Math for Judges and for Juries

If you consider yourself a rational person, you will probably be familiar with Bayesian Rationality. But what is Bayesianism? Less Wrong describes it as a mindset that takes three core tenets fully into account.

Developing thoughts

Firstly, anything you encounter has different possible causes. In order to draw the right conclusions, you are dependent on your previously acquired information.

Secondly, for that matter, how we interpret any event, and the new information we obtain from anything, depends on the information that we have already accumulated. If you experience something that you think could only be caused by an event A, ask yourself whether you’d expect to experience this with equal probability, if this event A did not exist. If the answer is “yes” then it probably was not caused by A.

Thirdly, we can use the concept of probability to measure our subjective beliefs in something taking place or not. In addition to that, we can apply the mathematical laws regarding probability. This helps us to choose between different possible expectations. If we want our expectations to be correct, we must do so.

The fact that anything can be caused by an infinite amount of things should emphasize that we need to be strict regarding the theories that we employ. It isn’t enough that a theory explains a phenomenon; if it can explain too many things at once, it isn’t a good theory. If you’d expected to experience something even when your supposed cause was irrelevant, then that would be no evidence for your cause. In other words, if a theory can explain anything you see then nothing you see can be evidence for the theory.

Knowing this, it will be quite easy to understand and apply a very similar bias called Representative Bias. The book definition gives us a better clue. This bias is a faulty heuristic based on the presumption that once people or events are categorized, they share all the features of other members in that category. Leading to the assumption that because someone shares one characteristic with a group of people, they share all characteristics.

But how do we apply this to our lives? There is an equation that helps us to calculate our beliefs.

P (A/B) = (P(B/A) x P(A)) / P (B)

A and B are events. P(A) and P(B) are the probabilities of observing A and B independently of each other. P(A/B) is a conditional probability, is the probability of observing event A given event B is true. P(B/A) is the probability of observing event B given event A is true.

This will help you calculate the probability of an event, based on prior knowledge of conditions that might be related to the event.

Summing up, knowing the likelihood of causes and events being related to each other is always worth it in order to evaluate probable outcomes!

How should lawyers apply all this to their work?

A simple example regarding the representativeness bias might give us a clue.

Imagine a person from a district of the city with a high crime rate who is also a drug addict is accused of a robbing a grocery store. A lot of people sitting in jury will be very skeptical about his or her innocence. This is not because there was any proof like fingerprints or DNA-evidence. It is only because they associate a group with a certain behavior. Solely belonging to this group might be enough in order to let them consider this person sharing the same attributes.

Summing up, this means that you should always listen to and look at the whole story of a case. Probabilities are not enough when looking at one particular case.

However, this is not only a rational approach but rather a kind and tolerant one!

Are you more of a visual type? Try this nice video of Julia Galef explaining Bayesian Thinking in every detail!