Consistency of crisp and fuzzy preference relations

In this paper we point out some difficulties in developing rationality measures of fuzzy preference relations, as defined by Cutello and Montero in a previous paper. In particular, we analyze some alternative approaches, taking into account that consistency can not be viewed as an univoque concept in a fuzzy framework, neither in the crisp context, where consistency should not be necessarily represented in terms of linear orders

Fuzzy and probabilistic choice functions: a new set of rationality conditions

IFSA-EUSFLAT'2015: 16th World Congress of the International Fuzzy Systems Association and 9th Conference of the European Society for Fuzzy Logic and Technlogy, July 2015, Gijón, SpainProbabilistic and fuzzy choice theory are used to describe decision situations in which a certain degree of imprecision is involved. In this work we propose a correspondence between probabilistic and fuzzy choice functions, based on implication operators. Given a probabilistic choice function a fuzzy choice function can be constructed and, furthermore, a new set of rationality conditions is proposed. Finally, we prove that under those conditions, the associated fuzzy choice function fulfills desirable rationality propertie

Fuzzy and probabilistic choice functions : a new set of rationality conditions

Probabilistic and fuzzy choice theory are used to describe decision situations in which a certain degree of imprecision is involved. In this work we propose a correspondence between probabilistic and fuzzy choice functions, based on implication operators. Given a probabilistic choice function a fuzzy choice function can be constructed and, furthermore, a new set of rationality conditions is proposed. Finally, we prove that under those conditions, the associated fuzzy choice function fulfills desirable rationality properties

Bridging probabilistic and fuzzy approaches to choice under uncertainty

Imprecise choices can be described using either a probabilistic or a fuzzy formalism. No relation between them has been studied so far. In this contribution we present a connection between the two formalisms that strongly makes use of fuzzy implication operators and t-norms. In this framework, Luce's Choice Axiom turns out to be a special case when the product t-norm is considered and other similar choice axioms can be stated, according to the t-norm in use. Also a new family of operators for transforming bipolar relations into unipolar ones is presented

Mayorías basadas en diferencias: análisis de la consistencia y extensiones

En esta tesis se estudian las mayorías por diferencia de votos y por diferencia de apoyo. Los capítulos 1 y 2 se centran en el análisis de la transitividad y de la triple-aciclicidad de la relación de preferencia fuerte generada por las mayorías por diferencia de apoyo, al agregar relaciones de preferencia recíprocas individuales. En el capítulo 3 se estiman las probabilidades con las que se producen resultados colectivos consistentes, tanto en las mayorías por diferencia de apoyo como en las mayorías por diferencia de votos. En el capítulo 4 se extienden las mayorías por diferencia de votos al contexto de las preferencias lingüísticas, a través de conjuntos difusos y del modelo de las 2-tuplas; se justifica la equivalencia entre ambas modelizaciones bajo determinadas condiciones de regularidad y se estudian las propiedades que cumplen estas mayorías lingüísticasDepartamento de Economía Aplicad

Houthakker and Ville's contributions to demand theory: a new look at the debate on integrability conditions.

Jean Ville gave, independently of Houthakker, and prior to him, a general one page proof of the integrability of demand functions in a revealed preference scheme. It happens that this essential contribution has been largely ignored in the literature. The comparison between Ville and Houthakker’s proofs makes room for discussing the assumptions necessary to encompass the discrete version of the acyclicity into a continuous version.

Causal Effects in Matching Mechanisms with Strategically Reported Preferences

A growing number of central authorities use assignment mechanisms to allocate students to schools in a way that reflects student preferences and school priorities. However, most real-world mechanisms give students an incentive to be strategic and misreport their preferences. In this paper, we provide an identification approach for causal effects of school assignment on future outcomes that accounts for strategic misreporting. Misreporting may invalidate existing point-identification approaches, and we derive sharp bounds for causal effects that are robust to strategic behavior. Our approach applies to any mechanism as long as there exist placement scores and cutoffs that characterize that mechanism's allocation rule. We use data from a deferred acceptance mechanism that assigns students to more than 1,000 university-major combinations in Chile. Students behave strategically because the mechanism in Chile constrains the number of majors that students submit in their preferences to eight options. Our methodology takes that into account and partially identifies the effect of changes in school assignment on various graduation outcomes

Towards a Model of Argument Strength for Bipolar Argumentation Graphs

UID/FIL/00183/2013Bipolar argument graphs represent the structure of complex pro and contra arguments for one or more standpoints. In this article, ampliative and exclusionary principles of evaluating argument strength in bipolar acyclic argumentation graphs are laid out and compared to each other. Argument chains, linked arguments, link attackers and supporters, and convergent arguments are discussed. The strength of conductive arguments is also addressed but it is argued that more work on this type of argument is needed to properly distinguish argument strength from more general value-based components of such argu- ments. The overall conclusion of the article is that there is no justifiably unique solution to the problem of argument strength outside of a particular epistemological framework.publishersversionpublishe

Desire, belief, and conditional belief

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Linguistics and Philosophy, 2008.Includes bibliographical references (leaves 127-132).This dissertation studies the logics of value and conditionals, and the question of whether they should be given cognitivist analyses. Emotivist theories treat value judgments as expressions of desire, rather than beliefs about goodness. Inference ticket theories of conditionals treat them as expressions of conditional beliefs, rather than propositions. The two issues intersect in decision theory, where judgments of expected goodness are expressible by means of decision-making conditionals. In the first chapter, I argue that decision theory cannot be given a Humean foundation by means of money pump arguments, which purport to show that the transitivity of preference and indifference is a requirement of instrumental reason. Instead, I argue that Humeans should treat the constraints of decision theory as constitutive of the nature of preferences. Additionally, I argue that transitivity of preference is a stricter requirement than transitivity of indifference. In the second chapter, I investigate whether David Lewis has shown that decision theory is incompatible with anti-Humean theories of desire. His triviality proof against "desire as belief' seems to show that desires can be at best conditional beliefs about goodness. I argue that within causal decision theory we can articulate the cognitivist position where desires align with beliefs about goodness, articulated by the decision making conditional. In the third chapter, I turn to conditionals in their own right, and especially iterated conditionals.(cont.) I defend the position that indicative conditionals obey the import-export equivalence rather than modus ponens (except for simple conditionals), while counterfactual subjunctive conditionals do obey modus ponens. The logic of indicative conditionals is often thought to be determined by conditional beliefs via the Ramsey Test. I argue that iterated conditionals show that the conditional beliefs involved in indicative supposition diverge from the conditional beliefs involved in learning, and that half of the Ramsey Test is untenable for iterated conditionals.by David Jeffrey Etlin.Ph.D