When Proving an Honest Claim Costs Money, Bankruptcy Rules Matter

Making false claims expensive sounds like a straightforward way to discourage dishonesty. But evidence requirements and legal proceedings can also make honest claims expensive. A new bankruptcy model asks which division rules can discourage exaggeration without rewarding people for claiming less than they are owed.

An estate cannot cover everyone’s claims. Dividing it proportionally may seem straightforward: each claimant receives the same fraction of what they claim. But if entitlements are not publicly known, the amounts submitted become strategic choices. Exaggerating might increase an award; reducing a legitimate claim might save enough legal expense to be worthwhile.

In the preprint Bankruptcy Rules for Strategic Agents, Yosef Zumer, Erel Segal-Halevi and David Sarne examine both incentives together. Their theoretical results suggest that a division rule cannot be evaluated separately from the costs of substantiating claims. This is a mathematical analysis, not evidence from court cases or an empirical test of legal reform.

Honesty has a price

The model starts with a fixed estate and at least two claimants whose true entitlements collectively exceed it. Each entitlement, and each permitted report, is capped at the size of the estate. That restriction matters: it excludes cases in which an individual creditor is owed more than the entire available estate.

A submitted claim has two possible components. The amount up to the claimant’s true entitlement is genuine; anything above it is false. Supporting each component incurs a constant cost per unit claimed, with false claims costing at least as much per unit as true ones. A claimant seeks to maximize their award minus these costs.

The central tension is marginal: how much additional award does another unit of reported claim buy? If supporting a genuine unit costs more than the award it adds, under-reporting can pay. If fabricating a unit costs less than the award it adds, exaggeration can pay.

The authors turn that observation into a criterion. Across all admissible conflicting claim profiles, the genuine-claim cost rate must not exceed the rule’s smallest marginal gain, while the false-claim cost rate must be at least its largest marginal gain. These bounds make truth-telling a best response throughout the model’s domain.

Why proportional division struggles

For the proportional rule, marginal gains can approach zero in some cases and one in others. Consequently, the authors find that it supports truthful reporting across the entire domain only when genuine claims are costless to establish and false claims cost at least one unit per unit fabricated.

This is not a claim that proportional division always produces dishonesty whenever legal expenses exist. It means that no positive genuine-claim cost rate provides the model’s universal truthfulness guarantee: some admissible situation permits a profitable deviation.

Constrained equal awards, which caps awards at a common level while paying smaller claims in full, also requires costless genuine claims for that guarantee. Constrained equal losses has the same obstacle with three or more claimants.

A wider range for truthful reporting

The strongest result concerns TAL–1/N, a member of the parameterized Talmud family, where N is the number of claimants. The family combines constrained equal awards and constrained equal losses using a parameter that determines the division.

For TAL–1/N, truthful reporting is a best response exactly when the genuine-claim cost rate is at most 1/N and the false-claim cost rate is at least 1 − 1/N. With three claimants, those thresholds are one-third and two-thirds respectively.

Within the paper’s class of piecewise smooth allocation rules, no rule supports truthfulness outside those universal bounds. TAL–1/N therefore accommodates every cost pair that any rule in that class can accommodate. Here, “optimal” means the widest truthful cost region—not a general verdict about which distribution is fairest.

With two claimants, the rule coincides with the Contested Garment rule and uniquely achieves that region on the model’s domain. For three or more, whether another rule outside the parameterized Talmud family also achieves it remains open.

The distinction between weak and strict incentives matters. At the stated boundaries, another report may tie with honesty. For TAL–1/N, truth-telling becomes the unique best response only when the genuine-claim rate is strictly below 1/N and the false-claim rate strictly above 1 − 1/N.

Deterrence is not free

The authors also allow the genuine-claim cost rate to rise as the false-claim rate rises. When truthful cost settings are feasible under that relationship, TAL–1/N can maximize total claimant welfare subject to truthfulness, measured as the estate minus claim-support costs. This welfare optimum need not be unique.

The policy implication is conditional but clear: stronger deterrence can burden honest claimants too. Under these assumptions, choosing how to divide the estate changes how much of that burden truthful reporting can withstand.