The Annals of Applied Statistics

Latent space modelling of multidimensional networks with application to the exchange of votes in Eurovision song contest

Silvia D’Angelo, Thomas Brendan Murphy, and Marco Alfò

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

The Eurovision Song Contest is a popular TV singing competition held annually among country members of the European Broadcasting Union. In this competition, each member can be both contestant and jury, as it can participate with a song and/or vote for other countries’ tunes. During the years, the voting system has repeatedly been accused of being biased by tactical voting; votes would represent strategic interests rather than actual musical preferences of the voting countries. In this work, we develop a latent space model to investigate the presence of a latent structure underlying the exchange of votes. Focusing on the period from 1998 to 2015, we represent the vote exchange as a multivariate network: each edition is a network, where countries are the nodes and two countries are linked by an edge if one voted for the other. The different networks are taken to be independent replicates of a conditional Bernoulli distribution, with success probability specified as a function of a common latent space capturing the overall relationships among the countries. Proximity denotes similarity, and countries close in the latent space are more likely to exchange votes. If the exchange of votes depends on the similarity between countries, the quality of the competing songs might not be a relevant factor in the determination of the voting preferences, and this would suggest the presence of some bias. A Bayesian hierarchical modelling approach is employed to estimate the parameters, where the probability of a connection between any two countries is a function of their distance in the latent space, network-specific parameters and edge-specific covariates. The estimated latent space is found to be relevant in the determination of edge probabilities, however, the positions of the countries in such space only partially correspond to their actual geographical positions.

Article information

Source
Ann. Appl. Stat., Volume 13, Number 2 (2019), 900-930.

Dates
Received: March 2018
Revised: August 2018
First available in Project Euclid: 17 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1560758432

Digital Object Identifier
doi:10.1214/18-AOAS1221

Mathematical Reviews number (MathSciNet)
MR3963557

Zentralblatt MATH identifier
07094840

Keywords
Eurovision latent space models multidimensional networks

Citation

D’Angelo, Silvia; Murphy, Thomas Brendan; Alfò, Marco. Latent space modelling of multidimensional networks with application to the exchange of votes in Eurovision song contest. Ann. Appl. Stat. 13 (2019), no. 2, 900--930. doi:10.1214/18-AOAS1221. https://projecteuclid.org/euclid.aoas/1560758432


Export citation

References

  • Airoldi, E. M., Blei, D. M., Fienberg, S. E. and Xing, E. P. (2008). Mixed-membership stochastic blockmodels. J. Mach. Learn. Res. 9 1981–2014.
  • Blangiardo, M. and Baio, G. (2014). Evidence of bias in the Eurovision song contest: Modelling the votes using Bayesian hierarchical models. J. Appl. Stat. 41 2312–2322.
  • Butts, C. T. and Carley, K. M. (2005). Some simple algorithms for structural comparison. Computational and Mathematical Organization Theory 11 291–305.
  • Clerides, S. and Stengos, T. (2006). Love thy neighbour, love thy kin: Strategy and bias in the Eurovision song contest. Discussion Paper Series of Centre for Economic Policy Research 5732 1–28.
  • D’Angelo, S., Murphy, T. B. and Alfò, M. (2019). Supplement to “Latent space modelling of multidimensional networks with application to the exchange of votes in Eurovision song contest.” DOI:10.1214/18-AOAS1221SUPP.
  • Dryden, I. L. and Mardia, K. V. (1998). Statistical Shape Analysis. Wiley Series in Probability and Statistics: Probability and Statistics. Wiley, Chichester.
  • Durante, D., Dunson, D. B. and Vogelstein, J. T. (2017). Nonparametric Bayes modeling of populations of networks. J. Amer. Statist. Assoc. 112 1516–1530.
  • Erdős, P. and Rényi, A. (1959). On random graphs. I. Publ. Math. Debrecen 6 290–297.
  • Erdős, P. and Rényi, A. (1960). On the evolution of random graphs. Magy. Tud. Akad. Mat. Kut. Intéz. Közl. 5 17–61.
  • Fenn, D., Sulemana, O., Efstathioub, J. and Johnson, N. F. (2006). How does Europe make its mind up? Connections, cliques, and compatibility between countries in the Eurovision song contest. Phys. A 360 576–598.
  • Fienberg, S. E., Meyer, M. M. and Wasserman, S. S. (1985). Statistical analysis of multiple sociometric relations. J. Amer. Statist. Assoc. 80 51-67.
  • Frank, O. and Strauss, D. (1986). Markov graphs. J. Amer. Statist. Assoc. 81 832–842.
  • Ginsburgh, V. and Noury, A. (2008). The Eurovision song contest. Is voting political or cultural?. European Journal of Political Economy 24 41–52.
  • Goldenberg, A., Zheng, A. X., Fienberg, S. E. and Airoldi, E. M. (2010). A survey of statistical network models. Found. Trends Mach. Learn. 2 129–233.
  • Gollini, I. and Murphy, T. B. (2016). Joint modeling of multiple network views. J. Comput. Graph. Statist. 25 246–265.
  • Greene, D. and Cunningham, P. (2013). Producing a unified graph representation from multiple social network views. Proceedings of the 5th Annual ACM Web Science Conference (Web-Sci’13) 118–121.
  • Handcock, M. S., Raftery, A. E. and Tantrum, J. M. (2007). Model-based clustering for social networks. J. Roy. Statist. Soc. Ser. A 170 301–354.
  • Hoff, P. D. (2005). Bilinear mixed-effects models for dyadic data. J. Amer. Statist. Assoc. 100 286–295.
  • Hoff, P. D. (2011). Hierarchical multilinear models for multiway data. Comput. Statist. Data Anal. 55 530–543.
  • Hoff, P. (2015). Dyadic data analysis with amen.
  • Hoff, P. D., Raftery, A. E. and Handcock, M. S. (2002). Latent space approaches to social network analysis. J. Amer. Statist. Assoc. 97 1090–1098.
  • Holland, P. W. and Leinhardt, S. (1981). An exponential family of probability distributions for directed graphs. J. Amer. Statist. Assoc. 76 33–65.
  • Holland, P. W., Laskey, K. B. and Leinhardt, S. (1983). Stochastic blockmodels: First steps. Soc. Netw. 5 109–137.
  • Krivitsky, P. N., Handcock, M. S., Raftery, A. E. and Hoff, P. D. (2009). Representing degree distributions, clustering, and homophily in social networks with latent cluster random effects models. Soc. Netw. 31 204–213.
  • Lynch, K. (2015). Eurovision recognised by Guinness world records as the longest-running annual TV music competition (international). Available at http://www.guinnessworldrecords.com/news/2015/5/eurovision-recognised-by-guinness-world-records-as-the-longest-running-annual-tv-379520.
  • Mantzaris, A. V., Rein, S. R. and Hopkins, A. D. (2018). Examining collusion and voting biases between countries during the Eurovision song contest since 1957. Journal of Artificial Societies and Social Simulation 21.
  • Murphy, T. B. (2016). Model-based clustering for network data. In Handbook of Cluster Analysis. Chapman & Hall/CRC Handb. Mod. Stat. Methods 337–357. CRC Press, Boca Raton, FL.
  • Robins, G., Pattison, P., Kalish, Y. and Lusher, D. (2007). An introduction to exponential random graph (p∗) models for social network. Soc. Netw. 29 173–191.
  • Rosén, B. (1972). Asymptotic theory for successive sampling with varying probabilities without replacement. I. Ann. Math. Stat. 4 373–397.
  • Saavedraa, S., Efstathioua, J. and Reed-Tsochasb, F. (2007). Identifying the underlying structure and dynamic interactions in a voting network. Phys. A 377 672–688.
  • Salter-Townshend, M. and McCormick, T. H. (2017). Latent space models for multiview network data. Ann. Appl. Stat. 11 1217–1244.
  • Salter-Townshend, M., White, A., Gollini, I. and Murphy, T. B. (2012). Review of statistical network analysis: Models, algorithms, and software. Stat. Anal. Data Min. 5 260–264.
  • Snijders, T. A. B. and Nowicki, K. (1997). Estimation and prediction for stochastic blockmodels for graphs with latent block structure. J. Classification 14 75–100.
  • Spiegelhalter, D. J., Best, N. G., Carlin, B. P. and van der Linde, A. (2002). Bayesian measures of model complexity and fit. J. R. Stat. Soc. Ser. B. Stat. Methodol. 64 583–639.
  • Spierdijk, L. and Vellekoop, M. (2006). Geography, culture, and religion: Explaining the bias in Eurovision song contest voting. Memorandum, Department of Applied Mathematics, University of Twente, Enschede 1794 1–30.
  • Sweet, T. M., Thomas, A. C. and Junker, B. W. (2013). Hierarchical network models for education research: Hierarchical latent space models. Journal of Educational and Behavioural Statistics 38 295–318.
  • Yair, G. (1995). “Unite unite Europe” the political and cultural structures of Europe as reflected in the Eurovision song contest. Soc. Netw. 17 147–161.

Supplemental materials

  • Supplement to “Latent space modelling of multidimensional networks with application to the exchange of votes in Eurovision song contest”. The Supplementary Material (D’Angelo, Murphy and Alfò (2019)) provide with the derivation of the full conditional and proposal distributions used to estimate the model, a table with the ISO3 codes for the countries participating in the Eurovision Song Contest in the period 1998–2015, the results of the analysis for the subperiods 1998–2007 and 2008–2015, the results of the different simulation scenarios and a pseudo-code of the algorithm used for parameter estimation.