In American civil trials, plaintiffs must prove their cases by a preponderance of the evidence. Courts often define this as “more likely than not,” and some courts and commentators define it as a greater than 50 percent probability of being true. Many courts have rejected the 50 percent definition, however, and Judge Richard Posner uses economic principles and the “Bus Hypothetical,” to explain why. The Bus Hypo, however, is inconsistent with other economic principles and may not be an appropriate economic explanation of these cases.
Smith v. Rapid Transit, Inc.
The leading case that implies that courts do not define preponderance of the evidence as a greater than 50 percent probability of being true is Smith v. Rapid Transit, Inc., 317 Mass. 469 (1945). In Smith, the plaintiff’s car was run off the road by a bus, but no party was able to demonstrate conclusively who owned the bus. The evidence that the defendant owned the bus included: 1) the defendant operated a bus route that traveled on the street where the incident happened; 2) no other bus company had a permit to operate a bus route on that street; and 3) the bus company’s timetable suggested that its bus would be at the location of the accident at the time of the accident. Because this was the only evidence, the district court directed a verdict for the defendant. The Supreme Judicial Court of Massachusetts upheld the directed verdict for the bus company because “[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 was not enough.” (Emphasis added.) The Court seemed to accept that a reasonable jury could have found that there was a greater than 50 percent chance that Rapid Transit caused the accident, but the plaintiff still had not proved her case by a preponderance of the evidence.
Economic Analysis of Law and Howard v. Wal-Mart
In his treatise, Economic Analysis of Law, Judge Posner interprets cases like Smith v. Rapid Transit to mean that courts do not define preponderance of the evidence as greater than 50 percent probability of being true. (7th ed. p. 650) To explain his analysis, Judge Posner uses the Bus Hypo, which is loosely based on the facts in Smith and strongly rooted in the analysis in Howard v. Wal-Mart Stores, Inc., 160 F.3d 358 (7th Cir. 1998).
In Howard v. Wal-Mart, Dolores Howard slipped and fell on liquid soap spilled on the floor of Wal-Mart. Although both sides investigated the issue, it was uncertain who spilled the soap–whether it was an employee or a different customer. Whoever spilled the soap was presumed negligent, so the only real dispute in the case was the identity of the soap spiller. If an employee spilled the soap, then Wal-Mart would be liable; if a customer spilled the soap, then Wal-Mart would not be liable. (Under Illinois law, Wal-Mart would be liable if a customer caused the spill and Wal-Mart should have cleaned it up before Howard slipped. There was no evidence how long the spill had been on the floor, so Howard could only recover if the facts proved an employee spilled the soap.) The evidence was ambiguous–some evidence suggested that a customer spilled the soap, but other evidence suggested that a Wal-Mart employee spilled the soap. Nevertheless, the factfinder had to choose, and the jury found that a Wal-Mart employee caused the spill and awarded Howard $18,750. Wal-Mart asked the judge to grant it judgment as a matter of law (essentially overturn the jury verdict), but the judge refused.
Wal-Mart appealed to the Seventh Circuit and argued that the evidence was too ambiguous to determine who caused the spill, and that the mere probability that a Wal-Mart employee caused the spill was not enough to find it liable. Said differently, Wal-Mart argued that Howard had not met her burden of persuasion and proved her case by a preponderance of the evidence. In a unanimous opinion, Judge Posner wrote that a reasonable jury could have found “that the balance of probabilities tipped in favor of the plaintiff, though surely only by a hair’s breadth.”
The Bus Hypo
The Howard appellate court answered the question, “Is a hair’s breadth enough, though?” by using the Bus Hypothetical. Loosely based on the facts in Smith, the Bus Hypo involves a plaintiff hit by a bus, but it is impossible to distinguish between two possible owners of the bus–Company A or Company B. The only evidence to determine which company owns the bus is based on a probability–on the road where the accident happened, 51 percent of the buses are owned by Company A, and 49 percent are owned by Company B. Based on only this evidence, the plaintiff sues Company A. Assume that the elements of negligence are met, and like the Howard case, the only dispute in the case is the identity of the negligent party. When this is the only evidence, then many courts dismiss the case or enter judgment as a matter of law in favor of the defendant. (Howard had non-statistical evidence to suggest that a Wal-Mart employee spilled the soap.)
Judge Posner says that courts should dismiss cases like this because there are only three possible scenarios where the plaintiff would bring this case, and each scenario dictates that the case should be dismissed. The court does not know which of the three scenarios is actually happening, but since all three require the dismissal of the case, it is not necessary for the court to know. In the first scenario, the plaintiff investigated and concluded that the owner is Company B, not Company A, yet the plaintiff sues Company A anyway. (The plaintiff might have sued Company A because Company B was judgment proof.) In this scenario, the plaintiff should lose because forcing Company A to pay for Company B’s negligence is so patently inefficient that Judge Posner does not explain further. We can deduce, however, that since Company A had nothing to do with the accident, it would be inefficient to hold Company A liable because there is nothing Company A could have done to prevent the accident.
In the second scenario, the plaintiff was too lazy to conduct an investigation. Judge Posner reasoned that it would be inappropriate for a court to expend resources when the plaintiff has not “conducted a sufficient investigation to make reasonably clear that an expenditure of public resources is likely to yield a significant social benefit.” Essentially, the plaintiff has not met her burden of production. Unless the plaintiff carries out a proper investigation that attempts to distinguish one owner from the other, courts should dismiss the case. From an economic perspective, however, it is not clear that the plaintiff should have to produce any more evidence. It might be best to assign the burden of production to the party that is the “cheapest evidence gatherer.” In this hypothetical, it is probably cheaper for the bus company to investigate the location of its buses than it is for the plaintiff to investigate. This suggests that the plaintiff has met her burden of production and that the bus company should have to answer the charges. On the other hand, Judge Posner argues that allowing plaintiffs to make accusations without sufficient investigation is a waste of judicial resources. The administrative costs of dealing with bogus claims might outweigh the inefficiency of forcing the plaintiff to gather evidence even when the plaintiff is not the cheapest evidence gatherer. The Bus Hypo does not clearly resolve the balance between burden of production and administrative costs, and it is unclear whether this scenario favors dismissal or not.
The third scenario comes from Judge Posner’s Economic Analysis of Law. In this scenario, both parties conduct a thorough investigation but cannot determine the owner of the bus–it is impossible to distinguish one company from the other. Judge Posner argues in his treatise that the court should still dismiss the case even though it is 51 percent likely that Company A is liable for the accident. If 1,000 cases were tried and decided, then Company A would be liable for all of them. This would result in 510 correct decisions (because Company A did cause the accident) and 490 errors (because Company A was found liable even though it did not actually cause the accident). Judge Posner then argues that dismissing all 1,000 cases would have only a slightly different error rate–490 correct cases (Company A did not cause the accident, so the dismissal is accurate) and 510 errors (Company A did cause the accident, so it is escaping liability). Dismissing the cases only causes 20 more errors, but it saves a massive amount of administrative costs because the court does not have to try 1,000 cases. Judge Posner further argues that holding Company A liable will mean that Company B has less incentive to take care because Company A will be liable for Company B’s accidents when it is impossible to distinguish one company from the other. the evidence about the bus’s owner is ambiguous. In economic terms, Company B will have externalized its accident costs when it is impossible to distinguish one company from the other.
The analysis of the third scenario is incomplete
Judge Posner’s conclusion, however, makes an assumption about the total economic benefits. What is the total economic benefit that comes from running 1,000 trials where 510 are correctly decided compared to the total economic benefit that comes from dismissing those 1,000 cases. Dismissing the cases does save administrative costs, but it also places the burden of accidents on plaintiffs. As a society, we lose the benefit of those 510 correctly decided decisions. It is not clear that saving the administrative costs is more valuable than the benefit of 510 correctly decided decisions. Furthermore, it is not clear where the “save on administrative argument ends.” Should courts dismiss small-value claims because the administrative costs are higher than the expected recovery?
To decide if courts should dismiss these cases, we must look at the economic effects of dismissing the cases. In the third scenario from the Bus Hypo, it is impossible for any party to distinguish the ownership of the bus between Company A and Company B. This lack of distinction is a cost–the cost of indistinction. Judge Posner assigns the cost of indistinction to the plaintiff because that reduces the administration costs of trying the cases. Normally, costs are assigned based on the cheapest way of avoiding the economic loss. If the only economic loss were the administrative costs of running a trial, then assigning the cost of indistinction to the plaintiff might be the most efficient alternative. Assigning the cost of indistinction to the plaintiff, however, creates some undesirable economic results.
If the cost of indistinction is assigned to the plaintiff, then the two bus companies now have an incentive to create more indistinction. With more indistinction, the bus companies will be able to avoid more liability for their negligent driving. As the bus companies create more indistinction, they are externalizing more of their accident costs. To combat the bus companies transferring of the costs of their negligence to the drivers, all potential plaintiffs will have an incentive to reduce indistinction.
If the cost of indistinction is assigned to one of the bus companies, however, that bus company will have an incentive to reduce indistinction. Because the company will be liable for any accident where the owner is indistinct, the company will spend money to create more distinction. A third possibility is to assign the cost of indistinction to multiple parties.
An economic analysis of the cost of indistinction would assign the cost of indistinction to the party or parties that can avoid indistinction for the least cost. (See the section titled “Hydraulic” Pressure. See also Posner § 6.4.) As shown below, it is more likely that the bus companies can avoid the cost of indistinction more easily than potential plaintiffs can.
Potential plaintiffs (all of the people that drive cars on streets with buses) can do a number of things to avoid indistinction if they are hit by a bus. 1) They can install video cameras on their cars. If they get into an accident, then the cameras will capture information about the buses. 2) They can decide not to drive on streets where the owner of a bus may not be distinct. 3) All potential plaintiffs can get together and pay bus companies never to use the same street as another bus company. Obviously, all of these solutions would cost a lot of money or have coordination problems.
The bus companies can also do things that improve their distinctiveness. 1) They can paint their buses distinctive colors, which may help witnesses distinguish one company from another. 2) They can install video cameras and GPS trackers on their buses. 3) They can keep detailed logs of the movements of their buses.
From these examples, it is easy to see that it costs the bus companies much less to improve distinctiveness than the total cost to all potential plaintiffs. If all potential plaintiffs wanted to improve distinctiveness by installing video cameras, for example, thousands of drivers would have to install the cameras. The bus companies, however, could install just a few dozen cameras on their buses and that would achieve the same improvement.
Judge Posner assigned the cost of indistinction to the plaintiff based only on the administrative costs. An analysis of the economic effects of assigning the cost of indistinction to the different parties, however, suggests that the cost should be assigned to the bus companies.
By placing the cost of indistinction on all of the bus companies, each bus company will have an incentive to reduce their indistinction. Alternatively, placing the cost on the bus company that operates the majority of the buses (Company A) gives that company an incentive to reduce indistinction. In either case, the bus company (or bus companies) can reduce indistinction cheaper than potential plaintiffs can.
Implications of the full evaluation of the Bus Hypo
In his treatise, Judge Posner proposed that courts do not define the preponderance standard with a simple 50%+ statistic. He used the Bus Hypo to support and explain his proposition. This analysis of the Bus Hypo merely shows that the Bus Hypo is not a good illustration of his proposition. This evaluation does not refute Judge Posner’s suggestion that courts do not like to define preponderance by using percentages.
At first glance, this evaluation of the Bus Hypo suggests that Smith v. Rapid Transit was wrongly decided. At best, this evaluation says that an economic analysis of Smith would lead to a different result. There are probably non-economic reasons, however, to support the holding in Smith. See Causation, Responsibility, Risk, Probability, Naked Statistics, and Proof: Pruning the Bramble Bush by Clarifying the Concepts, 73 Iowa Law Review 1001, 1049-1067 (1988).
My thanks go to Professor Henry H. Perritt, Jr. and Professor Richard Wright for their help.
