EASTERBROOK, Circuit Judge.

Rebecca and Quinthlyn Trammell obtained declaratory judgments from an Indiana court that their father was Lee A. Hudson. They obtained the judgments as part of their quest for children’s benefits under the Social Security Act. Hudson died on April 5, 1984, and his “children” within the meaning of 42 U.S.C. §§ 402(d)(3) and 416(h) are eligible for benefits. The Secretary of Health and Human Services denied the applications for children’s benefits, concluding that Rebecca and Quinthlyn are not statutory “children” even if Hudson was their father. Rebecca and Quinthlyn concede that they do not satisfy the statutory criteria but contend that the statute violates the due process clause of the fifth amendment to the Constitution.

The statute offers a person a multitude of ways to become a statutory “child”. The most common is for the mother to be — or be married to — the covered wage earner. 42 U.S.C. § 402(d)(3)(A). A child adopted by the insured person is treated the same as his own child. Ibid. Methods other than legitimate birth and adoption include:

—Eligibility to inherit property under intestate succession laws, 42 U.S.C. § 416(h)(2)(A), see Schaefer v. Heckler, 792 F.2d 81 (7th Cir.1986)

—Common law marriage of one’s parents, defined as a technically deficient marriage ceremony, 42 U.S.C. § 416(h)(2)(B)

—The insured person’s written acknowledgment of parentage,' 42 U.S.C. § 416(h)(3)(C)(i)(I)

—A court order requiring the insured person “to contribute to the support of the applicant because the applicant was his son or daughter”, 42 U.S.C. § 416(h)-(3)(C)(i)(III)

—A determination by the Secretary that the insured person was the parent of and “was living with ... the applicant [for benefits] at the time such insured individual died”, 42 U.S.C. § 416(h)(3)(C)(ii)

—A determination by the Secretary that the insured person was the parent of and was “contributing to the support of the applicant” for benefits when the insured person died, ibid.; see also Dubinski v. Bowen, 808 F.2d 611 (7th Cir.1986)

—A decree by a court that the insured person is the “father of the applicant”, provided that “such ... court decree ... was made before the death of such insured individual”, 42 U.S.C. § 416(h) (3) (C) (i)(II)

Rebecca and Quinthlyn do not qualify under any of these standards. Their mother, Willie B. Trammell, was never married to Lee Hudson and did not go through a defective marriage ceremony with him; Hudson did not adopt Rebecca or Quinthlyn; neither is eligible to inherit property from Hudson under the intestate succession laws of Indiana; Hudson never acknowledged in writing that he is the father of Rebecca or Quinthlyn; no court ordered Hudson to support them; Hudson never contributed to their support or lived with Willie Tram-mell; and although Rebecca and Quinthlyn obtained judgments that Hudson is their father, the judgments were obtained about four months after Hudson’s death. Because Rebecca and Quinthlyn come closest to qualifying under the judicial decree provision of § 416(h)(3)(C)(i)(II), they focus on it and contend that the rule requiring the decree to be obtained during the life of the insured person is irrational and unconstitutional. As they portray the rule, it is an unsupported swipe at the impartiality and competence of state courts. They add, relying on Jimenez v. Weinberger, 417 U.S. 628, 94 S.Ct. 2496, 41 L.Ed.2d 363 (1974), *169 that the rule creates a distinction that affects only illegitimate children, which requires closer scrutiny than courts usually afford to the categories entailed in social welfare legislation.

Although Rebecca and Quinthlyn insist that the sole reason they are not statutory children is the before-death rule in the judicial decree provision, it is more accurate to say that they are ineligible for benefits because they meet none of the many ways to qualify. Rebecca was born in 1970, Quinthlyn in 1975; Hudson died in 1984. They (more realistically, their mother Willie) had plenty of time to ask Hudson to acknowledge parentage in writing; their mother could have sought a judicial order to compel Hudson to support them; and if Hudson had lived with them or contributed to their support, that also would have sufficed. Whether the statutory scheme treats illegitimate children unconstitutionally depends on the interaction of all rules. The Trammells argue as if Congress had said: “Illegitimate children may receive benefits only if they obtain judicial orders establishing paternity before the father’s death.” That statute might have substantial problems under Jimenez and similar cases, but it is not what Congress enacted. True enough, once Hudson had died without acknowledging or supporting them in any way, the Trammells had only one hope: to obtain a court order and file this suit against the statutory rule. But this disregards the rest of the statute, the paths not taken. The Trammells’ ex post perspective on the qualification rules is not much different from the claim of someone who failed to file suit within the statute of limitations and complains that, given the expiration of the statute, it is unconstitutional absolutely to cut off all remedies on behalf of a person who has been injured.

Viewed as a system, the Social Security Act’s provisions defining “child” are constitutional. Like many other social welfare programs, children’s insurance benefits are designed to replace income lost on the death of someone who supplied money. See Mathews v. Lucas, 427 U.S. 495, 96 S.Ct. 2755, 49 L.Ed.2d 651 (1976). Yet an effort to find, case by case, who was “dependent” and who was not would be both complex (time-consuming and expensive for all concerned) and erratic — because different administrative law judges inevitably would have subtly different definitions of “dependent” and because different claimants would have different degrees of success in assembling the necessary evidence and presenting it in a persuasive way. The additional costs of such a system would tend to reduce the level of benefits; the delay would harm many in the worst hour of need; the greater variability of a system that would require adjudications in every case would tax the principle that likes should be treated alike. So Congress took the common path of choosing proxies for dependence. Cf. Bowen v. Owens, 476 U.S. 340, 106 S.Ct. 1881, 1885-86, 90 L.Ed.2d 316 (1986). Adoption, judicially required support, presence in the household, and so on, are indicators of dependence, although not guarantees of it. The statute errs on the side of generosity — many who can meet the requirements will not have been dependent on the insured person, yet anyone actually dependent but who cannot meet the other standards still can qualify by establishing that the insured person contributed to his support. 42 U.S.C. § 416(h)(3)(C)(ii). The question in any due process case is whether the system of rules and procedures makes too many mistakes in light of the gravity of the interests involved. See Mathews v. Eldridge, 424 U.S. 319, 334-35, 96 S.Ct. 893, 902-03, 47 L.Ed.2d 18 (1976) (a case dealing with procedures alone, but making a point equally applicable to the interaction of substantive and procedural rules when the two jointly determine eligibility). Mathews v. Lucas upheld the framework of this statute, despite an argument based on Jimenez; we concluded in Dubinski, 808 F.2d at 612, and Imani v. Heckler, 797 F.2d 508, 513 (7th Cir.1986), that the rules are rational in their general application. Given their bias in favor of benefits for non-dependent children, and the catch-all allowing benefits to be based on actual support, it is difficult to see how the system of rules could be unconstitutional as insufficiently favorable to *170 illegitimate children. Cf. King v. Schweiker, 647 F.2d 541 (5th Cir.1981).

The court-order rule, as one small part of a complex and generally sensible system, could be unconstitutional only if irrational. If there were no ground for believing that orders obtained before the father’s death are different from later orders, then the rule would be like a roulette wheel — and the parties assume for current purposes that a system handing out benefits based on chance or whim would be forbidden. (We need not decide whether lotteries, used for many purposes from the military draft to selecting people to receive scarce places in public housing projects, are indeed unconstitutional.) But there is a difference. Orders obtained during the supposed father’s life are more likely to be accurate because, if the child names the wrong person, he is apt to encounter resistance. The judicial declaration of paternity could be the basis of a later order requiring the father to support his child; one who is not actually the father is inclined to balk, and some real fathers also will endeavor to evade responsibility. A proceeding after the father’s death is ex parte or nearly so. (Hudson had a “legal representative” in the Indiana proceedings commenced after Hudson’s death — Willie Trammell’s son Michael Lewis Hudson.) To conclude that § 416(h)(3)(C)(i)(II) is constitutional, we need only believe that contested adjudications are more likely to be accurate than ex parte orders.

“More likely” is a necessary qualifier. The Trammells point out that an insured wage earner might consent during his life to the entry of a bogus finding of paternity, if sure that it would never lead to a later order of support; the “father” in such a case could bestow on the plaintiff a gift of Social Security coverage at the expense of the federal government, a nonparty that could not protect its interests in the litigation. But a potential to manipulate the court and obtain a spurious judgment does not mean that Congress’ decision — that contestable orders are more likely to be accurate than ex parte ones — is irrational. All legal rules depend on judgments about probabilities. It does not denigrate the courts of Indiana for Congress to conclude that decisions subject to meaningful adversarial contest are more likely to be accurate. The statute is constitutional.

Affirmed