Smith v. Rapid Transit, y’all! As you may have heard by now, SCOTUS threw out, by a vote of 7 to 2, Texas’s last-ditch effort to derail the election of former Vice President Joe Biden, but what you may not have heard of is the obscure but important case of Smith v. Rapid Transit. In brief, this case stands for the proposition that probabilistic proof, standing alone, i.e. without any corroborating or direct evidence of misconduct, is not enough to prove a fact. Before proceeding, can you already see why this case explains the result in the Texas case?
Instead of rehashing the merits of the Texas case, however, I will take a closer look at the Smith case. In summary, the plaintiff, Betty Smith, was driving down Main Street in the City of Winthrop, Massachusetts at about 1:00 a.m. on February 6, 1941. She saw a bus coming toward her at high speed and, to avoid a direct collision with the bus, she swerved and crashed into a parked car, but she did not actually see whose bus ran her off the road. Nevertheless, the plaintiff’s attorney later discovered that the defendant operated a bus line in the City of Winthrop and had an exclusive license to operate a bus route on Main Street, and according to the defendant’s timetable, the defendant’s buses were scheduled to travel down Main Street at 12:10 a.m., 12:45 a.m., 1:15 a.m., and 2:15 a.m. (A second bus company had a license to operate a bus line in the City of Winthrop but not on Main Street.)
Since this was a civil case, the plaintiff was required prove her case by “a preponderance of the evidence.” Stated in probabilistic terms, it must be more likely than not that the defendant’s bus caused the plaintiff to swerve into the parked car. The problem in the Smith case, however, was that the only evidence linking the defendant’s bus line to the scene of the accident is probabilistic in nature. That is, since by the plaintiff’s own admission she did not actually see which bus was going down Main Street at the time of the accident, the only evidence linking the defendant’s bus to the scene of the accident was the defendant’s published timetable or schedule.
This simple case thus presents a controversial legal issue, one that is relevant to the allegations of voter fraud in the 2020 presidential election. Stated simply, the issue is whether probabilistic proof alone is enough to prove an allegation. The trial judge in the Smith case ruled that probabilistic proof is not enough as a matter of law and entered a directed verdict in favor of the defendant bus line, and the Massachusetts Supreme Court then affirmed the trial court’s decision, holding that probabilistic proof, by itself, is not sufficient to prove one’s case. The Massachusetts Supreme Court explained its reasoning that “[t]he most that can be said of the evidence in the instant case is that perhaps the mathematical chances somewhat favor the proposition that a bus of the defendant caused the accident. This [is] not enough.” (Since then, most U.S. courts, State and federal, have followed this reasoning in subsequent cases.)
As it happens, I wrote about this case a few years ago in my paper “Visualizing Probabilistic Proof,” and for my part, I would ask, Does it make sense to draw this line between direct evidence and mere probabilistic proof? Specifically, isn’t all evidence, even direct proof like eyewitness testimony, ultimately probabilistic in nature?
Even 2+2 is not always 4. It probably is, but there’s a small probability that one is stating this proposition in the ternary number system, in which case 2+2 = 11. One might say that it is improbable for a person to be stating this proposition in something other than Base 10, but as you point out, it is not a certainty without the support of other “evidence” such as assertions by the proposer that she knows nothing about ternary numbers, which would have to be bolstered by evidence about the proposer’s educational background that show no record of ternary numbers ever having been discussed in any of her classes, ever, along with records of all television shows she may have watched on PBS, and scouring those shows for references to ternary numbers… but all this would be futile as it would amount to attempting to prove a negative, i.e., that the proposer knows nothing about ternary numbers. Therefore, 2+2 can never be assumed to equal 4.