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Activity Number: 192 - Using Ranking Data for Decision-Making
Type: Topic Contributed
Date/Time: Monday, August 8, 2022 : 2:00 PM to 3:50 PM
Sponsor: Social Statistics Section
Abstract #322720
Title: Ratings as Comparisons with Mileposts -- a Mallows Model
Author(s): Annelise Wagner* and Marina Meila
Companies: University of Washington and University of Washington
Keywords: ranked data; preferences; Mallows Model; Maximum Likelihood
Abstract:

We present the Landmark-GMM (L-GMM), a statistical model for preference data expressed either as rankings or ratings. These two modalities of eliciting preferences carry complementary information, and the L-GMM is designed to seamlessly and naturally integrate this information.

L-GMM also inherits the computational elegance, interpretability and flexibility that characterize the GMM family and models based on counting inversions. In particular, when complete rankings + ratings are available, the L-GMM is an exponential family model with a permutation as "location parameter"; the normalization constant can be computed in closed form; sufficient statistics are available. When only the rating information is complete, the L-GMM can be used to estimate a consensus rating AND ranking, with minor algorithmic changes w.r.t. the complete data


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