Marta Cardin

Università Ca' Foscari Venezia, Department of Economics, Faculty Member

Followers

Following

Co-authors

Mentions

Public Views

Catherine Rowett

University of East Anglia

Andreas Umland

National University of "Kyiv-Mohyla Academy"

Cristina Bicchieri

University of Pennsylvania

Remo Caponi

University of Cologne

Giulia Sissa

Ucla

Rachel E Smith

University of Aberdeen

Antonio Lafuente

CSIC (Consejo Superior de Investigaciones Científicas-Spanish National Research Council)

Francesca Gazzano

University of Genova

Nicola Lupo

LUISS Guido Carli

Juraj Marušiak

Slovak Academy of Sciences

Interests

Uploads

Papers by Marta Cardin

Mathematical Topics on Representations of Ordered Structures and Utility Theory

Studies in Systems, Decision and Control, 2020

A continuous multi-utility fully represents a not necessarily total preorder on a topological spa... more A continuous multi-utility fully represents a not necessarily total preorder on a topological space by means of a family of continuous increasing functions. While it is very attractive for obvious reasons, and therefore it has been applied in different contexts, such as expected utility for example, it is nevertheless very restrictive. In this paper we first present some general characterizations of the existence of a continuous order-preserving function, and respectively a continuous multi-utility representation, for a preorder on a topological space. We then illustrate the restrictiveness associated to the existence of a continuous multi-utility representation, by referring both to appropriate continuity conditions which must be satisfied by a preorder admitting this kind of representation, and to the Hausdorff property of the quotient order topology corresponding to the equivalence relation induced by the preorder. We prove a very restrictive result, which may concisely described as follows: the continuous multi-utility representability of all closed (or equivalently weakly continuous) preorders on a topological space is equivalent to the requirement according to which the quotient topology with respect to the equivalence corresponding to the coincidence of all continuous functions is discrete.

Download

Supermodular and ultramodular aggregations evaluators

Download

On the characterization of convex premium priciples

Comparing dependencies in multivariate risk portfolio by stochastic orders

Various Convexities and Some Relevant Properties of Consumer Preference Relations

Studia Universitatis „Vasile Goldis” Arad – Economics Series

The concept of convexity plays an important role in the study of economics and consumer theory. F... more The concept of convexity plays an important role in the study of economics and consumer theory. For the most part, such studies have been conducted on the assumption that consumer preferences are a binary relation that is complete, reflexive and transitive on the set X of consumption choices. However, each consumer is a biological being with multidimensional physiological needs so that possible consumptions from different dimensions cannot be compared by using preferences. By removing that unrealistic assumption, this paper examines how the various concepts of convex preferences and relevant properties can be re-established. We derive a series of 10 formal propositions and construct 6 examples to show that (a) a weighted combination of two possible consumptions is not necessarily comparable with any of the consumptions; (b) not every convergent sequence of a consumer’s preferred consumptions asymptotically preserves that consumer’s preference preordering; (c) not all preferences sat...

Download

Rights Systems and Aggregation Functions on Property Spaces

Mathematics

The notion of decisive coalitions of voters with different grades of decisiveness is a part of th... more The notion of decisive coalitions of voters with different grades of decisiveness is a part of the mathematical framework for many models in social choice theory. More generally, we study aggregation problems in which a subgroup of decision makers have the right to determine the properties of the aggregate. Then, we introduce property spaces and rights to properties and characterize aggregation operators that are consistent with rights to properties. Moreover, we define congruences in property spaces, and we propose a generalization of the Sugeno integral in our framework.

Download

Preferences and aggregation operators over property spaces

Aggregation

Aggregation functions: an approach using copulae Working Paper n. 159/2007

On multivariate m-concordance

Multivariate dependence modelling with copulas

SDOWA: A New OWA Operator for Decision Making

Ordered Weighted Aggregation operators (OWA) are widely analyzed and applied to real world proble... more Ordered Weighted Aggregation operators (OWA) are widely analyzed and applied to real world problems, given their appealing characteristic to reflect human reasoning, but are enable in the basic definition to include importance weights for the criteria. To obviate, some extensions were introduced, but we show how none of them can satisfy completely a set of required properties. Thus we introduce a new proposal, the Standard Deviation OWA (SDOWA) which conversely satisfy all the listed properties and seems to be more convincing then other ones.

Criteri di dominanza stocastica e fondi di investimento

Preferences in Abstract Convex Structures

Convexity of preferences is a canonical assumption in economic theory. In this paper we study a g... more Convexity of preferences is a canonical assumption in economic theory. In this paper we study a generalized definition of convex preferences that relies on the notion of a convex space, that is an abstraction of the standard notion of convexity in a linear space. We introduce also betweenness relations that characterize convex spaces. First we consider a ternary betweenness relation that gives rise to an interval space structure and then we propose a more general definition of betweenness.

Grading by Committees: An Axiomatic Approach

Advances in Biochemical Engineering/Biotechnology, 2019

We deal the problem of aggregation of individual judgments for a global evaluation of a candidate... more We deal the problem of aggregation of individual judgments for a global evaluation of a candidate or a product. In our theoretically oriented approach, aggregation operators are compared with each other based on their mathematical properties. We show that any monotone and strategy-proof operators is characterized by a particular collection of decision makers.

Inf- and Sup-preserving Aggregation Functions

Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP), 2021

We introduce inf-lattices, sup-lattices and convexity algebras and we define closure or interior ... more We introduce inf-lattices, sup-lattices and convexity algebras and we define closure or interior operators and congruences in these algebraic structures. We prove that any inflattice can be represented as a quotient of a power set lattice with respect to a congruence. Moreover we consider closure operators defined on a poset and we provide a characterization of inf-preserving maps between inf-lattices. Inf-preserving aggregation functions are described.

Download

Aggregation over Property-Based Preference Domains

Advances in Intelligent Systems and Computing, 2017

We provide an axiomatic characterization of preorders that are defined with respect to a set of p... more We provide an axiomatic characterization of preorders that are defined with respect to a set of properties. Moreover, it is proven that property-based posets are in natural correspondence with topological spaces. This paper propose also a characterization and a generalization of a Sugeno-type integral in our framework.

Sugeno Integral on Property-Based Preference Domains

Advances in Fuzzy Logic and Technology 2017, 2017

We consider decision problems in which we have to compare and rank a set of alternatives and each... more We consider decision problems in which we have to compare and rank a set of alternatives and each alternative is defined by its attributes or properties. We introduce and characterize property-based preference domains. This paper proposes also a characterization and a generalization of Sugeno integral in our framework.