In analyzing heterogeneous rank data, one of the classic issues is how to aggregate individual judgments in one single ordering that offers the best synthesis of the preferences expressed by the judges.  Nowadays dealing with preference rankings means not only dealing with judges intended as human beings, being the concept of “judge” changed over the time (i.e., rating agencies, Universities evaluation agencies, electronical instruments, etc.). The consequence is that the number of items to be ranked sometimes has become really large (the European universities, the restaurants in a city, the series transmitted by a streaming network, etc). 
The first speaker, Maurizio Romano, will present a heuristic algorithm devoted to find the consensus ranking when the number of items is large, searching the solution in the complete universe of rankings including all the possible ties.  

A second issue in the analysis of rankings is how to represent the differences among the rankings, hence among judges, in a concise way. Mixtures of Mallows models are a set of tools to highlight different preference structures considering a pool of judges. 
The second speaker,Cristina Mollica, will present a mixture of Mallows-Theta model, namely the Mallows model with the Spearman distance, that allows the inclusion of subject-specific covariates. 

 Another issue is the analysis of rank data considering partial orders and also a temporal dimension. The third speaker, Kate Lee, will present a Bayesian inference schema for partial orders representing social hierarchies, which nowadays present real order structures. The class of model is extended to handle several preference generation schemes (Mallows, Plackett-Luce), to consider time series data, and to take into account exogenous information.    

The discussant, Valeria Vitelli, will lead a critical discussion of the papers presented, highlighting the commonalities that the three approaches, at first glance totally different, may have, pointing the way to a possible new line of research.

 Summarizing, this session covers several major aspects of the analysis of rank data. Even though the talks use different methodological frameworks and models, their contents are strongly interconnected.