it from a risk-averse EU agent with a pessimistic belief. The JRU answer separates the φ curvature (ambiguity attitude over second-order beliefs) from u curvature (risk attitude), and derives a comparative static EU cannot produce: takeup falls as the spread of second-order beliefs widens even when the mean loss probability is held fixed. That prediction is the model's behavioral content and the bridge to the experiment in jru-identification.

When the model is borrowed, not built

Most JRU empirical and experimental papers adopt an existing representation rather than axiomatize a new one. The craft is then about disciplined use, not invention:

• Justify the choice of family against the closest alternative (why CPT and not RDU; why α-MEU and not smooth ambiguity) in terms of the behavior you need it to capture.
• Adopt the standard functional forms (Tversky–Kahneman or Prelec weighting, CRRA/expo-power utility) and say so, so the parameters are comparable to prior estimates.
• Do not silently modify a published representation; if you change the reference-point rule or the prior set, flag it and show the consequence.

A borrowed model held to the same content standard — predicts something, forbids something, parameters separately interpretable — is fully publishable at JRU; an idiosyncratic variant smuggled in without justification is not.

Output format

【Journal】Journal of Risk and Uncertainty
【Skill】jru-theory-model
【Verdict】sound / sharpen / rebuild representation
【Domain】risk (lotteries) / uncertainty (acts)
【Representation】family + characterizing axioms
【Behavioral content】one prediction it makes, one it forbids
【Parameter separation】u vs. w, or risk vs. ambiguity attitude
【Source status】verified / 待核实 / not asserted
【Next skill】jru-identification