The Analysis of Permutations

Plackett, R. L.

doi:10.2307/2346567

Cited by 486 publications

(348 citation statements)

References 8 publications

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“…An important special case of the above model is obtained assuming idiosyncratic components are i.i.d according to an extreme value distribution such as Gumbel. This model also referred to as the Plackett-Luce model and was proposed independently by Luce [2] and Plackett [4] and later McFadden [3] referred to it as a Multinomial logit model. The MNL model is by far the most popular model as both the estimation as well as the optimization problems are tractable for this model (see [6]).…”

Section: Introductionmentioning

confidence: 99%

A Markov Chain Approximation to Choice Modeling

Blanchet

Gallego

Goyal

2016

Operations Research

243

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Assortment planning is an important problem that arises in many industries such as retailing and airlines. One of the key challenges in an assortment planning problem is to identify the “right” model for the substitution behavior of customers from the data. Error in model selection can lead to highly suboptimal decisions. In this paper, we consider a Markov chain based choice model and show that it provides a simultaneous approximation for all random utility based discrete choice models including the multinomial logit (MNL), the probit, the nested logit and mixtures of multinomial logit models. In the Markov chain model, substitution from one product to another is modeled as a state transition in the Markov chain. We show that the choice probabilities computed by the Markov chain based model are a good approximation to the true choice probabilities for any random utility based choice model under mild conditions. Moreover, they are exact if the underlying model is a generalized attraction model (GAM) of which the MNL model is a special case. We also show that the assortment optimization problem for our choice model can be solved efficiently in polynomial time. In addition to the theoretical bounds, we also conduct numerical experiments and observe that the average maximum relative error of the choice probabilities of our model with respect to the true probabilities for any offer set is less than 3% where the average is taken over different offer sets. Therefore, our model provides a tractable approach to choice modeling and assortment optimization that is robust to model selection errors. Moreover, the state transition primitive for substitution provides interesting insights to model the substitution behavior in many real-world applications.

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Section: Introductionmentioning

confidence: 99%

A Markov Chain Approximation to Choice Modeling

Blanchet

Gallego

Goyal

2016

Operations Research

243

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“…which is called the Plackett-Luce model (Luce, 1959;Plackett, 1975). Let r i for i = 1, · · · , n be independent observations of ranking vectors, which are obtained from the ith searching in the IR system.…”

Section: Probability Modelmentioning

confidence: 99%

Revisiting the Bradley-Terry model and its application to information retrieval

Jeon¹,

Kim²

2013

Journal of the Korean Data and Information Science Society

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The Bradley-Terry model is widely used for analysis of pairwise preference data. We explain that the popularity of Bradley-Terry model is gained due to not only easy computation but also some nice asymptotic properties when the model is misspecified. For information retrieval required to analyze big ranking data, we propose to use a pseudo likelihood based on the Bradley-Terry model even when the true model is different from the Bradley-Terry model. We justify using the Bradley-Terry model by proving that the estimated ranking based on the proposed pseudo likelihood is consistent when the true model belongs to the class of Thurstone models, which is much bigger than the Bradley-Terry model.

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“…Stern (1993), Murphy and Martin (2003) and Busse et al (2007) use mixtures of distance-based models to characterize voting blocs in the American Psychological Association presidential election of 1980. Gormley and Murphy (2008a) use a mixture of Plackett-Luce (Plackett 1975) and Benter (Benter 1994) models to characterize voting blocs in the electorate for Irish governmental and Irish presidential elections. Spirling and Quinn (2010) use a Dirichlet process mixture model to study voting blocs in the U.K. House of Commons.…”

Section: Voting Blocsmentioning

confidence: 99%

“…, N = 1083) the probability density p(·) in the mixture of experts model (1.1) must have an appropriate form. The Plackett-Luce model (Plackett 1975) (or exploded logit model) for rank data provides a suitable model; Benter's model (Benter 1994) Under the Plackett-Luce model, given that voter i is a member of voting bloc g and given the 'support parameter' p g = (p g1 , . .…”

Section: A Mixture Of Experts Model For Ranked Preference Datamentioning

confidence: 99%