Building Bayesian priors for Unfair dismissal awards

A histogram showing the spread of awards for unfair dismissal in 2020

Each year solicitors’ firms publish summaries of the latest tribunal statistics on unfair dismissal (among other types of claim).

The summaries invariably include the following data – the maximum award, the mean, and the medium.

It occurs to me that this is not the most helpful format, since as statistical moments, the mean, median and maximum tell you very little indeed about the spread of awards.

As someone who advises on valuation, it was useful for me to be able to say what sort of distribution of awards might be expected (before looking at the data of a given case). I was surprised that this data is not readily available, leading me to make a Freedom of Information request.

The response from the MoJ politely declined my request, on the basis that the data is already in the public domain. I was sent the relevant link. In fact, that data is still not public – there are counts of awards within 18 separate bands, but nothing like a list of the actual award figures which one could build a distribution from.

But it is true that with some imputation it makes little difference: I build the above histogram by using a random number generator to simulate awards within each of the 18 bands. I don’t believe there is an alternative way to generate a useful distribution given the current constraints on what data is shared.

But I have followed the same process in respect of each type of claim, since reliable records began, and use these distributions to assist me in building prior models for the valuation of a claim, which I can then feed into a Bayesian Monte Carlo model.