We assume linear stochastic transitivity and address the problem of estimating the underlying probability matrix, the merit of the objects being compared and the underlying function from a paired comparison experiment. Our formulation yields a semidefinite programming problem that we use as a refinement step for a given estimator of the paired comparison probability matrix. We provide a detailed sensitivity analysis and as a result we extract statistical properties of the resulting estimator. By building on previous results and our sensitivity analysis we also provide bounds on the expected squared error of the estimated probability matrix within the round-robin setting and a paired comparison experiment with random encounters. Our novel contribution recovers not only the merits of the players within the game (which is the classical paired comparison setting) but also the underlying structure of the game described by the paired comparison function. Our methodology is illustrated with numerical experiments.
|Number of pages||6|
|State||Published - 2016|
|Event||2016 EURO Mini Conference: From Multicriteria Decision Aid to Preference Learning, DA2PL 2016 - Paderborn, Germany|
Duration: 7 Nov 2016 → 8 Nov 2016
|Conference||2016 EURO Mini Conference: From Multicriteria Decision Aid to Preference Learning, DA2PL 2016|
|Period||7/11/16 → 8/11/16|
Bibliographical noteFunding Information:
Future Research We can mention other questions that remain to be investigated in the field of linear stochastic transitivity relations. To begin with, little is known about the consequences of misspec-ification of function F in linear ranking models. Also we may inquire how to generalize the results in linear ranking models with unknown function F to incorporate multiplayer paired comparisons games with possibility of non-binary outcomes. At last our experiments indicate that the choice of the weights highly influence on the quality of the estimators derived in this article; we believe that this deserves further investigation and that this might reveal optimal procedures in the investigation of linear stochastic transitivity rankings. 7 Acknowledgments The research leading to these results has received funding from the European Research Council under European Union’s Horizon 2020 Program, ERC Grant agreement no. 682203 “SpeedInfTradeoff” and the research of Ori Davidov was partially supported by the Israeli Science Foundation Grant No. 1256/13. REFERENCES
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ASJC Scopus subject areas
- Decision Sciences (miscellaneous)