Issue: 2025/Vol.35/No.4, Pages
GENERIC NETWORKS OF VOTINGS
Ewa Zawiślak-Sprysak
, Paweł Zawiślak 
This is not yet the definitive version of the paper. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article.
Cite as: E. Zawiślak-Sprysak, P. Zawiślak. Generic networks of votings. Operations Research and Decisions 2025: 35(4). DOI 10.37190/ord/207393
Abstract
In this paper we propose the method for analysing the voting results of 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 \emph{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 to observe such 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 \emph{generic networks of votes}. These generic networks are randomly chosen according to precisely given probability measure on the space of all possible votings of a single juror (i.e. the space of permutations of contestants set). We use these methods to confirm the hypothesis that jurors of 2016 International Henryk Wieniawski Violin Competition were far away from being consistent.
Keywords: generic network, Lehmer norm, Borda count
Received: 5 March 2025 Accepted: 21 June 2025
Published online: 21 June 2025