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.

scholarly journals Measuring Fairness, Inequality, and Big Data: Social Choice Since Arrow

2019 ◽  
Vol 22 (1) ◽  
pp. 435-460
Author(s):  
John W. Patty ◽  
Elizabeth Maggie Penn
Keyword(s):  
Big Data ◽  
Social Choice ◽  
Institutional Design ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Impossibility Theorem ◽  
Axiomatic Method ◽  
Subsequent Work ◽  
Fundamental Interest ◽  
Starting Point

Kenneth J. Arrow was one of the most important intellectuals of the twentieth century, and his “impossibility theorem” is arguably the starting point of modern, axiomatic social choice theory. In this review, we begin with a brief discussion of Arrow's theorem and subsequent work that extended the result. We then discuss its implications for voting and constitutional systems, including a number of seminal results—both positive and negative—that characterize what such systems can accomplish and why. We then depart from this narrow interpretation of the result to consider more varied institutional design questions such as apportionment and geographical districting. Following this, we address the theorem's implications for measurement of concepts of fundamental interest to political science such as justice and inequality. Finally, we address current work applying social choice concepts and the axiomatic method to data analysis more generally.

scholarly journals Belief Merging and Judgment Aggregation in Fuzzy Setting

2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
Author(s):  
Ismat Beg ◽  
Nabeel Butt
Keyword(s):  
Fuzzy Logic ◽  
Social Choice ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Judgment Aggregation ◽  
Belief Merging ◽  
Aggregation Functions ◽  
Fuzzy Aggregation ◽  
Doctrinal Paradox ◽  
Fuzzy Setting

We explore how judgment aggregation and belief merging in the framework of fuzzy logic can help resolve the “Doctrinal Paradox.” We also illustrate the use of fuzzy aggregation functions in social choice theory.

A difficulty in Arrow’s impossibility theorem

2017 ◽  
Vol 44 (12) ◽  
pp. 1609-1621
Author(s):  
Khandakar Qudrat-I Elahi
Keyword(s):  
Social Choice ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Impossibility Theorem ◽  
Symbolic Logic ◽  
Social Scientists ◽  
Global Village ◽  
Content Type ◽  
Counter Example ◽  
Behavioural Characteristics

Purpose The purpose of this paper is twofold. First, it evaluates the impossibility proposition, called the “Arrow impossibility theorem” (AIT), which is widely attributed to Arrow’s social choice theory. This theorem denies the possibility of arriving at any collective majority resolution in any group voting system if the social choice function must satisfy “certain natural conditions”. Second, it intends to show the reasons behind the proliferation of this impossibility impression. Design/methodology/approach Theoretical and philosophical. Findings Arrow’s mathematical model does not seem to suggest or support his impossibility thesis. He has considered only one voting outcome, well known by the phrase “the Condorcet paradox”. However, other voting results are equally likely from his model, which might suggest unambiguous majority choice. This logical dilemma has been created by Arrow’s excessive dependence on the language of mathematics and symbolic logic. Research limitations/implications The languages of mathematics and symbolic logic – numbers, letters and signs – have definite advantages in scientific argumentation and reasoning. These numbers and letters being invented however do not have any behavioural characteristics, which suggests that conclusions drawn from the model merely reflect the author’s opinions. The AIT is a good example of this logical dilemma. Social implications The modern social choice theory, which is founded on the AIT, seems to be an academic assault to the system of democratic governance that is dominating current global village. By highlighting weaknesses in the AIT, this paper attempts to discredit this intellectual omission. Originality/value The paper offers a counter example to show that the impossibility of social choice is not necessarily implied by the Arrow’s model. Second, it uses Locke’s theory of human understanding to explain why the concerned social scientists are missing this point. This approach is probably entirely novel in this area of research.

scholarly journals Impossibility in Belief Merging (Extended Abstract)

2018 ◽  
Author(s):  
Amilcar Mata Diaz ◽  
Ramon Pino Perez
Keyword(s):  
Social Choice ◽  
Propositional Logic ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Impossibility Theorem ◽  
General Version ◽  
Representation Theorems ◽  
Belief Merging ◽  
Epistemic States ◽  
Standard Domain

With the aim of studying social properties of belief merging and having a better understanding of impossibility, we extend in three ways the framework of logic-based merging introduced by Konieczny and Pino Perez. First, at the level of representation of the information, we pass from belief bases to complex epistemic states. Second, the profiles are represented as functions of finite societies to the set of epistemic states (a sort of vectors) and not as multisets of epistemic states. Third, we extend the set of rational postulates in order to consider the epistemic versions of the classical postulates of social choice theory: standard domain, Pareto property, independence of irrelevant alternatives and absence of dictator. These epistemic versions of social postulates are given, essentially, in terms of the finite propositional logic. We state some representation theorems for these operators. These extensions and representation theorems allow us to establish an epistemic and very general version of Arrow's impossibility theorem. One of the interesting features of our result, is that it holds for different representations of epistemic states; for instance conditionals, ordinal conditional functions and, of course, total preorders.

Traditional Social Choice

2011 ◽  
Author(s):  
Michel Balinski ◽  
Rida Laraki
Keyword(s):  
Social Choice ◽  
Choice Theory ◽  
Condorcet Winner ◽  
Social Choice Theory ◽  
Choice Rule ◽  
Impossibility Theorem ◽  
Traditional Methods ◽  
Method Choice ◽  
Independence Of Irrelevant Alternatives ◽  
Strong Contender

This chapter offers information on traditional methods and concepts of social choice theory, including one proposed by Condorcet, known today as Copeland’s method, Borda’s method, Dasgupta-Maskin method, and Nanson’s method. Choice rule versions of Arrow’s impossibility theorem and the fundamentals of Arrow’s model that are comparisons between pairs of alternatives, competitors, or candidates, are also discussed. The Dasgupta-Maskin method focuses on the primacy of a Condorcet-winner that is a strong contender and is one of the dominant concepts in the theory of voting. Two important failures associated with Borda-ranking are its manipulability and violation of independence of irrelevant alternatives.

Liberal Rights in a Pareto-optimal Code

Utilitas ◽  
2006 ◽  
Vol 18 (1) ◽  
pp. 61-79 ◽  
Author(s):  
JONATHAN RILEY
Keyword(s):  
Social Choice ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Impossibility Theorem ◽  
Optimal Code ◽  
Personal Liberty ◽  
Key Steps ◽  
Individual Choices ◽  
Selection Of ◽  
Made In

A Millian response is presented to Sen's celebrated Paretian liberal impossibility theorem. It is argued that Millian Paretian liberalism is possible, if the application of Paretian norms is restricted to the selection of an optimal code of liberal justice and rights, as well as to individual choices made in compliance with the rules of the code. Key steps in outlining the Millian response include suitably modifying Sen's social choice formulation of the idea of claim-right to personal liberty, and incorporating within social choice theory the distinction between a right and its direction of exercise. The Millian response is illustrated in the context of Sen's original example of the ‘prude’ and the ‘lewd’. If the argument is successful, coherent and appealing liberal versions of Pareto-inclusive philosophies such as utilitarianism, contractualism and neo-republicanism are feasible in principle.

scholarly journals The Death of Welfare Economics

2019 ◽  
Vol 51 (5) ◽  
pp. 827-865 ◽  
Author(s):  
Herrade Igersheim
Keyword(s):  
Social Welfare ◽  
Social Choice ◽  
Social Welfare Function ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Welfare Economics ◽  
Impossibility Result ◽  
Impossibility Theorem ◽  
Individual Values ◽  
The Social

The death of welfare economics has been declared several times. One of the reasons cited for these plural obituaries is that Kenneth Arrow’s impossibility theorem, as set out in his pathbreaking Social Choice and Individual Values in 1951, has shown that the social welfare function—one of the main concepts of the new welfare economics as defined by Abram Bergson (Burk) in 1938 and clarified by Paul Samuelson in the Foundations of Economic Analysis—does not exist under reasonable conditions. Indeed, from the very start, Arrow kept asserting that his famous impossibility result has direct and devastating consequences for the Berg-son-Samuelson social welfare function, though he seemed to soften his position in the early eighties. On his side, especially from the seventies on, Samuelson remained active on this issue and continued to defend the concept he had devised with Bergson, tooth and nail, against Arrow’s attacks. The aim of this article is precisely to examine this rather strange controversy, which is almost unknown in the scientific community, even though it lasted more than fifty years and involved a conflict between two economic giants, Arrow and Samuelson, and, behind them, two distinct communities—welfare economics, which was on the wane, against the emerging social choice theory—representing two conflicting ways of dealing with mathematical tools in welfare economics and two different conceptions of social welfare.

Social choice

2018 ◽  
Author(s):  
Alan Hamlin
Keyword(s):  
Social Choice ◽  
Choice Theory ◽  
Formal Analysis ◽  
Social Choice Theory ◽  
Political Process ◽  
Impossibility Theorem ◽  
Social Evaluation ◽  
Individual Values ◽  
Individual Preferences ◽  
Famous Result

Social choice theory is the branch of economics concerned with the relationships between individual values, preferences and rights and collective decision making and evaluation. Social choice theory therefore provides connections between the formal analysis of rational choice, the debate on political process, and ethics. A central theme in social choice theory has been the aggregation of individual preferences into either a social decision rule or a social evaluation rule. The most famous result in social choice theory – Arrow’s impossibility theorem – is that such aggregation is impossible if individual preferences are conceived as ordinal in nature, and if the aggregation procedure is to satisfy certain apparently reasonable conditions. This result implies that neither a voting system nor a system of moral evaluation can be found that satisfies all of the required conditions. Further impossibility theorems arise from attempts to model the role of individual rights. Much of social choice theory is concerned with interpreting, extending and questioning these impossibility theorems in a variety of contexts. This discussion has generated an extensive interchange at the margins of economics and ethics on topics such as the commensurability of values and the relationship between morality and rationality.

Sign in / Sign up

Export Citation Format

Share Document