Every year, the Eurovision Song Contest brings with it fresh accusations that the results are affected more by politics than music. But how much of the outcome is in fact determined by mathematics?

## You're reading: Posts Tagged: Arrow’s impossibility theorem

### Electoral reforms and non-transitive dice

*Guest post by Andrew, of Manchester MathsJam. Andrew can be found on Twitter as @andrew_taylor and blogs occasionally about maths, among other things, at andrewt.net.*

“Grime Dice” are a set of five coloured dice with unusual combinations of numbers on them. The red die, for example, has five fours and a nine. The blue one has three twos and three sevens, so it loses to the red die about 58% of the time. The green die has five fives and a zero, and will lose to the blue one in 58% of rolls. What makes them interesting is that the green die will beat the red one in 69% of rolls. These three dice behave rather like rock-paper-scissors — in mathematical terms, they are ‘non-transitive’. The full set of Grime Dice also has a purple and a yellow die, so a better analogy would be rock-paper-scissors-lizard-Spock.