# What if Courts calculated probabilities?

23/09/2011 Leave a comment

The standard of proof applied in civil litigation in the UK is ‘the balance of probabilities’, which means that in order to win the case, the claimant needs to show that her case is more likely than not to be true. Take the example of damage claims. The amount of damages is governed by the ‘but for’ principle, the claimant is entitled to be placed in the position he would have been in but for the breach. For this it is inevitable to show what would have happened – *on the balance of probabilities* – absent the defendant’s behaviour. In the vast majority of these cases courts would apply a very simple comparator based method: what happened to those in a similar position who were not affected by the defendants conduct? Then the difference between the outcome observed for the plaintiff and this counterfactual is used as a basis for damages. But what if courts used more formal statistical methods?

There is a large volume of academic literature on how to quantify harm caused by anti-competitive cartels (a recent EC guidance paper gives a comprehensive and non-technical inventory of these). Assume for example that the damages claim needs to show on the balance of probabilities that the defendant’s conduct led to a price increase. Irrespective of the method used, the goal in this case would be to quantify the effect of the defendants’ behaviour on prices. Conventionally, this is done in a way that shows that the price change is at least 95 percent likely not to be just a random outcome of things. This seems to easily surpass the required balance of probabilities standard. But what happens to all the assumptions that we have to rely on for the actual statistical estimation to work? Say for example the choice of the counterfactual (i.e. the situation against which we are testing the effect of the defendant’s conduct). What is the probability that this counterfactual is the right one? Or what is the chance that the analysed price follows a distribution that is required for the chosen method to work? And how about the variance in price that is explained by factors that we do not observe in our analysis? What are the chances that we chose the right model? And the list could continue on pages and pages but what matters is that all these factors would have to be accounted for when computing the likelihood that the defendant’s conduct had an effect on prices.

Now assume that we did a really good job with our choice of method and we only need three assumptions, each of which has a high likelihood of 4/5 to be true. Then the estimated effect, which is 95 percent sure not to be a random effect, is true only with a (4/5)^3*0.95=0.49 chance, which means that strictly speaking, on the balance of probabilities we lost our damages claim even though as economists we would have been very satisfied with our analysis. So all in all, maybe it is lucky that courts do not do numbers.