Pairs Of Alternatives Research Articles

Selection of a representative set of parameters for robust ordinal regression outranking methods

We introduce the concept of a representative set of parameters for multiple criteria outranking methods: ELECTREGKMS and PROMETHEEGKS which apply the principle of robust ordinal regression. We exploit the necessary and the possible results provided by these methods to choose a single instance of the preference model, which would represent all other compatible instances. The representative set of parameters is selected within an interactive preference-driven procedure which allows combining some pre-defined targets into different scenarios. Each target concerns enhancement of the results of robust ordinal regression. Precisely, the DM may emphasize either the advantage of some alternatives over the others, acknowledged by all compatible outranking models, or ambiguity in the comparison for some other pairs of alternatives. Selecting the representative set of parameters, we satisfy the desire of some DMs of assigning precise values to variables of the model. We also enable exploitation of the outranking relation for these parameters in order to arrive at a representative recommendation in a traditional way.

Printed Identification Key or Web-Based Identification Guide: An Effective Tool for Species Identification?

Species identification is often done with the aid of traditional dichotomous keys. This printed material is based on one’s decision between two alternatives, which is followed by another pair of alternatives until the final species name is reached. With the advent of internet technology, the use of an online database offers an updatable and accumulative approach to species identification. It can also be accessed anytime, and this is very useful for fast-changing groups of organisms. In this paper, we report the preference of sophomore Bachelor of Science (B.Sc.) in Microbiology students to two identification guides as a tool in taxonomy. We wish to test our hypothesis that today’s students will prefer to use web-based ID guides over printed dichotomous keys. We also describe how these printed dichotomous key and web-based ID guides were used by the students as one of their laboratory activities in the course Biology of Algae and Fungi.

Automated decision making based on weak orderings

Ranking of help functions with respect to their usefulness is in the main focus of this work. A help function is regarded as useful to a student if the student has succeeded to solve a problem after using it. Methods from the theory of partial orderings are further applied facilitating an automated process of suggesting individualised advises on how to proceed in order to solve a particular problem. The decision making process is based on the common assumption that if given a choice between two alternatives, a person will choose one. Thus, obtained partial orderings appeared to be all linear orders since each pair of alternatives is compared. In this paper, we propose ranking help functions in an intelligent tutoring system with respect to their usefulness.

Random aggregation without the Pareto principle

Barbera-Sonnenschein (J Econ Theory 18:244–254, 1978) have shown that any binary and Paretian random social choice function can be associated with a mapping which associates a real number with each coalition of individuals. This function gives, for each coalition, the power that this group has in imposing on society, their common preference relation on a pair of alternatives. The aim of this paper is to extend this result, showing that the Pareto criterion is not a necessary condition for the existence of such a coalitional power function.

A quantitative Arrow theorem

Arrow’s Impossibility theorem states that any constitution which satisfies independence of irrelevant alternatives (IIA) and unanimity and is not a dictator has to be non-transitive. In this paper we study quantitative versions of Arrow theorem. Consider n voters who vote independently at random, each following the uniform distribution over the six rankings of three alternatives. Arrow’s theorem implies that any constitution which satisfies IIA and unanimity and is not a dictator has a probability of at least 6−n for a non-transitive outcome. When n is large, 6−n is a very small probability, and the question arises if for large number of voters it is possible to avoid paradoxes with probability close to 1. Here we give a negative answer to this question by proving that for every $${\epsilon > 0}$$ , there exists a $${\delta = \delta(\epsilon) > 0}$$ , which depends on $${\epsilon}$$ only, such that for all n, and all constitutions on three alternatives, if the constitution satisfies: Then the probability of a non-transitive outcome is at least δ. Our results generalize to any number k ≥ 3 of alternatives and to other distributions over the alternatives. We further derive a quantitative characterization of all social choice functions satisfying the IIA condition whose outcome is transitive with probability at least 1 − δ. Our results provide a quantitative statement of Arrow theorem and its generalizations and strengthen results of Kalai and Keller who proved quantitative Arrow theorems for k = 3 and for balanced constitutions only, i.e., for constitutions which satisfy for every pair of alternatives a, b, that the probability that the constitution ranks a above b is exactly 1/2. The main novel technical ingredient of our proof is the use of inverse-hypercontractivity to show that if the outcome is transitive with high probability then there are no two different voters who are pivotal with for two different pairwise preferences with non-negligible probability. Another important ingredient of the proof is the application of non-linear invariance to lower bound the probability of a paradox for constitutions where all voters have small probability for being pivotal.

ELECTRE GKMS: Robust ordinal regression for outranking methods

We present a new method, called ELECTRE GKMS, which employs robust ordinal regression to construct a set of outranking models compatible with preference information. The preference information supplied by the decision maker (DM) is composed of pairwise comparisons stating the truth or falsity of the outranking relation for some real or fictitious reference alternatives. Moreover, the DM specifies some ranges of variation of comparison thresholds on considered pseudo-criteria. Using robust ordinal regression, the method builds a set of values of concordance indices, concordance thresholds, indifference, preference, and veto thresholds, for which all specified pairwise comparisons can be restored. Such sets are called compatible outranking models. Using these models, two outranking relations are defined, necessary and possible. Whether for an ordered pair of alternatives there is necessary or possible outranking depends on the truth of outranking relation for all or at least one compatible model, respectively. Distinguishing the most certain recommendation worked out by the necessary outranking, and a possible recommendation worked out by the possible outranking, ELECTRE GKMS answers questions of robustness concern. The method is intended to be used interactively with incremental specification of pairwise comparisons, possibly with decreasing confidence levels. In this way, the necessary and possible outranking relations can be, respectively, enriched or impoverished with the growth of the number of pairwise comparisons. Furthermore, the method is able to identify troublesome pieces of preference information which are responsible for incompatibility. The necessary and possible outranking relations are to be exploited as usual outranking relations to work out recommendation in choice or ranking problems. The introduced approach is illustrated by a didactic example showing how ELECTRE GKMS can support real-world decision problems.

A generalization of Campbell and Kelly’s trade-off theorem

This article considers social choice theory without the Pareto principle. We revisit the trade-off theorem developed by Campbell and Kelly (Econometrica 61:1355–1365, 1993) and generalize their result. By introducing an alternative measure of decisive structure, a dominance relation, we show that if a social welfare function dominates another social welfare function, then the number of pairs of alternatives which social ranking is independently of individual preferences under the former is not more than that under the latter. Moreover, we offer two applications of our main result.

Assessing restorative components of small urban parks using conjoint methodology

Many studies have supported the proposition that natural environments contribute positively to psychological restoration. Less attention has been given to the relative importance of the physical environmental components that contribute to the restorative potential of such environments. The aim of the current study was to investigate the relative importance of environmental components, in small urban parks, for people looking for somewhere to sit down and rest. To address this aim, we used choice-based conjoint analysis, coupled with hierarchical Bayes estimation, to assess the utilities assigned to grass, bushes, trees, flower beds, water features, and the number of other people in the park. Via a web-based questionnaire, adult residents of Oslo, Norway ( N = 154) were presented with text describing successive pairs of park alternatives. Each alternative was comprised of a set of environmental components at different levels. The respondents were to choose the preferred alternative in each pair, given that they were fatigued and looking for a place to rest for a little while. The amounts of grass, trees and other people had the most influence on their choices among park alternatives. Responses across groups defined by age, gender and earlier experience with parks and nature were relatively homogenous. From a planning perspective, the findings indicate the importance of focusing on structural components such as grass and trees rather than decorative components such as flowers and water features.

Methods for comparison of alternatives described by interval estimations

An approach to comparing pairs of alternatives described by different modifications of interval estimations is proposed. Both mono and generalised interval estimations are considered. An expert, using methods of comparing based on the approach, may take into account different degrees of uncertainty in compared pairs of estimations: interval uncertainty, interval-probability one and also point estimations. Simple but fairly accurate empirical method of ‘direct’ comparing pairs of mono-intervals is discussed first. Then it gets a proper mathematical foundation. The connection between the method of comparing mono-intervals and Hurwitz principle is discussed. Results received for mono case are adapted to the generalised case.

One-dimensionality and stability in legislative voting

The widespread use in legislative studies of the one-dimensional model and its median-stability consequence raises a question: Do stability and one-dimensionality rest on evidence drawn from observed votes? They do not and cannot. I prove that every possible legislative history is compatible with a transitive majority preference (hence stability), and except in very special circumstances with a cyclic majority preference (hence instability) as well: observed votes can never refute and almost never confirm stability. One-dimensionality fares worse: any legislative history is compatible with the one-dimensional model if it includes no two votes with overlapping pairs of alternatives, but otherwise, I show, it is almost certainly incompatible with the model, even in those rare cases that ensure transitivity. Voting evidence aside, the one-dimensional model is unduly restrictive, and arguments in its defense do not survive scrutiny.

Rational Agents are the Quickest

Suppose an agent chooses by proceeding through a sequence of criteria: for any pair of alternatives the first criterion that ranks the pair determines the agent's choice. Given any constraint on the capacity of the criteria to discriminate, choices that maximize complete and transitive preferences are always the outcome of a 'quick' sequence that uses the minimum number of criteria. For any irrational preference on the other hand there is always a discrimination constraint such that the preference is not the outcome of a quick sequence. When an agent uses attributes to form criteria and each attribute is rationally ordered, a quick sequence that leads to rational preferences necessarily arises.

Accommodating spatial correlation across choice alternatives in discrete choice models: an application to modeling residential location choice behavior

This paper presents a modeling methodology capable of accounting for spatial correlation across choice alternatives in discrete choice modeling applications. Many location choice ( e.g., residential location, workplace location, destination location) modeling contexts involve choice sets where alternatives are spatially correlated with one another due to unobserved factors. In the presence of such spatial correlation, traditional discrete choice modeling methods that are often based on the assumption of independence among choice alternatives are not appropriate. In this paper, a Generalized Spatially Correlated Logit (GSCL) model that allows one to represent the degree of spatial correlation as a function of a multi-dimensional vector of attributes characterizing each pair of location choice alternatives is formulated and presented. The formulation of the GSCL model allows one to accommodate alternative correlation mechanisms rather than pre-imposing restrictive correlation assumptions on the location choice alternatives. The model is applied to the analysis of residential location choice behavior using a sample of households drawn from the 2000 San Francisco Bay Area Travel Survey (BATS) data set. Model estimation results obtained from the GSCL are compared against those obtained using the standard multinomial logit (MNL) model and the spatially correlated logit (SCL) model where only correlations across neighboring (or adjacent) alternatives are accommodated. Model findings suggest that there is significant spatial correlation across alternatives that do not share a common boundary, and that the GSCL offers the ability to more accurately capture spatial location choice behavior.

Patients' Benefit-Risk Preferences for Chronic Idiopathic Thrombocytopenic Purpura Therapies

Idiopathic thrombocytopenic purpura (ITP) primarily is a disorder of adults characterized by autoantibody-induced platelet destruction and reduced platelet production, leading to a low peripheral blood platelet count. The long-term management of many patients with chronic ITP is unsatisfactory, largely due to the variable efficacy and risks of severe adverse effects associated with current treatment options. To estimate patients' benefit-risk preferences for treatments for ITP. Patients' adverse event risk tolerance and the levels of benefit required to offset possible risks were evaluated using choice-format conjoint analysis. Subjects chose between pairs of hypothetical treatment alternatives defined by probability of achieving safe platelet levels, need for corticosteroids, mode of administration, risk of rebound, risk of elevated liver enzyme levels, and risk of thromboembolism. In this study, we demonstrate that patients have clear and measurable benefit-risk preferences that physicians should consider when discussing treatment options with their patients. Patients were willing to accept significant risks of adverse events in return for an increase in the probability of achieving safe platelet levels, to avoid corticosteroids, and for more convenient administration. Patients were willing to accept significant risks of rebound and elevated liver enzymes for improvements in outcomes. These results demonstrate that patients with ITP are willing to accept treatment-related risks in exchange for improvements in treatment efficacy and administration attributes and suggest the importance of considering a patient's benefit-risk preferences during discussions of therapeutic options.

Non-additive robust ordinal regression: A multiple criteria decision model based on the Choquet integral

Abstract Within the multicriteria aggregation–disaggregation framework, ordinal regression aims at inducing the parameters of a decision model, for example those of a utility function, which have to represent some holistic preference comparisons of a Decision Maker (DM). Usually, among the many utility functions representing the DM’s preference information, only one utility function is selected. Since such a choice is arbitrary to some extent, recently robust ordinal regression has been proposed with the purpose of taking into account all the sets of parameters compatible with the DM’s preference information. Until now, robust ordinal regression has been implemented to additive utility functions under the assumption of criteria independence. In this paper we propose a non-additive robust ordinal regression on a set of alternatives A, whose utility is evaluated in terms of the Choquet integral which permits to represent the interaction among criteria, modelled by the fuzzy measures, parameterizing our approach. In our methodology, besides holistic pairwise preference comparisons of alternatives from a subset of reference alternatives A ′ ⊆ A , the DM is also requested to express the intensity of preference on pairs of alternatives from A ′ , and to supply pairwise comparisons on the importance of criteria, and the sign and intensity of interaction among pairs of criteria. The output of our approach defines a set of fuzzy measures (capacities) such that the corresponding Choquet integral is compatible with the DM’s preference information. Moreover, using linear programming, our decision model establishes two preference relations for any a , b ∈ A : the necessary weak preference relation, if for all compatible fuzzy measures the utility of a is not smaller than the utility of b, and the possible weak preference relation, if for at least one compatible fuzzy measure the utility of a is not smaller than the utility of b.

Risk averse preference models for normalised lotteries based on simulation

In this paper, we propose a new risk-preference model for ranking pairs of normalised lotteries, random variables, each represents a risk factor obtained by converting the outcomes of the lottery into its mean multiplied by a risk factor. With the existence of an expected utility model, the preference ordering over a pair of such lotteries is converted into a risk-preference ranking over their risk factors. The proposed model is an efficient approximation model based on cumulative distribution functions using simulation. It can be used for analysing preferences between pairs of uncertain alternatives representing financial investment for risk-averse investors. Furthermore, unlike the other models, it can be applied to a variety of randomly distributed variables with different utility functions.

A method based on stochastic dominance degrees for stochastic multiple criteria decision making

In this paper, a novel method based on the stochastic dominance degree (SDD) is proposed to solve a discrete stochastic multiple criteria decision-making (MCDM) problem. Firstly, a concept of stochastic dominance degree is introduced to describe the degree that one alternative dominates another when the SD relation for each pair of alternatives is determined, and a computation formula of the SDD is given. Then, by calculating SDDs, the SDD matrix on pairwise comparisons of alternatives with respect to each criterion is built. Furthermore, the SDD matrices with respect to all the criteria are aggregated into an overall SDD matrix using the simple additive weighting method. Based on the overall SDD matrix, an approach based on the idea of the PROMETHEE-II is developed to obtain the ranking result of alternatives. Finally, two numerical examples are used to illustrate the applicability and effectiveness of the proposed method.

Choice in multi-alternative environments: A trial-by-trial implementation of the Sequential Choice Model

The sequential choice model (SCM) proposes that latencies to accept options presented alone can be used to predict preferences between these options when they are presented simultaneously. SCM has been proposed and tested in experiments where only two alternatives were present. To further challenge the model, we trained and tested European starlings (Sturnus vulgaris) in an environment with a background of four alternatives differing in delay to reinforcement. Unexpected binary choices between the six possible pairs of alternatives were used to assess preference. The model's predictions of the strength of preference roughly corresponded to the bird's choices for each of the six choice situations. More importantly, a trial-by-trial test of the model correctly predicted 84% of all individual choice trials.

FAIR CONSISTENCY EVALUATION FOR RECIPROCAL RELATIONS AND IN GROUP DECISION MAKING

In decision-making processes, it often occurs that the decision maker is asked to pairwise compare alternatives. His/her judgements over a set of pairs of alternatives can be collected into a matrix and some relevant properties, for instance, consistency, can be estimated. Consistency is a desirable property which implies that all the pairwise comparisons respect a principle of transitivity. So far, many indices have been proposed to estimate consistency. Nevertheless, in this paper we argue that most of these indices do not fairly evaluate this property. Then, we introduce a new consistency evaluation method and we propose to use it in group decision making problems in order to fairly weigh the decision maker's preferences according to their consistency. In our analysis, we consider two families of pairwise comparison matrices: additively reciprocal pairwise comparison matrices and multiplicatively reciprocal pairwise comparison matrices.

Recognizing one-dimensional Euclidean preference profiles

A preference profile has a one-dimensional Euclidean representation if it can be derived from an arrangement of individuals and alternatives on a line, with each individual preferring the nearer of each pair of alternatives. We provide a polynomial-time algorithm that determines whether a given preference profile has a one-dimensional Euclidean representation and, if so, constructs one. This result has electoral and mechanism design applications.

Building a binary outranking relation in uncertain, imprecise and multi-experts contexts: The application of evidence theory

We consider multicriteria decision problems where the actions are evaluated on a set of ordinal criteria. The evaluation of each alternative with respect to each criterion may be uncertain and/or imprecise and is provided by one or several experts. We model this evaluation as a basic belief assignment (BBA). In order to compare the different pairs of alternatives according to each criterion, the concept of first belief dominance is proposed. Additionally, criteria weights are also expressed by means of a BBA. A model inspired by ELECTRE I is developed and illustrated by a pedagogical example.