Binary Preference Research Articles

A numerical tool for multiattribute ranking problems

AbstractA large variety of techniques have been developed to solve or approximate the solution of multiattribute ranking problems. From such techniques, several implicit or explicit partial orders, defined on the same set of alternatives, are obtained (in many cases, by pairwise comparisons) with the goal of determining a linear order. Often, this goal is attained by assigning positive weights to each partial order relation. However, the imprecise judgments of the pairwise comparisons as well as other factors lead to inconsistencies which have been analyzed in an extensive literature devoted to this type of problem. In this paper, numerical results about linear extensions of weighted sum relations are applied to the recognition of pairwise imprecise judgments between alternatives as well as to the confirmation of a ranking solution as a linear extension of a quasi‐order defined by a weighted sum of binary preference relations. © 2003 Wiley Periodicals, Inc.

A general concept of majority rule

We develop a general concept of majority rule for finitely many choice alternatives that is consistent with arbitrary binary preference relations, real-valued utility functions, probability distributions over binary preference relations, and random utility representations. The underlying framework is applicable to virtually any type of choice, rating, or ranking data, not just the linear orders or paired comparisons assumed by classic majority rule social welfare functions. Our general definition of majority rule for arbitrary binary relations contains the standard definition for linear orders as a special case.

A Logical Analysis of the Relationship between Commitment and Obligation

In this paper, we analyze the relationship between commitment and obligation from a logical viewpoint. The principle of commitment implying obligation is proven in a specific logic of action preference which is a generalization of Meyer's dynamic deontic logic. In the proposed formalism, an agent's commitment to goals is considered as a special kind of action which can change one's deontic preference and one's obligation to take some action is based on the preference and the effects of the action. In this logic, it is shown that an agent has the obligation to take any action which is necessary for achieving as many committed goals as possible. The semantics of our logic is based on the possible world models for the dynamic logic of actions. A binary preference relation between possible worlds is associated with the model. Then the preference between actions are determined by comparing that of their consequences. According to the semantics, while the preference will influence the agent's choice of action, commitment is a kind of action that will change the agent's preference. Thus we can show how obligations arise from commitments via updating of deontic preference. The integrated semantics make it possible to express and reason about the mutual relationship among these mental attitudes in a common logic.

Extended preferences and freedom of choice

The common choice theory in economics is based on the assumption that an individual is defined in terms of a binary preference relation. This preference relation is defined over alternatives without taking into account menu dependence and, in particular, freedom of choice or, more generally, the set that contains the alternatives. In this study we clarify the nature and the significance of freedom of choice which may positively or negatively affect the individual's welfare. Our proposed extended preference relation of the individual takes into account both the particular alternative and the opportunity set that he faces. This extended relation does not induce ranking of opportunity sets. Its restriction to a particular opportunity set is the paradigmatic preference relation and it can capture the dependence of preferences on freedom of choice. Our main result establishes the inconsistency between dependence of extended preferences on freedom of choice and the existence of a utility that represents the paradigmatic preference relation and any of its restrictions.

Factors Influencing the Sensitivity of Binary Preference Assays for Determining Cereal Cultivar Resistance to Grasshoppers

The feeding behaviour of herbivorous insects has become the focus of renewed interest in recognition of its critical importance in screening cultivated plants for resistant germplasm. Determination of biotic potential was viewed as the ultimate test for resistance to grasshoppers in agro-ecosystems dominated by cereal monoculture, because of the direct relationship between it and population dynamics. Such studies, however, are labour-intensive and may extend over several months. As an alternative to more timeconsuming assay procedures, in this study we examined a behavioural assay and some of the factors that influence the results. In the majority of assays in the present study, the total number of grasshoppers visiting the plants were lower on the second day than the first day using second instar grasshoppers. In contrast, the total numbers of grasshoppers recorded on the plants was higher on the second day than the first day for the majority of assays using neonates. The extent of defoliation also was noticeably greater on the second day, except when both plants available to the grasshoppers were non-preferred. This difference which was reflected in greater sensitivity of the assays using neonates serves to highlight one of the problems when grasshoppers at later stages of development are used in binary preference assays. The observations of feeding patterns are discussed in terms of some recent concepts

Learning to Order Things

There are many applications in which it is desirable to order rather than classify instances. Here we consider the problem of learning how to order instances given feedback in the form of preference judgments, i.e., statements to the effect that one instance should be ranked ahead of another. We outline a two-stage approach in which one first learns by conventional means a binary preference function indicating whether it is advisable to rank one instance before another. Here we consider an on-line algorithm for learning preference functions that is based on Freund and Schapire's 'Hedge' algorithm. In the second stage, new instances are ordered so as to maximize agreement with the learned preference function. We show that the problem of finding the ordering that agrees best with a learned preference function is NP-complete. Nevertheless, we describe simple greedy algorithms that are guaranteed to find a good approximation. Finally, we show how metasearch can be formulated as an ordering problem, and present experimental results on learning a combination of 'search experts', each of which is a domain-specific query expansion strategy for a web search engine.

Probabilistic preferences and topset voting

Random utility theory offers a powerful modeling tool for group decision, voting and persuasion. I combine and extend three recent developments: (1) probabilistic choice models of approval voting, (2) general random utility representations for a variety of order relations, and (3) stochastic theories of persuasion. The present topset voting model merges (1) and (2) by generalizing probabilistic choice models for approval voting to arbitrary binary preference relations. Whereas the econometric literature emphasizes parametric random utilities (e.g. generalized logit and probit), I investigate parametrizations of the probabilistic relations. A new model for paneled subset choice combines (1) and (3).

Equivalence and compositions of fuzzy rationality measures

An axiomatic basis for fuzzy rationality measures has already been introduced by the authors in a previous paper [5], formalizing the fact that there exist degrees of consistency when preferences over a fixed set of alternatives are expressed in terms of fuzzy binary preference relations. This paper deals with some practical consequences. On the one hand, similarities and compositions of fuzzy rationality measures are considered, showing natural ways of deriving new measures; on the other, if basic stability properties are introduced in order to assure that small intensity measurement errors never lead to big changes in the associate rationality value, it is shown that crisp (i.e., binary) rationality measures present serious difficulties when applied to fuzzy preference relations.

Characterization of generalized weak orders and revealed preference

This short paper provides an alternative framework to axiomatize various binary preference relations such as semiorder, weak semiorder etc. A set of simple axioms is presented in terms of revealed-preferred and revealed-inferior alternatives which makes the connection between various binary preference relations transparent; and every single axiom is necessary and sufficient for the existence of a binary preference relation of a specified type.

Exploiting the normative aspect of preference: A deontic logic without actions

This paper is an attempt to clear the following charge leveled against preference logics: preference logics rest upon the mistaken belief that concept construction can satisfactorily be carried out in isolation from theory construction (J. Mullen, Metaphilosophy 10(1979)247–255). We construct a logic of preference that is fundamental in the sense that it does notcommit itself to any allegedlyobvious or intuitive — and in actuality,theory specific — preference principles. A unique feature of our construction is that preference orderings are placed upon possible worlds. While this has been done before in the work of S.O. Hansson and N. Rescher, among others, we do not derive a binary preference relation — from these orders — that acts on individual propositions. Instead, we provide the syntactic means to impose the preference orderings among worlds. Thus, unlike Hansson, we do not need to assumea priori that our preference orderings be transitive. Such properties can be axiomatized. The close connections between preferences and obligations, in particular their normative nature, then allow us to derive a deontic logic that is free of the paradoxes of standard deontic logic. It is interesting to note here that this work arose in an attempt to provide a logical characterization of document description and layout Layout directives can be succinctly represented as preference criteria.

Preferences for a Verb′s Complements and Their Use in Sentence Processing

We explore how subject′s preferences for complements of particular verbs affect the on-line processing of sentences. We conduct three experiments: The first experiment gathers binary preference choices for several verb types and their complements: the second and third experiments use these preference choices and find that a subject′s preference for a verb′s complements affects an initial parse in sentences that do not contain obvious structural ambiguities. These data are discussed in terms of the lexical entry-driven and phrase structure-driven models of sentence processing. We conclude that lexical information is used during the initial analysis of a sentence to set up possible paths the parser might take; when the structure of the sentence is incongruent with a subject′s preference, sentence processing performance is disrupted and reanalysis must occur

Indeterminate Probabilities on Finite Sets

This paper presents a quasi-Bayesian model of subjective uncertainty in which beliefs which are represented by lower and upper probabilities qualified by numerical confidence weights. The representation is derived from a system of axioms of binary preferences which differs from standard axiom systems insofar as completeness is not assumed and transitivity is weakened. Confidence-weighted probabilities may be elicited through the acceptance of bets with limited stakes, a generalization of the operational method of de Finetti. The model is applicable to the reconciliation of inconsistent probability judgments and to the sensitivity analysis of Bayesian decision models.

Universal maps for binary preference structure generating decision principle functors

The concept of a binary preference structure generating decision principle is proposed as a device to treat extremely complex decision situations. We argue two types of binary preference structure generating decision principles: the first is for complexity management of a dynamic environment by constructing a model of the environment. The second is the satisfaction decision principle for complexity management by increasing the internal complexity. For both cases we formulate the decision principles as decision principle functors in category theoretic terms to reveal new aspects of the decision principles. We also identify universal maps for the functors and investigate their decision theoretic meaning.

Multiple-criteria robust interactive decision analysis (MCRID) for optimizing public policies

Important public policy decisions are often very complex, involving many factors, large uncertainties, and multiple conflicting objectives. Decision analysis, which is a formal framework for dealing with such issues, has been applied to a variety of public-sector problems over the last two decades. A limitation of using decision analysis is the often onerous assessment burden it places on the decision maker (DM). We have developed a novel interactive procedure and Decision Support System (DSS) for performing decision analysis on the personal computer, called robust interactive decision analysis (RID), which avoids the difficult problems of precisely assessing a DM's utility and state probability functions associated with traditional decision treee analysis. The RID method permits a DM to voluntarily and interactively express strong (viz, sure) binary preferences for actions, partial decision functions, and full decision functions, and only imprecise probability and utility function assessments. The inputs are used with various dominance operators via a mathematical programming framework to prune the state probability, utility, and decision space until there is convergence on a relatively small subset of efficient strategies or an optimal choice strategy. Conceptually, the operation of the RID method can be regarded as a state-pruning system and its computer implementation as a DSS. In this paper, we extended the RID concept and DSS to deal with multiple-criteria decisions, obviating the need to precisely and completely assess attribute weights (tradeoffs), consequences, and/or value/utility functions. The approach, which we call multiple-criteria robust interactive decision analysis, MCRID, is developed, illustrated, and shown to be effective in eliminating many inefficient alternatives. However, since the aggregate utility of each alternative is interval-valued, it then becomes difficult to intuitively choose an optimal alternative from among the remaining efficient ones since the intervals are not defined by any specific probability distributions. We have tentatively shown that aggregate utility intervals ultimately converge toward a normal density function, and can be so approximated with relatively few attributes. Hence, stochastic dominance is employed to further filter out alternatives. An interactive goal programming (GP) technique is then developed to assist the DM in choosing an optimal alternative.

Revealed preference and the axiomatic foundations of intransitive indifference: The case of asymmetric subrelations

This paper provides an axiomatic structure for various binary preference relations that are reflexive, connected, and transitive in their asymmetric subrelations known as quasi-transitive orderings. A choice function generates various (distinct) binary preference relations, such as the base relation, the revealed preference relation, and the wide revealed preference relation. For each interpretation of a binary preference relation, we present an axiom that ensures the existence of a quasi-transitive preference ordering. A description of a choice procedure is considered which one often observes in real life and it is shown that the path independence of such a procedure is a sufficient condition for a quasi-transitive ordering of various binary preference relations.

Preference-Order Recursion for Finding Relevant Pure, Admissible and Optimal Statistical Decision Functions

A preference-order recursion algorithm for obtaining a relevant subset of pure, admissible (non-dominated, efficient) decision functions which converges towards an optimal solution in statistical decision problems is proposed. The procedure permits a decision maker to interactively express strong binary preferences for partial decision functions at each stage of the recursion, from which an imprecise probability and/or utility function is imputed and used as one of several pruning mechanisms to obtain a reduced relevant subset of admissible decision functions or to converge on an optimal one. The computational and measurement burden is thereby mitigated significantly, for example, by not requiring explicit or full probability and utility information from the decision maker. The algorithm is applicable to both linear and nonlinear utility functions. The results of behavioral and computational experimentation show that the approach is viable, efficient, and robust.

Intransitivities of preferences, lexicographic shifts and the transitive dimension of oriented graphs

Intransitivities in preference relations are usually explained by shifts in choice criteria, i.e. shifts in points of view. This paper is concerned with the following problem: assume that a preference relation R on a finite set of alternatives is observed and that no information about choice criteria is provided, how many shifts of point of view are needed, at a minimum, to explain all the intransitivities of R? A model is proposed that takes into account lexicographic shifts in point of view, and some bounds are computed for the minimal number required. One of the results of this paper is that this number is relatively small: if p binary preferences are expressed, then it is bounded by a function in O(log p).

Algorithms constructing a representative vector criterion for a binary preference relation

Algorithms constructing a representative vector criterion for a binary preference relation

Robust interactive decision‐analysis (RID): Behavioral results and implications

AbstractWe have proposed a novel interactive procedure for performing decision analysis, called Robust Interactive Decision Analysis (RID), which permits a decision maker (DM) to voluntarily and interactively express strong (viz, sure) binary preferences for actions, partial decision functions, and full decision functions, and only imprecise probability and utility function assessments. These serve as INPUTS TO operators to prune the state probability space and decision space until an optimal choice strategy is obtained. The viability of the RID approach depends on a DM's ability to provide such information consistently and meaningfully. On a limited scale we experimentally investigate the behavioral implications of the RID method in order to ascertain its potential operational feasibility and viability. More specifically, we examine whether a DM can (1) express strong preferences between pairs of vectors of unconditional and conditional payoffs or utilities consistently; (2) provide imprecise (ordinal and interval) state probabilities that are individually as well as mutually consistent with the state probabilities imputed from the expressed strong preferences. The results show that a DM can provide strong individually and mutually consistent preference and ordinal probability information. Moreover, most individuals also appear to be able to provide interval probabilities that are individually and mutually consistent with their strong preference inputs. However, the several violations observed, our small sample size, and the limited scope of our investigation suggest that further experimentation is needed to determine whether and/or how such inputs should be elicited. Overall, the results indicate that the RID method is behaviorally viable.

Applied Statistics: A Handbook of BMDP Analyses

BMDP programs used (or suggested) for the examples.- Some points on the BMDP instructions.- Examples.- A Admissions to intensive care unit.- B Intervals between adjacent births.- C Statistical aspects of literary style.- D Temperature distribution in a chemical reactor.- E A 'before and after' study of blood pressure.- F Comparison of industrial processes in the presence of trend.- G Cost of construction of nuclear power plants.- H Effect of process and purity index on fault occurrence.- I Growth of bones from chick embryos.- J Factorial experiment on cycles to failure of worsted yarn.- K Factorial experiment on diets for chickens.- L Binary preference data for detergent use.- M Fertilizer experiment on growth of cauliflowers.- N Subjective preference data on soap pads.- O Atomic weight of iodine.- P Multifactor experiment on a nutritive medium.- Q Strength of cotton yarn.- R Biochemical experiment on the blood of mice.- S Voltage regulator performance.- T Intervals between the failure of air-conditioning equipment in aircraft.- U Survival times of leukemia patients.- V A retrospective study with binary data.- W Housing and associated factors.- X Educational plans of Wisconsin schoolboys.- Further Sets of Data.- Set 3 Survival times of rats.- Set 14 Grouping of perfumes.- References.