Yesterday, UCL News Office issued this press release which mentions our (that's Marta and me) paper on the Eurovision contest, which has just been published in the Journal of Applied Statistics.
The idea of the paper was to try and quantify the presence of "bias" in the votes, as is sometimes (in fact quite often) suggested in the media.
In the model, we have "controlled" for some contextual and act-specific related factors (such as the sex of the performer and the language of the song), but really what we wanted to model was the "residual", structured effect, which could explain (at least partially) why two performers sharing common features get different scores from different voters.
Basically we modelled a structured effect $\alpha_{vp}$ for each combination of voters ($v$) and performers ($p$) over the repeated measurements in the last 20 years or so. This is defined as a function of three main factors:
- A "geographical" effect $\psi$, which accounts for potential bias due to spatial proximity;
- A "cultural" effect $\delta_{{R_v}p}$, which we use to describe the underlying "clustering" of voters in a set of groups $-$ we term this "cultural" in a rather broad sense. The clustering estimation is embedded in the model;
- A "migration" effect $\phi$, which accounts for the fact that voters where a large population originally from the performer's country may inflate the voting pattern in their favour.
As it happens, our model doesn't seem to uncover any evidence of negative bias $-$ no systematic low scores for any given performer $-$ although there is some (rather weak) evidence of positive bias, eg some countries showing higher propensity to score some performers higher than others.
By "standardising" the effects $\alpha_{vp}$ (centering them around their mean and re-scaling in terms of their standard deviation), we can compare them. This is the graph of propensity to vote for the UK.
We arbitrarily (but reasonably, as the $\alpha_{vp}$ are pretty much Normally distributed in their posteriors) set the threshold for "substantial" bias at $\pm$ 1.96. As you can see, while a couple of voters (Ireland, Malta and Italy) show on average a positive attitude towards the UK acts, nothing is really going on $-$ basically all credible intervals intersect 0. Most importantly, none is above or below the "bias thresholds".
We're starting to get some coverage (in some cases from the most unexpected sources!) $-$ some examples are here, here. I've also been called on the phone by The Sun (I was quite nervous about it $-$ hopefully I haven't embarrassed myself...)
