The Social Security Act establishes many ways for children to recover benefits on their father's account. See Trammell v. Bowen, 819 F.2d 167, 168 (7th Cir.1987). After Frank Jones died in 1983, Lucy Brown filed an application for benefits on behalf of Atlanda, Frank, and Amber Brown, who she said were Frank Jones's children, born between 1969 and 1972. Lucy Brown sought to establish eligibility under 42 U.S.C. Sec. 416(h)(2)(A), which provides that children eligible to inherit property from the insured person under the intestate succession laws of the state where they live (Illinois, in this case) may receive benefits on his account. See Schaefer v. Heckler, 792 F.2d 81 (7th Cir.1986). Illinois law provides that a person may take by intestate succession only if he establishes by "clear and convincing evidence" that he is the child of the decedent. Ill.Rev.Stat. ch. 110 1/2 p 2-2(h).

The Secretary commenced paying benefits promptly after Lucy Brown applied for them but concluded after a year that the evidence of paternity was insufficient; he sought to recover the $16,542 paid out so far. An administrative law judge heard the case on cross-applications: the Secretary wanted the money back, and Lucy Brown wanted an order confirming her right to benefits. The ALJ denied both requests, concluding that Brown had not established by clear and convincing evidence that Frank Jones was the children's father, but that she had "enough evidence to justify her action in filing for children's benefits" to make her "without fault", and so entitled to keep the money under 42 U.S.C. Sec. 404(b). The Appeals Council let this decision stand. The district judge granted summary judgment to the Secretary on Lucy Brown's petition for review, holding that substantial evidence lay behind the decision. Plaintiff thinks this irrational. How could the ALJ both find that she had enough evidence to escape repayment and conclude that the children are not Frank Jones's? She believes, too, that the ALJ committed an error of law by assuming that only written evidence may be "clear and convincing". Plaintiff believes that she has plenty of uncontradicted evidence and that the three children are entitled to benefits as a matter of law.

Lucy Brown testified in the administrative hearing that she met Frank Jones in 1969 and was intimate with him occasionally until 1973, when she became a Jehovah's Witness and saw him no more. During those years, Lucy stated, she had sexual relations with no one else. Atlanda, Frank, and Amber Brown testified that they knew Frank Jones as their father, that they saw him occasionally until his death and called him "daddy", that he gave them small presents and acknowledged them openly as his children on chance meetings at the grocery store or in the schoolyard, and that he sometimes came to their house. (This is in some tension with Lucy's testimony that Frank was excluded from the Brown household after 1973.) John Brown and Velma Garnett, two of the elder siblings of Atlanda, Frank, and Amber, testified that they knew during 1969-73 that Frank Jones was seeing their mother and that Jones visited the family once or twice a month after 1973; John added that when he met Jones on the street, Jones would inquire after the three. John recalled one Christmas morning when Jones visited the Brown house and played the role of paterfamilias, trying to inveigle little Frank to talk into the tape recorder Jones had brought. The Browns produced some snapshots of the family at a picnic with a man they identified as Frank Jones.

The Brown household received welfare payments throughout this period. When Atlanda was born, Lucy informed her welfare caseworker but did not (initially) seek an increase in benefits, stating that Frank Jones would provide for the child. Lucy said that Frank acknowledged his role and during 1970 accompanied her to the welfare office and filled out some papers promising to pay $10 per week for Atlanda. Neither Lucy nor the welfare officials could find those papers. This process was repeated for the next child, but in February 1972 Atlanda and Frank Brown were added to the welfare rolls. Forms for all three children have a space for the father's signature; each signature line is blank. A form filled out by the welfare agency in 1972 noted that Lucy named Frank as the father, but that Frank was not to be contacted at his home. It is common ground that if Frank Jones ever contributed anything to the children's support, he stopped in 1975. (Before then, Lucy Brown testified, she occasionally visited Jones at work to pick up cash when she needed it.) No judicial order of support was sought, and Jones never acknowledged the children in writing. Their birth certificates do not give a father.

The caution not to contact Jones at home may have been prudent, because he was married to Thelma Jones--and had been since 1941. Thelma testified that she had never heard of Lucy Brown or her children. Thelma painted Frank as a good husband and provider who gambled with money he made from extra plumbing jobs and sometimes stayed out all night on Friday or Saturday but who was otherwise reliable. She allowed that Frank would not have told her of any affair he may have had, but added: "He would tell me about everything, ... and so that ... I say I don't see how Frank could keep that a secret...." Thelma's testimony was corroborated by two neighbors and friends of the Jones family, who testified that they too had never heard of or seen Lucy Brown.

The administrative law judge laid out this evidence and wrote:

[T]he evidence of parentage comes solely from the testimony of the mother Lucy Brown, the three children who claim benefits on the record of Frank Jones, Lucy Brown's eldest daughter Velma Garnett, and John Brown, a son of Lucy. No documentary or other clear and convincing evidence has been submitted to corroborate their testimony. The birth certificates make no reference to Frank Jones as the father.... The records which have been submitted by Public Aid do not contains [sic] any acknowledgement of paternity by the wage earner. Accordingly the Administrative Law Judge must find that the evidence of record the Public Aid records plus the testimony of Lucy Brown and her children is insufficient to establish parentage under Illinois law.

Plaintiff reads this as requiring a written acknowledgement, or at least documentary evidence, in order to establish paternity, which would be an error of state law. On top of that, plaintiff says, the ALJ had no good reason to reject the uncontradicted evidence; the only reason he might have had, lack of credibility, he did not invoke--and could not very well have invoked in light of his conclusion that Lucy Brown had enough evidence to be "without fault" in collecting $16,542. If she was lying, Lucy observes, she was at fault, and if she was not lying, she and the children are entitled to benefits.

Evidence may be clear and convincing although not memorialized. The testimony of a single witness--even one with a perjury conviction--can supply proof beyond a reasonable doubt in a criminal case. If the ALJ imposed a written-acknowledgment requirement, he commited an error that would require a remand. And the opinion is ambiguous; one could read it as the Browns do. One also could read it the other way. The opinion states that all of the testimony comes from the Brown family and that there is no "documentary or other " evidence to "corroborate" this self-serving information. Thelma Jones had never heard of Lucy Brown. It is plausible to suppose that she would have learned of his philandering even if he did not tell her. As Lucy Brown and her children portray things, the Browns and Joneses lived in the same neighborhood and frequently met on the street or at stores. If Frank Jones had told grocery clerks that he was father to the Brown children, it could only have been a matter of time before Thelma Jones got wind of it. The ALJ's opinion does not suggest that if Thelma (or even the grocer in whom Frank supposedly confided) had supported Lucy's testimony, the ALJ still would have denied the claim for want of written evidence. The ALJ later wrote that Atlanda, Frank, and Amber "do not qualify as Frank Jones [sic] children under section 216(h)(3) because there is no written acknowledgment of paternity, judicial finding of paternity, or support order." This sentence, dealing with a statutory provision that treats written acknowledgment as conclusive in the children's favor, suggests that the ALJ knew the difference between a legal requirement of acknowledgment (to qualify under Sec. 216(h)(3)) and the role of acknowledgments (or their absence) as the basis of a factual inference (under the Illinois law of intestate succession).

There is no sure way to resolve the ambiguities in the opinion. The more likely reading, however, the one drawn from the text read as a whole, leads us to believe that the ALJ was simply looking for something more than the testimony of the Browns. This is the prerogative of a trier of fact under these circumstances. We shall not pretend to certainty; maybe the ALJ was confused; but almost any opinion can be read in a way that is consistent with legal error, and if resolving doubts against the trier of fact were appropriate, we would remand a large percentage of all cases. If the ALJ thought that the clear-and-convincing standard required written proof, he was making a very foolish error. Rather than read a passing remark as a colossal mistake, we accord the decision a presumption of regularity--which the remaining language in this opinion suggests this ALJ deserves.

This leaves the question whether the ALJ was inconsistent, believing the Browns for the purpose of excusing recoupment but not for the purpose of establishing entitlement to benefits. Perhaps--and if so he may have been doing the Browns a favor rather than an injury, cf. United States v. Powell, 469 U.S. 57, 105 S. Ct. 471, 83 L. Ed. 2d 461 (1984)--but we do not think there is inconsistency here. The burdens of persuasion are different, and different burdens are a good reason to reach different outcomes on the same facts. United States v. One Assortment of 89 Firearms, 465 U.S. 354, 104 S. Ct. 1099, 79 L. Ed. 2d 361 (1984). The ALJ may excuse repayment whenever recoupment would be inequitable, and he may approach the question with a thumb on the scales in favor of the claimants. Under Illinois law there is a heavy presumption the other way on the question of paternity. The standard is "clear and convincing evidence", which at least one Illinois court has analogized to the "reasonable doubt" standard in a paternity case. Morelli v. Battelli, 68 Ill.App.3d 410, 25 Ill. Dec. 57, 386 N.E.2d 328 (1st Dist.1979). See also Estate of Ragen, 79 Ill.App.3d 8, 34 Ill. Dec. 523, 398 N.E.2d 198 (1st Dist.1979). The ALJ rationally could have said, on a record such as this, that the Browns had established their claim by a preponderance of the evidence but not by clear and convincing evidence; that it was more likely than not that Frank Jones was the father, but that the proof did not permit a conclusion more confident than that.

All burdens of persuasion deal with probabilities. The preponderance standard is a more-likely-than-not rule, under which the trier of fact rules for the plaintiff if it thinks the chance greater than 0.5 that the plaintiff is in the right. The reasonable doubt standard is much higher, perhaps 0.9 or better. The clear-and-convincing standard is somewhere in between. Litigation rarely produces enough information to permit the announcement of a confident probability estimate, though the trier of fact may be able to come up with a range; at all events, the levels of confidence required by the burdens of proof are themselves variable. "Beyond a reasonable doubt" means one thing in a misdemeanor case and another in a capital case, even though both use the same verbal formula. The more serious the consequences (and therefore the higher the costs of error), the more asymmetric the stakes (in a criminal case, the defendant stands to lose more than the prosecution stands to gain), the higher the level of certainty required. See Addington v. Texas, 441 U.S. 418, 99 S. Ct. 1804, 60 L. Ed. 2d 323 (1979) (giving this reason for adopting the clear-and-convincing standard for civil commitment). Illinois treats the determination of paternity for intestate succession as a serious matter, in which the risk of error is potentially high--the person said to be the father is in no position to deny the contention, and the evidence therefore may be lopsided. The increased burden of persuasion counteracts the effects of the inability to have a truly adversarial presentation of evidence.

The administrative law judge did not announce his decision in these terms, but he drew a line based on burdens of persuasion. He observed that the Browns had enough to escape recoupment but not enough to be clear and convincing. A trier of fact need not articulate such a decision in terms of probabilities (an unnatural locution for a lawyer even if a common means of treating uncertainties). It is enough if the ALJ indicates the path of decision. Burnett v. Bowen, 830 F.2d 731, 735 (7th Cir.1987); Orlando v. Heckler, 776 F.2d 209 (7th Cir.1985); Stephens v. Heckler, 766 F.2d 284, 287 (7th Cir.1985); Zblewski v. Schweiker, 732 F.2d 75 (7th Cir.1984). The administrative tribunal need not spell out every step in the reasoning, if it provides enough of the steps that the full course may be discerned. The ALJ's opinion here may be decoded. It is logical to draw a distinction based on the different burdens of persuasion, and substantial evidence supports the decision.