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Title: Bayesian rank aggregation for (mixtures of) Plackett-Luce models Authors:  Stephen Johnson - Newcastle University (United Kingdom) [presenting]
Abstract: Ranked data are central to many applications in science and social science and arise when rankers (individuals) use some criterion to order a set of entities. Rank aggregation aims to produce a single overall ranking that is representative of a collection of rankers. One approach is to consider models that rely on strong assumptions of homogeneity. However, in general, this assumption is not likely to be plausible. We suggest that the data should instead be modelled in a manner as flexible as possible; with the intention of obtaining good model fit. Then, once an adequate model has been obtained, the aggregate ranking should be that with the largest predictive probability, that is, the mode of the posterior predictive distribution. Unfortunately, the dimension of the predictive distribution grows factorially with the number of entities, so it is often unobtainable. We consider methods for performing posterior predictive checks and also for obtaining the aggregate ranking under (mixtures of) Plackett-Luce models; with approximations becoming necessary when the number of entities is large. The methodology is illustrated through simulation studies and we provide insight as to when approximations are likely to perform well.