What Does Eurovision 2015 Tell Us about Voting Systems?

Would a different voting system have produced a different result in Eurovision 2015? And what are the implications for our understanding of the merits of different electoral rules? In this post, Dr Alan Renwick investigates.

The Eurovision Song Contest is over for another year and Sweden has been crowned the winner. But can we be confident that Sweden really deserve the crown? We know that different electoral systems can produce very different outcomes. That applies to Eurovision just as much as to any other contest: in 2011, for example, while Azerbaijan won the official vote, other voting systems that are widely used in public elections around the world would have given the top spot to Bosnia and Italy. So could different counting rules have selected a different winner this time round?

 

The basic answer is ‘no’, but there is some interesting variation in who comes second. The table below shows who would have ended up first, second, and third under a variety of defensible voting rules. Sweden would have won under any system – though under one of these it would have had to share the top spot with Italy. Russia and Italy vie for the second and third places.

The actual result is based on what political scientists refer to as a modified form of the Borda Count system. Each ‘voter’ – in this case, each country – ranks the acts in order of preference. The top ten preferences are then assigned points. Under the simple Borda Count system, shown in the second row of the table, the points are a simple sliding scale from 10 down to 1. Under the modified Eurovision system, the top two preferences are given a slight boost – 12 and 10 points rather than 10 and 9 – in order to reward first and second places slightly more. The table also shows a third version of the Borda Count, where the top preference secures a full point, the second preference half a point, the third preference a third of a point, and so on. This gives much more weight to the first preference than the other Borda systems: a first preference is worth twice as much as a second place.

 

Results for Eurovision 2015 under Alternative Voting Systems

Electoral System

First

Second

Third

Actual result (Modified Borda Count)

Sweden

Russia

Italy

Simple Borda Count*

Sweden

Russia

Italy

Ratio Borda Count**

Sweden

Italy

Russia

First Past the Post

Sweden

Italy

Russia

Alternative Vote

Sweden

Italy

Russia

Supplementary Vote

Sweden

Italy

Russia

Approval voting (voters able to approve 2 candidates)

Sweden

Russia

Italy

Approval voting (voters able to approve 3 candidates)

Sweden

Russia

Italy

Approval voting (voters able to approve 4 candidates)

Sweden

Russia

Italy

Approval voting (voters able to approve 10 candidates)

Sweden and Italy (joint first)

Russia

*Scores are 10, 9, 8, 7, 6, 5, 4, 3, 2, 1.

*Scores are 1, 1/2, 1/3, 1/4, …, 1/10.

 

The next system in the table is the familiar First Past the Post (or Single-Member Plurality) system. This is the extreme system that gives weight only to first preferences – all other preferences are completely disregarded. So here we just add up the number of 12s for each country and ignore everything else.

The Alternative Vote and Supplementary Vote systems again give extra weight to first preferences, but in a rather different way: candidates need to secure a decent share of the first preferences (in the case of the Supplementary Vote, they need to come either first or second in terms of first preferences) in order to get into subsequent rounds of counting. (I won’t give complete explanations of all these systems here, but they are widely available on Wikpedia and elsewhere.)

Finally, the table shows four versions of Approval Voting, where voters can indicate which of the candidates they approve of, without ranking them. Approval Voting systems are at the opposite extreme from First Past the Post: they make no distinction at all between first and lower preferences. As a commenter on my post on Eurovision 2014 noted, pure Approval Voting allows voters to express support for as many candidates as they wish. Here, however, I have calculated the outcome under alternative versions where voters can support two, three, four, or ten acts.

The results in the table show two basic patterns. First, as already noted, Sweden always wins.

Second, who comes second depends on the degree to which the voting rules place special emphasis on winning the top spot in the voting countries’ rankings. Italy secured more first places than Russia (nine to five, with Sweden on twelve). That is all that matters under First Past the Post, so Italy clearly comes out ahead of Russia here. It’s also what matters most under Ratio Borda Count, Alternative Vote, and Supplementary Vote. Under Simple Borda Count and the actual Eurovision system, it matters much less – indeed, it’s possible under these systems for a country to win the contest having come top in no single country’s ranking. And under Approval Voting, whether a preference is a first preference or a lower preference matters not at all. Russia secured far fewer 12s than Italy, but it won many more 10s, so it comes out ahead under Approval Voting. The only exception is the Approval Voting system where each country’s top ten preferences are all counted. Italy was in the top ten for more voting countries than was Russia – so it came out ahead here.

What do we learn from all of this? One thing we learn is that, if there is a clear winner, than a wide variety of electoral systems will produce the same outcome.

But we also see that voting systems do make an important difference, because they treat voters’ preferences in different way. First Past the Post occupies one extreme, attaching value to first preferences only. Approval Voting occupies the other stream, giving equal weight to all of the preferences that the vote expresses. Borda Count systems occupy a variety of intermediate positions, depending on the degree of extra weight that they place on higher preferences. Alternative Vote and Supplementary Vote systems are intermediate too: they look initially at first preferences, but they also count lower preferences in some circumstances.

There are no general principles that can tell us which of these systems is ‘best’. In Eurovision, we have not single voters with ranked preferences, but countries with vote totals that are summed across jury members and public voters. That’s a very different situation from a public election where each voter casts a separate ballot. Many other factors – such as the number of voters, number of candidates, the nature of the information available from opinion surveys and other sources in advance of the vote, and so on – also matter when considering the optimal system.

But at least we can see that it does make a difference. And so thinking carefully about which system is best for any particular contest is well worth while.

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