Inequality averse criteria for evaluating infinite utility streams: The impossibility of Weak Pareto

This paper investigates ethical aggregation of infinite utility streams by representable social welfare relations. We prove that the Hammond Equity postulate and other variations of it like the Pigou-Dalton transfer principle are incompatible with positive responsiveness to welfare improvements by every generation. The case of Hammond Equity for the Future is investigated too.Social welfare function; Equity; Inequality aversion; Pareto axiom; Intergenerational justice

Liberal approaches to ranking infinite utility streams: When can we avoid interferences?

In this work we analyse social welfare relations on sets of infinite utility streams that verify various types of liberal non-interference principles. Earlier contributions have established that (finitely) anonymous and strongly Paretian quasiorderings exist that agree with axioms of that kind together with weak preference continuity and further consistency. Nevertheless Mariotti and Veneziani prove that a fully liberal non-interfering view of a finite society leads to dictatorship if weak Pareto optimality is imposed. We first prove that extending the horizon to infinity produces a reversal of such impossibility result. Then we investigate a related problem: namely, the possibility of combining “standard” semicontinuity with efficiency in the presence of non-interference. We provide several impossibility results that prove that there is a generalised incompatibility between continuity and non-interference principles, both under ordinal and cardinal views of the problem. Our analysis ends with some insights on the property of representability in the presence of non-interference assumptions. In particular we prove that all social welfare functions that verify a very mild efficiency property must exert some interference (penalising both adverse and favorable changes) on the affairs of particular generations.Pareto axiom; Intergenerational justice; Social welfare relation; Non-interference; Continuity

Intertemporal Choice of Fuzzy Soft Sets

This paper first merges two noteworthy aspects of choice. On the one hand, soft sets and fuzzy soft sets are popular models that have been largely applied to decision making problems, such as real estate valuation, medical diagnosis (glaucoma, prostate cancer, etc.), data mining, or international trade. They provide crisp or fuzzy parameterized descriptions of the universe of alternatives. On the other hand, in many decisions, costs and benefits occur at different points in time. This brings about intertemporal choices, which may involve an indefinitely large number of periods. However, the literature does not provide a model, let alone a solution, to the intertemporal problem when the alternatives are described by (fuzzy) parameterizations. In this paper, we propose a novel soft set inspired model that applies to the intertemporal framework, hence it fills an important gap in the development of fuzzy soft set theory. An algorithm allows the selection of the optimal option in intertemporal choice problems with an infinite time horizon. We illustrate its application with a numerical example involving alternative portfolios of projects that a public administration may undertake. This allows us to establish a pioneering intertemporal model of choice in the framework of extended fuzzy set theorie

Ordering infinite utility streams: set-theoretical and topological issues

[EN]Invited talk at the Eighth Italian-Spanish Conference on General Topology and its Applications

Liberal approaches to ranking infinite utility streams: When can we avoid interference?

[EN]In this work we analyse social welfare relations on sets of finite and infinite utility streams that satisfy various types of liberal non-interference principles. Earlier contributions have established that (finitely) anonymous and strongly Paretian quasiorderings exist that verify non-interference axioms together with weak preference continuity and further consistency. Nevertheless Mariotti and Veneziani prove that a fully liberal non-interfering view of a finite society leads to dictatorship if the weak Pareto principle is imposed. We first prove that this impossibility result vanishes when we extend the horizon to infinity. Then we investigate a related problem: namely, the possibility of combining \standard" semicontinuity with eficiency in the presence of non-interference. We provide several impossibility results that prove that there is a generalised incompatibility between relaxed forms of continuity and non- interference principles, both under ordinal and cardinal views of the problem

Computation of Choquet integral for finite sets: Notes on a ChatGPT-driven experience

The Choquet integral, credited to Gustave Choquet in 1954, initially found its roots in decision making under uncertainty following Schmeidler's pioneering work in this field. Surprisingly, it was not until the 1990s that this integral gained recognition in the realm of multi-criteria decision aid. Nowadays, the Choquet integral boasts numerous generalizations and serves as a focal point for intensive research and development across various domains. Here we share our journey of utilizing ChatGPT as a helpful assistant to delve into the computation of the discrete Choquet integral using Mathematica. Additionally, we have demonstrated our ChatGPT experience by crafting a Beamer presentation with its assistance. The ultimate aim of this exercise is to pave the way for the application of the discrete Choquet integral in the context of N-soft sets

The impossibility of social evaluations of infinite streams with strict inequality aversion

[EN]We are concerned with the problem of aggregating infinite utility streams and the possible adoption of consequentialist equity principles. We find a virtually universal incompatibility between the Basu–Mitra approach (that advocates for social welfare functions and renounces continuity assumptions) and postulates that capture various forms of strict preference for a reduction in inequality like the Strong Equity Principle, the Pigou–Dalton Transfer principle, or Altruistic Equity. We also prove that the Hara–Shinotsuka–Suzumura–Xu impossibility for semicontinuous social welfare relations remains under the latter distributional postulate

Finite sets of data compatible with multidimensional inequality measures

[EN]By using a general solution to the problem of extending a preorder conditional on a list of ex-ante comparisons between pairs, we elucidate when a finite set of predetermined comparisons can be incorporated to a multidimensional inequality measure even if the population size is variable

Fuzzy sets from the ethics of social preferences: slides for ESTYLF 2014

[EN]We show that the problem of evaluating infinite sequences (or streams) of utilities by a unique utility (or social welfare function) can be stated in terms of fuzzy subsets of the set of infinite utility sequences. For each stream, its evaluation can be viewed as its degree of membership to the subset of ‘ethically acceptable’ streams within the set of possible sequences. Since the property ‘being ethically acceptable’ is not well defined and cannot be exactly measured, the fuzzy approach seems especially adequate

Goodness of fit in optimizing consumer's model

We provide two new indices of efficiency for determining the degree of coherence in an agent's consumption decisions. We analyze to which extent they improve the efficiency displayed by Varian's (Journal of Econometrics, 1990) index. We report on the results of a Montecarlo experiment that confirms that strict improvements of Varian's vector-index appear on a regular basis.Consumer behavior; GARP; revealed preference; goodness of fit