scholarly journals On a Theorem due to Alan D. Taylor about Aggregation of Preferences

2018 ◽  
Vol 18 (1) ◽  
pp. 17-31 ◽  
Author(s):  
Somdeb Lahiri
Keyword(s):  
Social Welfare ◽  
Individual Preference ◽  
Utility Functions ◽  
Aggregation Rule ◽  
Impossibility Theorem ◽  
Preference Aggregation ◽  
Individual Utility ◽  
Domain Restriction ◽  
Aggregation Of Preferences ◽  
Pareto Criterion

In this paper, we show that there does not exist any triple acyclic preference aggregation rule that satisfies Majority property, weak Pareto criterion and a version of a property due to Alan Taylor. We also show that there are non-dictatorial preference aggregation rules and in particular non-dictatorial social welfare functions which satisfy the weak Pareto criterion and Taylor’s Independence of Irrelevant Alternatives. Further, we are able to obtain analogous results for preference aggregation functionals by suitably adjusting the desired properties to fit into a framework which uses individual utility functions rather than individual preference orderings. Our final result is a modest generalisation of Sen’s version of Arrow’s impossibility theorem which is shown to hold under our mild domain restriction. JEL: D71

scholarly journals Low-Distortion Social Welfare Functions

2019 ◽  
Vol 33 ◽  
pp. 1788-1795 ◽  
Author(s):  
Gerdus Benadè ◽  
Ariel D. Procaccia ◽  
Mingda Qiao
Keyword(s):  
Social Welfare ◽  
Utility Functions ◽  
Preference Aggregation ◽  
Worst Case ◽  
Aggregation Methods ◽  
Lack Of Information ◽  
Low Distortion ◽  
Latent Utility ◽  
Optimal Ranking

Work on implicit utilitarian voting advocates the design of preference aggregation methods that maximize utilitarian social welfare with respect to latent utility functions, based only on observed rankings of the alternatives. This approach has been successfully deployed in order to help people choose a single alternative or a subset of alternatives, but it has previously been unclear how to apply the same approach to the design of social welfare functions, where the desired output is a ranking. We propose to address this problem by assuming that voters’ utilities for rankings are induced by unknown weights and unknown utility functions, which, moreover, have a combinatorial (subadditive) structure. Despite the extreme lack of information about voters’ preferences, we show that it is possible to choose rankings such that the worst-case gap between their social welfare and that of the optimal ranking, called distortion, is no larger (up to polylogarithmic factors) than the distortion associated with much simpler problems. Through experiments, we identify practical methods that achieve nearoptimal social welfare on average.

Assessment criteria for aggregate social welfare

2020 ◽  
Vol 19 (12) ◽  
pp. 2358-2371
Author(s):  
S.A. Moskal'onov
Keyword(s):  
Social Welfare ◽  
Mathematical Analysis ◽  
Exchange Economy ◽  
Assessment Criteria ◽  
Impossibility Theorem ◽  
New Approaches ◽  
History Of Development ◽  
Arrow's Impossibility Theorem ◽  
History Of

Subject. The article addresses the history of development and provides the criticism of existing criteria for aggregate social welfare (on the simple exchange economy (the Edgeworth box) case). Objectives. The purpose is to develop a unique classification of criteria to assess the aggregate social welfare. Methods. The study draws on methods of logical and mathematical analysis. Results. The paper considers strong, strict and weak versions of the Pareto, Kaldor, Hicks, Scitovsky, and Samuelson criteria, introduces the notion of equivalence and constructs orderings by Pareto, Kaldor, Hicks, Scitovsky, and Samuelson. The Pareto and Samuelson's criteria are transitive, however, not complete. The Kaldor, Hicks, Scitovsky citeria are not transitive in the general case. Conclusions. The lack of an ideal social welfare criterion is the consequence of the Arrow’s Impossibility Theorem, and of the group of impossibility theorems in economics. It is necessary to develop new approaches to the assessment of aggregate welfare.

A Comment on Arrow’s Impossibility Theorem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Alec Sandroni ◽  
Alvaro Sandroni
Keyword(s):  
Social Choice ◽  
Choice Function ◽  
Social Preference ◽  
Social Choice Function ◽  
Individual Preference ◽  
Impossibility Theorem ◽  
Preference Order ◽  
Individual Choice ◽  
Choice Functions ◽  
Preference Orders

AbstractArrow (1950) famously showed the impossibility of aggregating individual preference orders into a social preference order (together with basic desiderata). This paper shows that it is possible to aggregate individual choice functions, that satisfy almost any condition weaker than WARP, into a social choice function that satisfy the same condition (and also Arrow’s desiderata).

Equilibrium Strategies and Optimal Control for a Double-Ended Queue

2016 ◽  
Vol 33 (03) ◽  
pp. 1650022 ◽  
Author(s):  
Ying Shi ◽  
Zhaotong Lian
Keyword(s):  
Social Welfare ◽  
Death Process ◽  
Birth And Death Process ◽  
Individual Utility ◽  
Decentralized System ◽  
Taxi Drivers ◽  
Equilibrium Strategies ◽  
The Social ◽  
The Government ◽  
Centralized System

In this paper, we study a passenger–taxi matching queue system. The system is modeled as a birth-and-death process. Since the system is so complex, we mainly focus on numerical analysis. A centralized system and a decentralized one are considered. In the centralized system, the government sets thresholds for both passengers and taxis to maximize the social welfare. We analyze the performance measures of this model, discuss the range of two thresholds that ensures positive social welfare, and numerically give the upper bound of threshold. In the decentralized system, passengers and taxis determine whether to join the system or balk based on their individual utility functions. Further, we consider the government’s tax and subsidy to the taxi drivers. Numerical results show that the social welfare function in the centralized system is concave with respect to the thresholds and the government central planning benefits the society. In the decentralized system, no matter what the passenger and taxi arrival rates are, the social welfare is concave with respect to the taxi fare. Moreover, we analyze the effect of the arrival rates and the benefits of the tax and subsidy.

Arrow’s Theorem

2020 ◽  
Author(s):  
Conal Duddy ◽  
Ashley Piggins
Keyword(s):  
Social Welfare ◽  
Social Choice ◽  
Social Welfare Function ◽  
Social Preference ◽  
Social Choice Theory ◽  
Impossibility Theorem ◽  
Preference Ordering ◽  
Individual Values ◽  
Arrow’S Theorem ◽  
Arrow's Theorem

Kenneth Arrow’s “impossibility” theorem is rightly considered to be a landmark result in economic theory. It is a far-reaching result with implications not just for economics but for political science, philosophy, and many other fields. It has inspired an enormous literature, “social choice theory,” which lies on the interface of economics, politics, and philosophy. Arrow first proved the impossibility theorem in his doctoral dissertation—Social Choice and Individual Values—published in 1951. It is a remarkable result, and had Arrow not proved it, it is unlikely that the theorem would be known today. A social choice is simply a choice made by, or on behalf of, a group of people. Arrow’s theorem is concerned more specifically with the following problem. Suppose that we have a given set of options to choose from and that each member of a group of individuals has his or her own preference over these options. By what method should we construct a single ranking of the options for the group as a whole? Any such method may be represented mathematically by a “social welfare function.” This is a function that receives as its input the preference ordering of each individual and then generates as its output a social preference ordering. Arrow defined some properties that would seem to be essential to any reasonable social welfare function. These properties are called “unrestricted domain,” “weak Pareto,” “independence of irrelevant alternatives,” and “non-dictatorship.” Each of these properties, when taken alone, does appear to be very necessary indeed. Yet, Arrow proved that these properties are in fact mutually incompatible. This troubling fact has been central to the study of social choice ever since.

A Hybrid Utility Estimation Model for Conjoint Analysis

1981 ◽  
Vol 45 (1) ◽  
pp. 33-41 ◽  
Author(s):  
Paul E. Green ◽  
Stephen M. Goldberg ◽  
Mila Montemayor
Keyword(s):  
Individual Differences ◽  
Data Collection ◽  
Conjoint Analysis ◽  
Utility Functions ◽  
Individual Utility ◽  
Estimation Model ◽  
Utility Measurement ◽  
Antibiotic Drug ◽  
Utility Estimation

Increasingly, appliers of conjoint analysis are being faced with the need to reduce data collection demands on respondents while still obtaining enough data to estimate individual utility functions. The authors propose a model that combines the ease of self-explicated utility measurement with the greater generality of decompositional models to develop estimated utility functions that maintain individual differences. The model is applied to a conjoint study involving physicians’ evaluations of a new antibiotic drug. The paper concludes with suggestions for possible extensions of the approach.

scholarly journals Efficiency, equity, and social rationality under uncertainty

2021 ◽  
Author(s):  
Kaname Miyagishima
Keyword(s):  
Simple Model ◽  
Social Welfare ◽  
Expected Utility ◽  
Risk Preferences ◽  
Utility Functions ◽  
Subjective Expected Utility ◽  
Risk Averse ◽  
Social Rationality ◽  
Certainty Equivalents ◽  
Ex Post

AbstractIn a simple model where agents’ monetary payoffs are uncertain, this paper examines the aggregation of subjective expected utility functions which are interpersonally noncomparable. A maximin social welfare criterion is derived from axioms of efficiency, ex post equity, and social rationality, combined with the independence of beliefs and risk preferences in riskless situations (Chambers and Echenique in Games Econ Behav 76:582–595, 2012). The criterion compares allocations by the values of the prospects composed of the statewise minimum payoffs evaluated by the certainty equivalents. Because of this construction, the criterion is egalitarian and risk averse.

On the Aggregation of Preferences in Engineering Design

2001 ◽  
Author(s):  
Beth Allen
Keyword(s):  
Engineering Design ◽  
Collaborative Design ◽  
Design Space ◽  
Decision Makers ◽  
Impossibility Theorem ◽  
Von Neumann ◽  
Aggregation Of Preferences ◽  
Ordinal Preferences ◽  
Additive Separability ◽  
Alternative Designs

Abstract This paper considers the possibility for aggregation of preferences in engineering design. Arrow’s Impossibility Theorem applies to the aggregation of individuals’ (ordinal) preferences defined over a finite number of alternative designs. However, when the design space is infinite and when all individuals have monotone preferences or have von Neumann-Morgenstern (cardinal) utilities defined over lotteries, possibility results are available. Alternative axiomatic frameworks lead to additional aggregation procedures for cardinal utilities. For these results about collaborative design, aggregation occurs with respect to decision makers and not attributes, although some of the possibility results preserve additive separability in attributes.

scholarly journals Neutrality and relative acceptability in judgment aggregation

2019 ◽  
Vol 55 (1) ◽  
pp. 25-49
Author(s):  
Zoi Terzopoulou ◽  
Ulle Endriss
Keyword(s):  
Social Choice ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Practical Interest ◽  
Judgment Aggregation ◽  
Aggregation Rule ◽  
Impossibility Theorem ◽  
Collective Acceptance ◽  
Special Case

AbstractOne of the fundamental normative principles in social choice theory is that of neutrality. In the context of judgment aggregation, neutrality is encoded in the form of an axiom expressing that, when two possible judgments enjoy the same support amongst the individuals, then either both or neither of them should be accepted. This is a reasonable requirement in many scenarios. However, we argue that for scenarios in which individuals are asked to pass judgment on very diverse kinds of propositions, a notion of relative acceptability is better suited. We capture this notion by a new axiom that hinges on a binary “acceptability” relation A between propositions: if a given coalition accepting a proposition p entails the collective acceptance of p, then the same should be true for every other proposition q related to p via A. Intuitively, pAq means that p is at least as acceptable as q. Classical neutrality is then a special case where all propositions are equally acceptable. We show that our new axiom allows us to circumvent a classical impossibility theorem in judgment aggregation for certain scenarios of practical interest. Also, we offer a precise characterisation of all scenarios that are safe, in the sense that any aggregation rule respecting the relative acceptability between propositions will always return logically consistent outcomes.

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