Incomplete paired comparisons in case of multiple choice and general log-concave probability density functions

A scoring method based on paired comparison allowing multiple choice is investigated. We allow general log-concave probability density functions for the random variables describing the difference of the objects. This case involves Bradley–Terry models and Thurstone models as well. A sufficient condi...

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Bibliographic Details
Published in:Central European journal of operations research 2019-06, Vol.27 (2), p.515-532
Main Authors: Orbán-Mihálykó, Éva, Mihálykó, Csaba, Koltay, László
Format: Article
Language:English
Subjects:
Analysis
Business and Management
Decision-making
Distribution (Probability theory)
Economic models
Estimation theory
Mathematical models
Maximum likelihood estimates (Statistics)
Maximum likelihood estimation
Methods
Operations research
Operations Research/Decision Theory
Original Paper
Parameter estimation
Probability density functions
Random variables
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Summary:A scoring method based on paired comparison allowing multiple choice is investigated. We allow general log-concave probability density functions for the random variables describing the difference of the objects. This case involves Bradley–Terry models and Thurstone models as well. A sufficient condition is proved for the existence and uniqueness of the maximum likelihood estimation of the parameters in case of incomplete comparisons. The axiomatic properties of the method are also investigated.
ISSN:1435-246X
1613-9178
DOI:10.1007/s10100-018-0568-1