Generic Networks of Votes

In this paper, we propose a method for analysing the voting results of a given kind of competition. Suppose that a competition is given, with the Borda Count used as a voting method. For every such competition, there is a weighted network (called a voting network) associated in a natural way. Namely, the nodes set corresponds to jurors, and link weights correspond to correlation coefficients of voting results of adequate jurors. However, all main correlation coefficients, as well as related metrics considered as distance on rankings, do not distinguish between changes in high places in the competition and changes in low places. We propose a new distance on rankings that allows us to observe such a distinction. We analyse the results of 2016 International Henryk Wieniawski Violin Competition by comparing the properties of its voting network to the statistical properties of generic networks of votes. These generic networks are randomly chosen according to a precisely given probability measure on the space of all possible votings of a single juror (i.e., the space of permutations of the contestant set). We use these methods to confirm the hypothesis that jurors of the 2016 International Henryk Wieniawski Violin Competition were far from being consistent.