What is the test for sustaining a statutory presumption of illegal possession of firearms?

51. In Tot v. United States, 319 U.S. 463 (1943), Roberts J. outlined the following test at pp. 467‑68: ... a statutory presumption cannot be sustained if there be no rational connection between the fact proved and the ultimate fact presumed, if the inference of the one from proof of the other is arbitrary because of lack of connnection between the two in common experience. The comparative convenience of producing evidence was also acknowledged as a corollary test. The case involved a presumption to be drawn, from the possession of firearms by a person convicted of a previous crime of violence, that the firearms were illegally obtained through interstate or foreign commerce. Of note was Roberts J.'s comment that even if a rational connection had been proved, the statutory presumption could not be sustained because of the prejudical reliance on a past conviction as part of the basic fact. The accused would be discredited in the eyes of the jury even before he attempted to disprove the presumed fact.

52. In Leary v. United States, 395 U.S. 6 (1969), Harlan J. articulated a more stringent test for invalidity at p. 36: ... a criminal statutory presumption must be regarded as "irrational" or "arbitrary", and hence unconstitutional, unless it can at least be said with substantial assurance that the presumed fact is more likely than not to flow from the proved fact on which it is made to depend. Harlan J. also noted that since the statutory presumption was invalid under the above test, "we need not reach the question whether a criminal presumption which passes muster when so judged must also satisfy the criminal `reasonable doubt' standard if proof of the crime charged or an essential element thereof depends upon its use" (footnote 64).