Pareto Condition Research Articles

Temptation and self‐control for the impure benevolent planner: The case of heterogeneous discounting

AbstractThis paper presents a “behavioral” model of a normative benevolent social planner, who faces a self‐control problem when he/she is in charge of aggregating diverse and conflicting preferences of individuals. The model is presented in the context of aggregating preferences over intertemporal streams of social outcomes, in which Zuber and Jackson and Yariv have shown the impossibility of a time‐consistent and Paretian social objective function. Unlike previous studies, our investigation focuses on the compatibility of the Pareto condition with the impure social planner who has a dynamically consistent self‐control utility function characterized by Gul and Pesendorfer. Assuming that the social planner is tempted to adopt the majority's opinion when there is a conflict of opinions among individuals, the paper characterizes an aggregation form in which the planner is allowed to depart from dictatorship in ex‐post choice under noncommitment.

An Evolutionary Approach of Grasp Synthesis for Sheet Metal Parts With Multitype Grippers

AbstractRobot-mounted grippers are used to position, immobilize, and manipulate parts and assemblies during manufacturing. In the design of these systems, the gripper assembly, comprising the grippers that grasp the part and the frame that holds them together, is customized to each part. Due to the large number of design variables and unique design needs for each gripper, automation of gripper assemblies has been limited, especially where multiple gripper types are used to grasp a part. To this end, this article presents an evolutionary approach that synthesizes and optimizes grasps and gripper assembly layouts using two different gripper types—suction cups and magnets—from the geometric models of sheet metal parts. The method first generates an option space of gripper placement on the suitable faces of the part model. Then, a genetic algorithm generates grasps on this option space by varying both the count and locations of each gripper type. Through generations, these grasps are optimized against five criteria and one constraint: factor of safety, cost, residual moment, deflection, frame weight, and gripper clearance. These criteria are then combined into a single criterion that represents a pareto condition for assessing the grasps. The algorithm is implemented in software code for validation, and the article presents detailed validation of the algorithm using four sheet metal parts. The results show that the algorithm improves the grasp from all six aspects, when started from either program-assigned or user-defined initial grasps. The high agreement between the final grasp designs resulting from multiple runs of the algorithm on a part illustrates the stability and repeatability of the algorithm.

Utilitarianism and social discounting with countably many generations

We extend Harsanyi’s (1955) utilitarianism theorem to an infinite-horizon multi-generation setting: Under some additional assumptions, the Pareto condition is equivalent to utilitarian aggregation and the utilitarian weights are unique. We analyze the properties of utilitarian weights, such as the limiting behavior of utilitarian weights for distant future generations, and the comparative statics of utilitarian weights as the social discount factor or the social risk attitude changes. Among other findings, we show that a higher social discount rate is associated with a more unequal assignment of utilitarian weights across generations.

Smooth aggregation of Bayesian experts

I study the ex-ante aggregation of preferences of Bayesian agents in a purely subjective framework. I relax the assumption of a Bayesian social preference while keeping the Pareto condition. Under a simple axiom that relates society's preference to those of the agents, I obtain an additively separable representation of society's preference. Adding an ambiguity aversion axiom I obtain a representation that resembles the Smooth Ambiguity Criterion of Klibanoff et al. (2005). I then briefly consider applications of this framework to inequality and treatment choice under ambiguity.

Roberts’ weak welfarism theorem: a minor correction

Roberts’ “weak neutrality” or “weak welfarism” theorem concerns Sen social welfare functionals which are defined on an unrestricted domain of utility function profiles and satisfy independence of irrelevant alternatives, the Pareto condition, and a form of weak continuity. Roberts (Rev Econ Stud 47(2):421–439, 1980) claimed that the induced welfare ordering on social states has a one-way representation by a continuous, monotonic real-valued welfare function defined on the Euclidean space of interpersonal utility vectors—that is, an increase in this welfare function is sufficient, but may not be necessary, for social strict preference. A counter-example shows that weak continuity is insufficient; a minor strengthening to pairwise continuity is proposed instead and its sufficiency demonstrated.

Social decision for a measure society

Preference aggregation is here investigated for a society defined as a measure space of individuals and called a measure society. Individual preferences are represented through continuous vnm utilities. It is shown that aggregating preferences in an utilitarian way for any kind of measure society is possible under adapted Pareto conditions.

Utilitarian Aggregation with Heterogeneous Beliefs

The utilitarian aggregation rule requires social utility and beliefs to be a convex combination of individual utilities and beliefs, respectively. Since, in the case of belief heterogeneity, the standard Pareto condition is incompatible with such a separate aggregation, a new condition, called the belief-proof Pareto condition, is proposed to alleviate occurrences of spurious agreement by restricting unanimity to beliefs that can be considered reasonable by society. Then, we show, in the Anscombe-Aumann and the Savage framework, that the belief-proof Pareto condition is equivalent to separate aggregation of individual beliefs and tastes. (JEL D11, D71, D83)

Expert group information formalization based on Z-numbers

A model for formalizing expert group information with a given level of reliability was developed in the paper. To formalize the information Z-numbers were used, components of which are formalizations (fuzzy numbers) of terms of Full Orthogonal Semantic Scopes (linguistic variables with the properties of completeness and orthogonality). If experts evaluate a characteristic X of objects, then individual expert criteria for evaluating this characteristic are represented as a set of Z-numbers, the first components of which are formalizations of the terms of Full Orthogonal Semantic Scope with the title X, and the second component are formalizations of the terms of Full Orthogonal Semantic Scope with the title “Reliability”. The group expert criterion is also determined in the form of a set of Z-numbers, first components of which satisfy the Pareto condition. For Z-numbers, aggregation segments are determined, which are used to determine the distance between two Z-numbers and to recognize the reliability of the group expert criterion. Reliability recognition and identification with one of the linguistic terms (and, accordingly, with the fuzzy number formalizing this term) of the semantic scope “Reliability” is based on a comparative analysis of the distances between Z-number belonging to the group criterion and Z-numbers, the first component of which coincides with the first component of Z-number from the group criterion, and the second components are formalizations of the terms of semantic scope “Reliability”. The reliability of expert group evaluation (the second component of Z-number from the group criterion) is determined by the linguistic value (and, accordingly the fuzzy number formalizing this value) that corresponds to the minimum distance.

Endogenous Fertility, Externality and Phase Out of Pensions

This paper exploits a well accepted inefficiency that arises out of Pay-As-You-Go (PAYG) pensions itself to phase it out in a Pareto way. The positive externality of having children in a PAYG pension system is carefully utilized to phase the pensions out. In a model with endogenous fertility the paper first confirms the sub-optimality of parent’s choices and recommends an intergenerationally balanced childcare subsidy to correct for the externalities in a PAYG system. However, if PAYG pension program needs to be dismantled for various reasons, it can be phased out from there infinite time and, more importantly, just by exploiting the above mentioned externalities keeping the Pareto conditions intact. This phase out plan under Pareto satisfies all the standard efficiency criteria suggested in the literature when fertility is endogenous.

Countably Infinite Utilitarian Aggregation

We extend Harsanyi's (1955) utilitarianism theorem to an infinite-horizon multi-generation setting: Under some additional assumptions, the Pareto condition is equivalent to utilitarian aggregation and the utilitarian weights are unique. Our results facilitate analysis of the properties of utilitarian weights, such as the limiting behavior of utilitarian weights for distant future generations, and the comparative statics of utilitarian weights as the social discount factor or the social risk attitude changes. Among other findings, we show that a higher social discount rate is associated with a more unequal assignment of utilitarian weights across generations.

Social preference under twofold uncertainty

We investigate the conflict between the ex ante and ex post criteria of social welfare in a new framework of individual and social decisions, which distinguishes between two sources of uncertainty, here interpreted as being objective and subjective, respectively. This framework makes it possible to endow the individuals and society not only with ex ante and ex post preferences, as is usually done, but also with interim preferences of two kinds, and correspondingly, to introduce interim forms of the Pareto principle. After characterizing the two social welfare criteria, we present two compromises between them, one based on the ex ante criterion and absorbing as much as possible of the ex post criterion (Theorem 1), the other based on the ex post criterion and absorbing as much as possible of the ex ante criterion (Theorem 2). Both solutions translate the assumed Pareto conditions into weighted additive utility representations, as in Harsanyi’s Aggregation Theorem, and both attribute to the individuals common probability values on the objective source of uncertainty, and different probability values on the subjective source. We discuss these solutions in terms of the by now classic spurious unanimity argument and a novel informational argument labeled complementary ignorance. The paper complies with the standard economic methodology of basing probability and utility representations on preference axioms.

Smooth Aggregation of Bayesian Agents

I study the ex-ante aggregation of preferences of Bayesian agents in a purely subjective framework. Unlike Gilboa et al. (2004), I relax the assumption of Bayesian society while keeping the Pareto condition. Under a simple axiom that relates society’s preference to those of the agents, I obtain an additive separable representation of society’s preference. A strengthening of this axiom leads to a representation that resembles the Smooth Ambiguity Criterion of Klibanoff et al. (2005). I then study the properties of this representation, characterizing when society can be deemed to be ambiguity averse. I then briefly consider applications of this framework to study the Precautionary Principle and treatment choice under ambiguity.

On linear aggregation of infinitely many finitely additive probability measures

We discuss Herzberg’s (Theory Decis 78(2):319–337, 2015) treatment of linear aggregation for profiles of infinitely many finitely additive probabilities and suggest a natural alternative to his definition of linear continuous aggregation functions. We then prove generalizations of well-known characterization results due to (J Am Stat Assoc 76(374):410–414, 1981). We also characterize linear aggregation of probabilities in terms of a Pareto condition, de Finetti’s notion of coherence, and convexity.

An axiomatic approach to axiological uncertainty

How ought you to evaluate your options if you’re uncertain about which axiology is true? One prominent response is Expected Moral Value Maximisation (EMVM), the view that under axiological uncertainty, an option is better than another if and only if it has the greater expected moral value across axiologies. EMVM raises two fundamental questions. First, there’s a question about what it should even mean. In particular, it presupposes that we can compare moral value across axiologies. So to even understand EMVM, we need to explain what it is for such comparisons to hold. Second, assuming that we understand it, there’s a question about whether EMVM is true. Since there are many plausible rivals, we need an argument to defend it. In this paper, I’ll introduce a representation theorem for axiological uncertainty to answer these two questions. Roughly, the theorem shows that if all our axiologies satisfy the von Neumann–Morgenstern axioms, and if the facts about which options are better than which in light of your uncertainty also satisfy these axioms as well as a Pareto condition, then these facts have a relevantly unique expected utility representation. If I’m right, this theorem at once affords us a compelling way to understand EMVM—and specifically intertheoretic comparisons—and a systematic argument for its truth.

Securing basic well-being for all

The purpose of this article is to examine the possibility of a social choice rule to implement a social policy for “securing basic well-being for all.” The article introduces a new scheme of social choice, called a social relation function (SRF), which associates a reflexive and transitive binary relation over a set of social policies to each profile of individual well-being appraisals and each profile of group evaluations. As part of the domains of SRFs, the available class of group evaluations is constrained by three conditions. Furthermore, the non-negative response (NR) and the weak Pareto condition (WP) are introduced. NR demands giving priority to group evaluation, while treating the groups as formally equal relative to each other. WP requires treating impartially the well-being appraisals of all individuals. In conclusion, this article shows that under some reasonable assumptions, there exists an SRF that satisfies NR and WP.

On a Theorem Due to Alan D. Taylor about Aggregation of Preferences

In this paper we show that there does not exist any triple acyclic voting rule that satisfies Condorcet’s property, Pareto condition and a version of a property due to Alan Taylor. We also show that there are non-dictatorial voting rules and in particular non-dictatorial social welfare functions which satisfy the Pareto criterion and Taylor’s Independence of Irrelevant Alternatives.

Social Preference Under Twofold Uncertainty

We investigate the conflict between the ex ante and ex post criteria of social welfare in a novel axiomatic framework of individual and social decisions, which distinguishes between a subjective and an objective source of uncertainty. This framework permits us to endow the individuals and society not only with ex ante and ex post preferences, as is classically done, but also with interim preferences of two kinds, and correspondingly, to introduce interim forms of the Pareto principle. After characterizing the ex ante and ex post criteria, we present a first solution to their conflict that amounts to extending the former as much possible in the direction of the latter. Then, we present a second solution, which goes in the opposite direction, and is our preferred one. This solution combines the ex post criterion with an objective interim Pareto principle, which avoids the pitfalls of the ex ante Pareto principle, and especially the problem of "spurious unanimity" discussed in the literature. Both solutions translate the assumed Pareto conditions into weighted additive utility representations, and both attribute common individual probability values only to the objective source of uncertainty.

Arrow-type results under fuzzy preferences based on filter and ultrafilter

In this paper, we determine, for a given t-norm T, the algebraic structures of the set of decisive coalitions of a Fuzzy Aggregation Rule (FAR) defined from the set of profiles of fuzzy T-pre-orders to the set of fuzzy T-pre-orders. More precisely, we show that the set of decisive coalitions is a pre-filter on the finite set of voters when the FAR satisfies Pareto Condition (PC). When the FAR satisfies PC and Independence of Irrelevant Alternatives (IIA), we determine additional conditions on social preferences (range) under which the set of decisive coalitions is respectively a filter and an ultrafilter on the set of voters. From these two results, we outline two fuzzy Arrow-type results: the generator of the filter is an oligarchy (that is a decisive coalition where every member has a veto) for the FAR and the generator of the ultrafilter is a dictator for the FAR. We deduce that the usual FAR, defined in Dutta (1987) [7] and analyzed in Fono and Andjiga (2005) [8], is an oligarchy by showing that its set of decisive coalitions is the filter having the set of voters as unique element.

Social choice without the Pareto principle under weak independence

We show that the class of social welfare functions that satisfy a weak independence condition identified by Campbell (J Econ 12:259–272, 1976) and Baigent (J Econ 47(4):407–411, 1987) is fairly rich and freed of a power concentration on a single individual. This positive result prevails when a weak Pareto condition is imposed. Moreover, under weak independence, an impossibility of the Wilson (J Econ 5:478–486, 1972) type vanishes.

Singularity and Arrow’s paradox

In this thesis we establish a completion theory of Arrow’s work, extending it from quasi-form to absolute form and generalizing it to a degree theorem of various forms. It is proved that Arrow’s independence of irrelevant alternatives (AI ) is inconsistent with some forms of Pareto condition, e.g. with the strong Pareto condition. Based on these observations, we try to resolve Arrow’s paradox by introducing the “extent principle” and set up a weak Arrow’s framework to show the consistency of the weak AI , the weak Pareto condition, anonymity, no decisive minority group and other widely-accepted rationality principles. Singularity is the core concept of the paper.