Permutation Models for Collaborative Ranking

We study the problem of collaborative filtering where ranking information is available. Focusing on the core of the collaborative ranking process, the user and their community, we propose new models for representation of the underlying permutations and prediction of ranks. The first approach is based on the assumption that the user makes successive choice of items in a stage-wise manner. In particular, we extend the Plackett-Luce model in two ways - introducing parameter factoring to account for user-specific contribution, and modelling the latent community in a generative setting. The second approach relies on log-linear parameterisation, which relaxes the discrete-choice assumption, but makes learning and inference much more involved. We propose MCMC-based learning and inference methods and derive linear-time prediction algorithms

LOGIT MODELS FOR POOLED CONTINGENT VALUATION AND CONTINGENT RATING AND RANKING DATA: VALUING BENEFITS FROM FOREST BIODIVERSITY CONSERVATION

Contingent valuation and contingent rating and ranking methods for measuring willingness-to-pay for non-market goods are compared by using random coefficient models and data pooling methods. Pooled models on CV data and CR data on the preferred choice accept pooling if scale differences between the model estimates of CV and CR methods are allowed for. More detailed response models, such as pooled CV model and rank-ordered models for two or three ranks, reject pooling of the data.Resource /Energy Economics and Policy,

Epitope profiling via mixture modeling of ranked data

We propose the use of probability models for ranked data as a useful alternative to a quantitative data analysis to investigate the outcome of bioassay experiments, when the preliminary choice of an appropriate normalization method for the raw numerical responses is difficult or subject to criticism. We review standard distance-based and multistage ranking models and in this last context we propose an original generalization of the Plackett-Luce model to account for the order of the ranking elicitation process. The usefulness of the novel model is illustrated with its maximum likelihood estimation for a real data set. Specifically, we address the heterogeneous nature of experimental units via model-based clustering and detail the necessary steps for a successful likelihood maximization through a hybrid version of the Expectation-Maximization algorithm. The performance of the mixture model using the new distribution as mixture components is compared with those relative to alternative mixture models for random rankings. A discussion on the interpretation of the identified clusters and a comparison with more standard quantitative approaches are finally provided.Comment: (revised to properly include references

Optimal choice of electoral preference data

Electoral researchers are so much accustomed to analyzing the choice of the single most preferred party as the left-hand side variable of their models of electoral behavior that they often ignore revealed preference data. Drawing on random utility theory, their models predict electoral behavior at the extensive margin of choice. Since the seminal work of Luce and others on individual choice behavior, however, many social science disciplines (consumer research, labor market research, travel demand, etc.) have extended their inventory of observed preference data with, for instance, multiple paired comparisons, complete or incomplete rankings, and multiple ratings. Eliciting (voter) preferences using these procedures and applying appropriate choice models is known to considerably increase the efficiency of estimates of causal factors in models of (electoral) behavior. In this paper, we demonstrate the efficiency gain when adding additional preference information to first preferences, up to full ranking data. We do so for multi-party systems of different sizes. We use simulation studies as well as empirical data from the 1972 German election study. Comparing the practical considerations for using ranking and single preference data results in suggestions for choice of measurement instruments in different multi-candidate and multi-party settings

MULTI CRITERIA DECISION MAKING MODELS: AN OVERVIEW ON ELECTRE METHODS

In portfolio analysis, there are a few models that can be used. Therefore, the aim of this paper is to make an overview on multi criteria decision making models, in particular, on ELECTRE methods. We discuss the different versions of ELECTRE, which exist and why they exist. So, when speaking about ELECTRE methods structure, we have to consider two main procedures: construction of one or several outranking relation(s) procedure, and exploitation procedure. In the exploitation procedure, recommendations are elaborated from the results obtained in the first phase. The nature of the recommendation depends on the problematic: choosing, ranking or sorting. Each method is characterized by its construction and exploitation procedure. For choice problem, we can apply ELECTRE I, ELECTRE Iv, and ELECTRE IS; for ranking problem, we can apply ELECTRE II, ELECTRE III, ELECTRE IV and ELECTRE-SS; and for sorting problem we can apply ELECTRE TRI. Finally, some failings on ELECTRE methods assumptions are discussed, for instance, rank reversals. So, when analyzing portfolio management decision problem, the literature suggests AHP method and PROMETHEE family.CAPM; decision problem; multi criteria decision making models; ELECTRE family; ELECTRE rank reversals

Independence of alternatives in ranking models

When Luce (1959) introduced his Choice Axiom, this raised immediate criticism by Debreu (1960), pointing out inconsistencies when items are ranked from inferior to superior (instead of ranking them from superior to inferior). As recently shown by Breitmoser (2019), Luce’s Independence of Irrelevant Alternatives (IIA) is equivalent to Luce’s Choice Axiom when positivity holds. This fact seems to have escaped attention so far and might suggest that Debreu’s critique also applies to the notion of IIA, which is widely used in the literature. Furthermore, this notion could potentially be intuitively misleading, as the consequences of this axiom seem to be different than the name suggests. This might spill over to the intuitive interpretation of theoretical results that build on this axiom. This paper motivates the introduction of the notion of Independece of Alternatives (IoA) in the context of ranking models. IoA postulates a property of independence which seems intuitively reasonable (as it exactly captures what Luce himself describes when speaking about IIA), but does not exclusively hold in models where Luce’s Choice Axiom applies. Assuming IoA, expected ranks in the ranking of multiple alternatives can be determined from pairwise comparisons. The result holds in many models which do not satisfy IIA (e.g. certain Thurstone V models, Thurstone (1927)), can significantly simplify the calculation of expected ranks in practice and potentially facilitate analytic methods that build on more general approaches to model the ranking of multiple alternatives

Divergent mathematical treatments in utility theory

In this paper I study how divergent mathematical treatments affect mathematical modelling, with a special focus on utility theory. In particular I examine recent work on the ranking of information states and the discounting of future utilities, in order to show how, by replacing the standard analytical treatment of the models involved with one based on the framework of Nonstandard Analysis, diametrically opposite results are obtained. In both cases, the choice between the standard and nonstandard treatment amounts to a selection of set-theoretical parameters that cannot be made on purely empirical grounds. The analysis of this phenomenon gives rise to a simple logical account of the relativity of impossibility theorems in economic theory, which concludes the paper