The Eurovision Song Contest was founded 70 years ago as a way for Europe, divided after war, to come together by celebrating its music. Every year, several dozen countries across the continent – and, more recently, far beyond – compete in what is considered the world’s most viewed non-sporting event.
As a cultural institution that last year attracted around 166 million viewers, the results of Eurovision have a big impact – not least by deciding the venue of the following year’s event. Yet the issue of bloc voting, where countries tend to vote more favourably within regional or cultural blocs, has long been a controversial aspect of the contest.
In 2008, the BBC’s Eurovision commentator Terry Wogan spoke out against bloc voting by Eastern European countries, saying: “You have to say that this is no longer a music contest. I have to decide whether I want to do this again.” He didn’t – it was his final show in the commentary hotseat.
On occasion, suspiciously friendly voting has strayed into something even more troubling. The 1968 contest, held at the Royal Albert Hall in London, saw a major upset when home favourite Congratulations, sung by Cliff Richard, was pipped by the Spanish entry La, La, La.
Forty years later, Spanish Eurovision host Jose Maria Inigo claimed that the vote had been rigged at the behest of Spain’s military dictator, Franco. His claims were later supported by an Irish TV investigation.
The modern, expanded Eurovision features two semi-finals as well as the grand final, held this year in Vienna on May 16. Its scoring combines a jury panel with a public vote, reducing the impact of each jury. But that didn’t stop another major voting scandal emerging in 2022.
The 2022 scandal
During the 2022 grand final in Turin, Italy, the European Broadcasting Union (EBU) announced that six juries’ scores from the second semi-final – Azerbaijan, Georgia, Montenegro, Poland, Romania and San Marino – had been nullified after “certain irregular voting patterns were identified in the results of [these] countries”.
The countries’ votes were replaced with an aggregate score “based on the results of other countries with similar voting records” for both the semi-final and grand final. This process was acknowledged by Eurovision’s Independent Voting Monitor.
The countries’ broadcasters strongly denied any wrongdoing, with Georgia even suggesting their first-place vote in the final had been wrongly allocated as a result of the imposed system. Among online audiences, there was immediate speculation of a cover-up. After the final, the EBU issued a long explanation for their decision.
So had there really been collusion? Colleagues and I from the University of Stirling, including Riley Uttley, have re-assessed the 2022 voting scandal using applied statistical methods.
Each five-member Eurovision jury selected their ten favourite songs, with 12 points going to their favourite, ten points for second, then eight down to one for their tenth-best song. A similar points system was used to reflect each country’s public vote, doubling the total number of votes awarded by each country.
The jury results prior to the EBU’s intervention are shown below. The six juries whose scores were nullified – marked in red – awarded each other a total of 251 points. This is just seven points shy of the absolute maximum they could have given each other: 6 x (12+10+8+7+6) = 258 points.
Eurovision jury scores, 2022 second semi-final
Robin Hankin, CC BY
If the scores were allocated randomly, the odds of the six countries awarding each other 251 points would be less than 1 in 10,000. Such a low probability provides strong objective evidence that the six juries were indeed colluding.
But applied statistics can precisely quantify the strength of this collusion – using a version of the Bradley-Terry (BT) method of paired comparisons, first published in December 1952.
Calculating the strength of collusion
Say we have two songs, a and b, and want to know the probability that a is judged better than b. Using the BT method, this probability is:
p(a) / p(a) + p(b)
where p(a) and p(b) are the respective strengths of the two songs.
This idea can be extended to the ranking of any number of songs. If we observe, say, that a ≻ b ≻ c ≻ d ≻ e (that is, song a is the best, then b, down to e), the probability of this voting decision is:
This is known as a Plackett-Luce likelihood function. While calculating each value is difficult, we can use standard optimisation techniques to maximise this probability, and thereby estimate the strengths of the songs.
When it comes to identifying the strength of collusion in the 2022 contest, my own technique known as reified Bradley-Terry can be applied to this likelihood function.
The unfair advantage of collusion is represented by adding an extra strength term to any competitor who benefitted from collusion. In the equation below, S represents the strength of the collusion effect, and is applied to song b. So, we replace every occurrence of p(b) with p(b)+S. Then, the probability of a ≻ b ≻ c ≻ d ≻ e is now:
The Eurovision 2022 semifinal had 18 songs and 21 juries, leading to a probability equation like the one above – but with a total of 220 terms. While this is a lot for a person to work with, it can be easily handled by the R programming language, an open-source statistical tool designed to handle masses of data and produce graphics and visualisations.
The removed juries all appeared to have very similar behaviour, so we represented the strength of the collusion of all six as a single number S, which we calculated to be 0.262. We then calculated the probability of S being as high, or higher, than this value on the assumption of no collusion.
We calculated this probability to be one in 58,000. Put another way, if you have 2.5km of matchsticks laid out end-to-end and burn one, it’s the probability of picking the burnt one. We can, therefore, confidently conclude that collusion did take place.
A final quirk
The 2022 Eurovision voting scandal had ramifications beyond the nullification of the six collusive scores. Jury voting for semi-finals was discontinued from 2023 until this year’s contest. Perhaps perversely, this made the juries carry more weight in each grand final.
With the semi-finals decided purely by public votes, which tend to be more dispersed and unpredictable, this meant the juries’ more concentrated voting patterns played a more significant role in deciding the ultimate winner.
Jury voting was reinstated for the semi-finals of this year’s contest. However, the juries are larger (seven members rather than five) and chosen from a more diverse background.
The clear favourites, Finland, will hope this is another step towards eradicating the controversial voting patterns that have haunted past contests – and made Eurovision a focus of keen interest for some applied statisticians.
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