# Necessary and possible preference structures

Published on Mar 1, 2013in Journal of Mathematical Economics0.63
· DOI :10.1016/j.jmateco.2013.01.001
Alfio Giarlotta7
Estimated H-index: 7
(University of Catania),
Salvatore Greco52
Estimated H-index: 52
(University of Catania)
Cite
Abstract
A classical approach to model a preference on a set A of alternatives uses a reflexive, transitive and complete binary relation, i.e. a total preorder. Since the axioms of a total preorder do not usually hold in many applications, preferences are often modeled by means of weaker binary relations, dropping either completeness (e.g. partial preorders) or transitivity (e.g. interval orders and semiorders). We introduce an alternative approach to preference modeling, which uses two binary relations–the necessary preference ≿N and the possible preference ≿P–to fulfill completeness and transitivity in a mixed form. Formally, a NaP-preference (necessary and possible preference) on A is a pair (≿N,≿P) such that ≿N is a partial preorder on A and ≿P is an extension of ≿N satisfying mixed properties of transitivity and completeness. We characterize a NaP-preference (≿N,≿P) by the existence of a nonempty set R of total preorders such that ⋂R=≿N and ⋃R=≿P. In order to analyze the representability of NaP-preferences via families of utility functions, we generalize the notion of a multi-utility representation of a partial preorder by that of a modal utility representation of a pair of binary relations. Further, we give a dynamic view of the family of all NaP-preferences on a fixed set A by endowing it with a relation of partial order, which is defined according to the stability of the information represented by each NaP-preference.
• References (38)
• Citations (27)
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References38
Published on Jul 1, 2014in Order
Alfio Giarlotta7
Estimated H-index: 7
(University of Catania)
A NaP-preference (necessary and possible preference) on a set A is a pair $${\left(\succsim^{^{_N}}\!,\,\succsim^{^{_P}}\!\right)}$$ of binary relations on A such that its necessary component $${\succsim^{^{_N}} \!\!}$$ is a partial preorder, its possible component $${\succsim^{^{_P}} \!\!}$$ is a completion of $${\succsim^{^{_N}} \!\!}$$, and the two components jointly satisfy natural forms of mixed completeness and mixed transitivity. We study additional mixed transitivity properties of a NaP-...
Published on Feb 1, 2014in American Economic Journal: Microeconomics1.45
Ehud Lehreryz27
Estimated H-index: 27
Roee Teper6
Estimated H-index: 6
Quite often, decision makers face choices that involve new aspects and alternatives never considered before. Scenarios of this sort may arise, for instance, as a result of technological progress or from individual circumstances such as growing awareness. In such situations, simple inference rules, past experience, and knowledge about historic choice problems may prove helpful in determining what would be a reasonable action to take vis-a-vis a new problem. In the context of decision making under...
Published on Jan 17, 2014
Salvatore Corrente15
Estimated H-index: 15
(University of Catania),
Salvatore Greco52
Estimated H-index: 52
(University of Catania)
+ 1 AuthorsRoman Slowifiski67
Estimated H-index: 67
(PUT: Poznań University of Technology)
Within disaggregation–aggregation approach, ordinal regressionaims at inducing parameters of a preference model, for example, parameters of a value function, which represent some holistic preference comparisons of alternatives given by the Decision Maker (DM). Usually, from among many sets of parameters of a preference model representing the preference information given by the DM, only one specific set is selected and used to work out a recommendation. For example, while there exist many value f...
Published on May 1, 2012in Journal of Mathematical Economics0.63
Gerhard Herden11
Estimated H-index: 11
,
Estimated H-index: 5
(Central Economics and Mathematics Institute)
We prove the existence of arbitrary (resp., semicontinuous, continuous) utility representations for arbitrary (resp., semicontinuous, continuous) preorders satisfying some weakened Debreu order separability conditions. In this way we widely generalize a classical result for total preorders that essentially is due to Debreu.
Published on Jan 1, 2012in Econometrica4.28
Efe A. Ok28
Estimated H-index: 28
(NYU: New York University),
Pietro Ortoleva11
Estimated H-index: 11
(California Institute of Technology),
Gil Riella6
Estimated H-index: 6
(UnB: University of Brasília)
We investigate the classical Anscombe–Aumann model of decision-making under uncertainty without the completeness axiom. We distinguish between the dual traits of “indecisiveness in beliefs” and “indecisiveness in tastes.” The former is captured by the Knightian uncertainty model, the latter by the single-prior expected multi-utility model. We characterize axiomatically the latter model. Then we show that, under independence and continuity, these two models can be jointly characterized by means o...
Published on Aug 1, 2011in Journal of Mathematical Economics0.63
Özgür Evren6
Estimated H-index: 6
(New Economic School),
Efe A. Ok28
Estimated H-index: 28
(NYU: New York University)
We develop the ordinal theory of (semi)continuous multi-utility representation for incomplete preference relations. We investigate the cases in which the representing sets of utility functions are either arbitrary or finite, and those cases in which the maps contained in these sets are required to be (semi)continuous. With the exception of the case where the representing set is required to be finite, we find that the requirements of such representations are surprisingly weak, pointing to a wide ...
Published on Dec 1, 2010in European Journal of Operational Research3.81
Salvatore Greco52
Estimated H-index: 52
(University of Catania),
Vincent Mousseau26
Estimated H-index: 26
(ECP: École Centrale Paris),
Roman Slowifiski67
Estimated H-index: 67
(PUT: Poznań University of Technology)
We present a new multiple criteria sorting method that aims at assigning actions evaluated on multiple criteria to p pre-defined and ordered classes. The preference information supplied by the decision maker (DM) is a set of assignment examples on a subset of actions relatively well known to the DM. These actions are called reference actions. Each assignment example specifies a desired assignment of a corresponding reference action to one or several contiguous classes. The set of assignment exam...
Published on Feb 1, 2010in European Journal of Operational Research3.81
Silvia Angilella10
Estimated H-index: 10
(University of Catania),
Salvatore Greco52
Estimated H-index: 52
(University of Catania),
Benedetto Matarazzo34
Estimated H-index: 34
(University of Catania)
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...
Published on Jan 1, 2010
Salvatore Greco52
Estimated H-index: 52
,
Roman Slowifiski67
Estimated H-index: 67
+ 1 AuthorsVincent Mousseau26
Estimated H-index: 26
Published on Dec 1, 2008in European Journal of Operational Research3.81
Salvatore Greco52
Estimated H-index: 52
(University of Catania),
Vincent Mousseau26
Estimated H-index: 26
(Paris Dauphine University),
Roman Slowifiski67
Estimated H-index: 67
(PUT: Poznań University of Technology)
We present a new method, called UTAGMS, for multiple criteria ranking of alternatives from set A using a set of additive value functions which result from an ordinal regression. The preference information provided by the decision maker is a set of pairwise comparisons on a subset of alternatives ARÂ [subset, double equals]Â A, called reference alternatives. The preference model built via ordinal regression is the set of all additive value functions compatible with the preference information. Usi...
Cited By27
Published on Dec 1, 2019in Economics Letters0.88
Metin Uyanık1
Estimated H-index: 1
(UQ: University of Queensland),
M. Ali Khan24
Estimated H-index: 24
(Johns Hopkins University)
Abstract Under a continuity hypothesis on bi-preferences defined on a topologically-connected choice-set, as formalized by Giarlotta-Greco (2013), this letter reports that a mildly consistent, double-minded decision-maker is single-minded in the sense of being fully consistent and decisive. The results generalize recent work of Giarlotta-Watson (2019), and thereby provide a far-reaching generalization of a result of Schmeidler (1971) that has received considerable recent attention, and extend to...
Published on Apr 1, 2019in European Journal of Operational Research3.81
Salvatore Greco52
Estimated H-index: 52
(University of Catania),
Alessio Ishizaka23
Estimated H-index: 23
+ 1 AuthorsGianpiero Torrisi7
Estimated H-index: 7
(University of Catania)
Abstract We propose a methodology to employ composite indicators for performance analysis of units of interest using and extending the family of Stochastic Multiattribute Acceptability Analysis. We start evaluating each unit by means of weighted sums of their elementary indicators in the whole set of admissible weights. For each unit, we compute the mean, μ , and the standard deviation, σ , of its evaluations. Clearly, the former has to be maximized, while the latter has to be minimized as it de...
Published on Mar 1, 2019in Information Fusion10.72
José Carlos R. Alcantud15
Estimated H-index: 15
(University of Salamanca),
Alfio Giarlotta7
Estimated H-index: 7
(University of Catania)
Abstract We propose an extension of Torra’s notion of hesitant fuzzy set, which appears to be well suited to group decision making. In our model, indecisiveness in judgements is described by two nested hesitant fuzzy sets: the smaller, called necessary, collects membership values determined according to a rigid evaluation, whereas the larger, called possible, comprises socially acceptable membership values. We provide several instances of application of our methodology, and accordingly design su...
Published on Feb 1, 2019in Social Choice and Welfare0.53
Domenico Cantone15
Estimated H-index: 15
(University of Catania),
Alfio Giarlotta7
Estimated H-index: 7
(University of Catania),
Stephen Watson10
Estimated H-index: 10
(York University)
A choice space is a finite set of alternatives endowed with a map associating to each menu a nonempty subset of selected items. A congruence on a choice space is an equivalence relation that preserves its structure. Intuitively, two alternatives are congruent if the agent is indifferent between them, and, in addition, her choice is influenced by them in exactly the same way. We give an axiomatic characterization of the notion of congruence in terms of three natural conditions: binary fungibility...
Published on Jan 1, 2019
Alfio Giarlotta7
Estimated H-index: 7
(University of Catania),
We give an overview of some new trends in preference modeling, utility representation, and choice rationalization. Several recent contributions on these topics point in the same direction: the use of multiple tools—may they be binary relations, utility functions, or rationales explaining a choice behavior—in place of a single one, in order to more faithfully model economic phenomena. In this stream of research, the two traditional tenets of economic rationality, completeness and transitivity, ar...
Published on Jan 1, 2019in Theoretical Economics2.16
José Heleno Faro4
Estimated H-index: 4
(Insper),
José Heleno Faro1
Estimated H-index: 1
+ -1 AuthorsJean-Philippe Lefort6
Estimated H-index: 6
(Paris Dauphine University)
We characterize prior-by-prior Bayesian updating using a model proposed by Gilboa, Maccheroni, Marinacci and Schmeidler (2010) that jointly considers objective and subjective rationality. These rationality concepts are subject to the Bewley unanimity rule and maxmin expected utility, respectively, with a common set of priors and the same utility over consequences. We use this setup with two preference relations to develop a novel rationale for full Bayesian updating of maxmin expected utility pr...
Published on Jan 1, 2019
Salvatore Corrente15
Estimated H-index: 15
(University of Catania),
Salvatore Greco52
Estimated H-index: 52
(University of Catania),
Roman Slowifiski67
Estimated H-index: 67
(PUT: Poznań University of Technology)
In this chapter, we present a methodology of decision aiding that helps to build a ranking of a finite set of alternatives evaluated by a family of hierarchically structured criteria. The presentation has a tutorial character, and takes as an example the ranking of universities. Each university is generally evaluated on several aspects, such as quality of faculty and research output. Moreover, their performance on these macro-criteria can be further detailed by evaluation on some subcriteria. To...
Paula Sarabando5
Estimated H-index: 5
(IPN: Instituto Politécnico Nacional),
Luis C. Dias24
Estimated H-index: 24
(UC: University of Coimbra),
Rudolf Vetschera17
Estimated H-index: 17
(University of Vienna)
Published on Oct 19, 2018in Economic Theory0.96
Simone Cerreia-Vioglio11
Estimated H-index: 11
(Bocconi University),
Alfio Giarlotta7
Estimated H-index: 7
(University of Catania)
+ 2 AuthorsMassimo Marinacci37
Estimated H-index: 37
(Bocconi University)
We study a decision maker characterized by two binary relations. The fi rst reflects his judgments about well-being, his mental preferences. The second describes the decision makers choice behavior, his behavioral preferences, the ones that govern choice (see Rubin- stein and Salant, 2008a,b). Specifi cally, in the context of decision making under uncertainty, we propose axioms that may describe the rationality of these two relations. These axioms allow a joint representation by a single set of ...
Published on 2018in Knowledge Based Systems5.10
Silvia Angilella10
Estimated H-index: 10
(University of Catania),
Pierluigi Catalfo2
Estimated H-index: 2
(University of Catania)
+ 3 AuthorsMarcella Rizzo3
Estimated H-index: 3
(University of Catania)
Abstract The evaluation of sustainable development –and, in particular, rural development– through composite indices requires taking into account a plurality of indicators, which are related to economic, social, and environmental aspects. The points of view evaluated by these indices are naturally interacting: thus, a bonus has to be recognized to units performing well on synergic criteria, whereas a penalisation has to be assigned on redundant criteria. An additional difficulty of the modelizat...
View next paperOrdinal regression revisited: Multiple criteria ranking using a set of additive value functions