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Alfio Giarlotta

Publications and source records attributed to Alfio Giarlotta.

10 recordsLinked to original sources
arXiv2026

The Effects of Social Pressure on Fundamental Choices: Indecisiveness and Deferral

In mainstream neoclassical economics, utility maximization is the only engine of individual action, and the other or the social, if it is modeled for decisions deemed fundamental, it is done as a tacit externality parameter affecting an agent's maximized payoff. And even when hitched to a social reference point, a fully decisive and immediate response is invariably assumed. In this paper, we propose a non-standard articulation of the trade-off between personal utility and social distance, one motivated by experimental evidence from psychology, management science, and economics. Our approach deconstructs non-recurrent consumer choice to two stages: a non-decisive first stage in which a binary relation, called one-many ordering, yields an interval, the consideration set, to which the deferred choice is confined; a decisive second stage in which the distance from the average social choice, and future social expectations, are taken into account in present utility. Finally, we embed this indecisive consumer in an exploratory game-theoretic setting, and show that indecisiveness and choice deferral may cause social loss.

econ.TH↗
arXiv2025

Separable joint choices

We introduce a novel choice dataset, called joint choice, in which options and menus are multidimensional. In this general setting, we define a notion of choice separability, which requires that selections from some dimensions are never affected by those performed on the remaining dimensions. This generalizes the classical definition of separability for discrete preference relations and utility functions, to encompass a class of choice behaviors that may lack a preference or utility representation. We thoroughly investigate the stability of separability across dimensions, and then suggest effective tests to check whether a joint choice is separable. Upon defining rationalizable joint choices as those explained by the maximization of a relation of revealed preference, we examine the interplay between the notions of rationalizability and separability. Finally, we show that the rationalizability of a separable joint choice can be tested by verifying the rationalizability of some derived joint choices over fewer dimensions.

econ.TH↗
arXiv2023

A rational measure of irrationality

All possible types of deterministic choice behavior are classified by their degree of irrationality. This classification is performed in three steps: (1) select a benchmark of rationality, for which this degree is zero; (2) endow the set of choices with a metric to measure deviations from rationality; and (3) compute the distance of any choice behavior from the selected benchmark. The natural candidate for step 1 is the family of all rationalizable behaviors. A possible candidate for step 2 is a suitable variation of the metric described by Klamler (2008), which displays a sharp discerning power among different types of choice behaviors. In step 3 we use this new metric to establish the minimum distance of any choice behavior from the benchmark of rationality. Finally we describe a measure of stochastic irrationality, which employs the random utility model as a benchmark of rationality, and the Block-Marschak polynomials to measure deviations from it.

econ.TH↗
arXiv2022

Extending rational choice behavior: The decision problem for Boolean set theory with a choice correspondence

Given the family $P$ of all nonempty subsets of a set $U$ of alternatives, a choice over $U$ is a function $c \colon Ω\to P$ such that $Ω\subseteq P$ and $c(B) \subseteq B$ for all menus $B \in Ω$. A choice is total if $Ω= P$, and partial otherwise. In economics, an agent is considered rational whenever her choice behavior satisfies suitable axioms of consistency, which are properties quantified over menus. Here we address the following lifting problem: Given a partial choice satisfying one or more axioms of consistency, is it possible to extend it to a total choice satisfying the same axioms? After characterizing the lifting of some choice properties that are well-known in the economics literature, we study the decidability of the connected satisfiability problem for unquantified formulae of an elementary fragment of set theory, which involves a choice function symbol, the Boolean set operators, the singleton, the equality and inclusion predicates, and the propositional connectives. In two cases we prove that the satisfiability problem is NP-complete, whereas in the remaining cases we obtain NP-completeness under the additional assumption that the number of choice terms is constant.

cs.LO↗
arXiv2022

Rationalization of indecisive choice behavior by majoritarian ballots

We describe a model that explains possibly indecisive choice behavior, that is, quasi-choices (choice correspondences that may be empty on some menus). The justification is here provided by a proportion of ballots, which are quasi-choices rationalizable by an arbitrary binary relation. We call a quasi-choice $s$-majoritarian if all options selected from a menu are endorsed by a share of ballots larger than $s$. We prove that all forms of majoritarianism are equivalent to a well-known behavioral property, namely Chernoff axiom. Then we focus on two paradigms of majoritarianism, whereby either a simple majority of ballots justifies a quasi-choice, or the endorsement by a single ballot suffices - a liberal justification. These benchmark explanations typically require a different minimum number of ballots. We determine the asymptotic minimum size of a liberal justification.

econ.TH↗
arXiv2022

Semantics meets attractiveness: Choice by salience

We describe a context-sensitive model of choice, in which the selection process is shaped not only by the attractiveness of items but also by their semantics ('salience'). All items are ranked according to a relation of salience, and a linear order is associated to each item. The selection of a single element from a menu is justified by one of the linear orders indexed by the most salient items in the menu. The general model provides a structured explanation for any observed behavior, and allows us to to model the 'moodiness' of a decision maker, which is typical of choices requiring as many distinct rationales as items. Asymptotically all choices are moody. We single out a model of linear salience, in which the salience order is transitive and complete, and characterize it by a behavioral property, called WARP(S). Choices rationalizable by linear salience can only exhibit non-conflicting violations of WARP. We also provide numerical estimates, which show the high selectivity of this testable model of bounded rationality.

econ.TH↗
arXiv2021

Resolutions of Convex Geometries

Convex geometries (Edelman and Jamison, 1985) are finite combinatorial structures dual to union-closed antimatroids or learning spaces. We define an operation of resolution for convex geometries, which replaces each element of a base convex geometry by a fiber convex geometry. Contrary to what happens for similar constructions -- compounds of hypergraphs, as in Chein, Habib and Maurer (1981), and compositions of set systems, as in Mohring and Radermacher (1984) -- , resolutions of convex geometries always yield a convex geometry. We investigate resolutions of special convex geometries: ordinal and affine. A resolution of ordinal convex geometries is again ordinal, but a resolution of affine convex geometries may fail to be affine. A notion of primitivity, which generalize the corresponding notion for posets, arises from resolutions: a convex geometry is primitive if it is not a resolution of smaller ones. We obtain a characterization of affine convex geometries that are primitive, and compute the number of primitive convex geometries on at most four elements. Several open problems are listed.

math.CO↗
arXiv2018

Robust sustainable development assessment with composite indices aggregating interacting dimensions: the hierarchical-SMAA-Choquet integral approach

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 penalization has to be assigned on redundant criteria. An additional difficulty of the modelization is the elicitation of the parameters for the composite indices, since they are typically affected by some imprecision. In most approaches, all these critical points are usually neglected, which in turn yields an unpleasant degree of approximation in the computation of indices. In this paper we propose a methodology that allows one to simultaneously handle these delicate issues. Specifically, to take into account synergy and redundancy between criteria, we suitably aggregate indicators by means of the Choquet integral. Further, to obtain recommendations that take into account the space of fluctuation related to imprecision in nonadditive weights (capacity of the Choquet integral), we adopt the Robust Ordinal Regression (ROR) and the Stochastic Multicriteria Acceptability Analysis (SMAA). Finally, to study sustainability not only at a comprehensive level (taking into account all criteria) but also at a local level (separately taking into account economic, social and environmental aspects), we apply the Multiple Criteria Hierarchy Process (MCHP). We illustrate the advantages of our approach in a concrete example, in which we measure the rural sustainability of 51 municipalities in the province of Catania, the largest city of the East Coast of Sicily (Italy).

math.OC↗
arXiv2017

The Satisfiability Problem for Boolean Set Theory with a Choice Correspondence

Given a set U of alternatives, a choice (correspondence) on U is a contractive map c defined on a family Omega of nonempty subsets of U. Semantically, a choice c associates to each menu A in Omega a nonempty subset c(A) of A comprising all elements of A that are deemed selectable by an agent. A choice on U is total if its domain is the powerset of U minus the empty set, and partial otherwise. According to the theory of revealed preferences, a choice is rationalizable if it can be retrieved from a binary relation on U by taking all maximal elements of each menu. It is well-known that rationalizable choices are characterized by the satisfaction of suitable axioms of consistency, which codify logical rules of selection within menus. For instance, WARP (Weak Axiom of Revealed Preference) characterizes choices rationalizable by a transitive relation. Here we study the satisfiability problem for unquantified formulae of an elementary fragment of set theory involving a choice function symbol c, the Boolean set operators and the singleton, the equality and inclusion predicates, and the propositional connectives. In particular, we consider the cases in which the interpretation of c satisfies any combination of two specific axioms of consistency, whose conjunction is equivalent to WARP. In two cases we prove that the related satisfiability problem is NP-complete, whereas in the remaining cases we obtain NP-completeness under the additional assumption that the number of choice terms is constant.

cs.LO↗