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Aggregation Theorems and the Combination of Probabilistic Rank Orders

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Probability Models and Statistical Analyses for Ranking Data

Part of the book series: Lecture Notes in Statistics ((LNS,volume 80))

Abstract

There are many situations where we wish to combine multiple rank orders or other preference information on a fixed set of options to obtain a combined rank order. Two of the most common applications are determining a social rank order on a set of options from a set of individual rank orders on those options, and predicting (or prescribing) an individual’s overall rank order on a set of options from the rank orders on a set of component dimensions of the options. In this paper, I develop solutions to this class of problems when the rank orders can occur probabilistically. I develop aggregation theorems that are motivated by recent theoretical work on the combination of expert opinions and I discuss various models that have the property that the representations are ‘of the same form’ for both the component and overall rank order probabilities. I also briefly discuss difficulties in actually using such probabilistic ranking models in the social choice situation.

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Author information

Authors and Affiliations

  1. Department of Psychology, McGill University, 1205 Docteur Penfield Avenue, Montreal, Quebec, Canada, H3A 1B1

    A. A. J. Marley

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  1. A. A. J. Marley
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Editor information

Editors and Affiliations

  1. Department of Statistics, The Ohio State University, Columbus, OH, 43210, USA

    Michael A. Fligner  & Joseph S. Verducci  & 

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© 1993 Springer-Verlag New York, Inc.

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Marley, A.A.J. (1993). Aggregation Theorems and the Combination of Probabilistic Rank Orders. In: Fligner, M.A., Verducci, J.S. (eds) Probability Models and Statistical Analyses for Ranking Data. Lecture Notes in Statistics, vol 80. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2738-0_12

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  • DOI: https://doi.org/10.1007/978-1-4612-2738-0_12

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-97920-5

  • Online ISBN: 978-1-4612-2738-0

  • eBook Packages: Springer Book Archive

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