Distance-based and ad hoc consensus models in ordinal preference ranking

BackgroundIn survey studies on health-state valuations, ordinal ranking exercises often are used as precursors to other elicitation methods such as the time trade-off (TTO) or standard gamble, but the ranking data have not been used in deriving cardinal valuations. This study reconsiders the role of ordinal ranks in valuing health and introduces a new approach to estimate interval-scaled valuations based on aggregate ranking data.MethodsAnalyses were undertaken on data from a previously published general population survey study in the United Kingdom that included rankings and TTO values for hypothetical states described using the EQ-5D classification system. The EQ-5D includes five domains (mobility, self-care, usual activities, pain/discomfort and anxiety/depression) with three possible levels on each. Rank data were analysed using a random utility model, operationalized through conditional logit regression. In the statistical model, probabilities of observed rankings were related to the latent utilities of different health states, modeled as a linear function of EQ-5D domain scores, as in previously reported EQ-5D valuation functions. Predicted valuations based on the conditional logit model were compared to observed TTO values for the 42 states in the study and to predictions based on a model estimated directly from the TTO values. Models were evaluated using the intraclass correlation coefficient (ICC) between predictions and mean observations, and the root mean squared error of predictions at the individual level.ResultsAgreement between predicted valuations from the rank model and observed TTO values was very high, with an ICC of 0.97, only marginally lower than for predictions based on the model estimated directly from TTO values (ICC = 0.99). Individual-level errors were also comparable in the two models, with root mean squared errors of 0.503 and 0.496 for the rank-based and TTO-based predictions, respectively.ConclusionsModeling health-state valuations based on ordinal ranks can provide results that are similar to those obtained from more widely analyzed valuation techniques such as the TTO. The information content in aggregate ranking data is not currently exploited to full advantage. The possibility of estimating cardinal valuations from ordinal ranks could also simplify future data collection dramatically and facilitate wider empirical study of health-state valuations in diverse settings and population groups.

In this paper, we study a maximum likelihood estimation (MLE) approach to voting when the set of alternatives has a multi-issue structure, and the voters' preferences are represented by CP-nets.We first consider general multi-issue domains, and study whether and how issue-by-issue voting rules and sequential voting rules can be represented by MLEs. We first show that issue-by-issue voting rules in which each local rule is itself an MLE (resp. a candidate scoring rule) can be represented by MLEs with a weak (resp. strong) decomposability property. Then, we prove two theorems that state that if the noise model satisfies a very weak decomposability property, then no sequential voting rule that satisfies unanimity can be represented by an MLE, unless the number of voters is bounded.We then consider multi-issue domains in which each issue is binary; for these, we propose a general family of distance-based noise models, of which give an axiomatic characterization. We then propose a more specific family of natural distance-based noise models that are parameterized by a threshold. We identify the complexity of winner determination for the corresponding MLE voting rule in the two most important subcases of this framework.

This paper considers a model of centralized college admission under the Boston mechanism where students may have uncertainty about their priorities. Students have homogeneous ordinal preferences over colleges, but their preference intensities vary, and the exam scores determine their priorities. In equilibrium, student application strategies take a cutoff form. The strategies depend on their exam scores under post‐score submissions, on preference intensities under pre‐exam submissions, and on both preference intensities and signals about their exam scores under pre‐score submissions. Given these equilibrium strategies, students are better off under pre‐exam and pre‐score submissions than post‐score submissions. When students with the same preference intensities and exam scores receive signals of different qualities, those with bad signals could be hurt by those with good signals.

Distance-based tree models for ranking data

Manipulation in elections with uncertain preferences

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 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 the 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 then compared with 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.

We consider the problem of helping a decision maker (DM) choose from a set of multiattributed objects when her preferences are “concavifiable,” i.e. representable by a concave value function. We establish conditions under which preferences or preference intensities are concavifiable. We also derive a characterization for the family of concave value functions compatible with a set of such preference statements expressed by the DM. This can be used to validate dominance relations over discrete sets of alternatives and forms the basis of an interactive procedure. We report on the practical use of this procedure with several DMs for a flat-choice problem and its computational performance on a set of project-portfolio selection problem instances. The use of preference intensities is found to provide significant improvements to the performance of the procedure.

We show that Approval voting need not trigger sincere behavior in equilibrium of Poisson voting games and hence might lead a strategic voter to skip a candidate preferred to his worst preferred approved candidate. We identify two main rationales for these violations of sincerity. First, if a candidate has no votes, a voter might skip him. Notwithstanding, we provide sufficient conditions on the voters’ preference intensities to remove this sort of insincerity. On the contrary, if the candidate gets a positive share of the votes, a voter might skip him solely on the basis of his ordinal preferences. This second type of insincerity is a consequence of the correlation of the candidates’ scores. The incentives for sincerity of rank scoring rules are also discussed.

In many school choice practices, scores, instead of ordinal rankings, are used to indicate students’ qualification. We study school choice problems where students have ordinal preference over schools while their priorities at schools are in the form of cardinal scores. The cardinality of scores allows us to measure the intensity of priority violations and hence relax stability by proposing epsilon-stability. We also propose the epsilon-EADA mechanism to select the constrained efficient matching under epsilon-stability.

rankdist is a recently developed R package which implements various distance-based ranking models. These models capture the occurring probability of rankings based on the distances between them. The package provides a framework for fitting and evaluating finite mixture of distance-based models. This paper also presents a new probability model for ranking data based on a new notion of weighted Kendall distance. The new model is flexible and more interpretable than the existing models. We show that the new model has an analytic form of the probability mass function and the maximum likelihood estimates of the model parameters can be obtained efficiently even for ranking involving a large number of objects.

Mixtures of weighted distance-based models for ranking data with applications in political studies

PurposeThe mere presence of categories, irrespective of their content, positively influences the satisfaction of choosers who are unfamiliar with the choice domains. In the present research the main goal is to analyze how a complex product category is categorized internally by consumers, with and without price information available, and explore the effect of product involvement and category knowledge on such structures within the wine category.Design/methodology/approachAdditive tree analysis allows us to visualize the perceptual structure of complex sets of alternatives and the multinomial logit model enables us to analyze the influence of these inherent personal characteristics.FindingsThe results show that consumers organize information on red wines and rosés according to a “type→origin” cognitive construct and use “price”, if available, as a third attribute. Consumers comparing red wines and white wines organize the available information according to a “type” construct in which “price”, even if available, plays no role. Subjects with a greater knowledge of the category exhibit more complex structures.Research limitations/implicationsA broader database would be necessary to draw further conclusions with respect to the specific category of wine. Another possible limitation may arise from the chosen set of alternatives. There are more red wines among the stimuli for the survey. As a result of this numerical imbalance between the red wines on the one hand and the rosé/white wines on the other, the red are perceived to be more similar to each other. It would therefore be useful in future research to try to obtain the same number of alternatives for each attribute level. Meanwhile, research on other product categories would be useful to provide further validation of these findings.Practical implicationsThe main implication of the authors' findings for retailers is that an understanding of the internal categorization structures underlying consumers' product similarity judgments will enable them to organize their shelf space layout to match the way it is processed by consumers. Furthermore, the findings suggest that high‐knowledge consumers may be selectively targeted by using store layouts arranged on the basis of complex structures, while low‐knowledge consumers may be selectively targeted using store layouts organized on the basis of simple structures.Originality/valueThe main contribution of this paper to the existing literature on perceptual organization is an analysis of the influence of price on respondents' internal categorization structures, when price is considered a key variable in the formation of consumers' impressions of a product. Furthermore, in the novel context of the wine category, the authors describe the moderating effect of two variables, involvement and knowledge, on the results of previous literature on perceptual organization. These two variables have potential as segmentation criteria to enable category managers to tailor their products to target markets. Secondly, though no less importantly, the authors accompany the qualitative additive tree methodology used to derive the perceived structures with an analysis of variance to achieve a more objective interpretation of the additive trees.

The Every Child Achieves Act of 2015 has drawn greater attention to the academic achievement of students considered at risk who attend alternative schools. Due to problems both inside and outside of schools, students in alternative education settings may struggle with academic content and require a different educational approach. This comprehensive literature review critically examined experimental intervention studies that were conducted in alternative schools published between 1990 and 2013. Eighteen studies met the inclusion criteria. Academic intervention studies conducted in alternative educational settings, limitations, practical implications, and future directions are discussed.

Purpose – The purpose of this paper is to investigate the impact of different mathematical formulations of the problem of optimal design of electrical machines on the results obtained using a local optimization solver. The aim is to investigate the efficiency and reliability of standard local solvers when handling different mathematical formulations. This could provide guidelines for designers in practical engineering applications.

Political Utopias: Contemporary Debates