Representations of votes based on pairwise information: Monotonicity versus consistency

Conditions for simple majority decision functions with intransitive individual indifference

Social Choice and Game Theory: Recent Results with a Topological Approach

The problem ofjustifying democracy arises when a society sees the need for cooperative, collective action. Collective action may be needed to solve coordination problems, public goods problems, Prisoner's Dilemmas, and other structural problems of human interaction or perhaps to realize common ideals of justice in concrete political institutions. Once the need for collective action is established, one must ask how the goals of a cooperative endeavor are to be secured. Cooperation requires that individuals, at least over a specified range of activity, pursue a joint strategy. To assure voluntary compliance in a joint venture, cooperation must be to each person's advantage. However, each person may have an incentive to induce others to cooperate and to defect from the joint strategy in the hope of enjoying the fruits of cooperation without incurring the opportunity costs of compliance. This is the essence of the Prisoner's Dilemma, and considerations of this sort suggest that if collective action is to succeed, policies or strategies formed collectively must be coercively enforceable. Coercion, however, requires justification. Because solving the problem of rational noncompliance requires that collective decisions be coercively enforceable, the rules by which collective decisions are reached require justification. Douglas Rae neatly puts the problem of justification that emerges when political solutions are coercively enforceable as follows: "Once a political community has decided which of its members are to participate directly in the making of collective policy, an important question remains: 'How many of them must agree before a policy is imposed on the community?"" This is essentially the question to which the principle of democratic rule provides an answer: by what process are collective decisions to be made? Answering Rae's question requires a normative framework. We could say that a procedure for making collective decisions is justified if and

This is an advance summary of a forthcoming article in the Oxford Research Encyclopedia of Politics. Please check back later for the full article.Narrowly understood, social choice theory is a specialized branch of applied logic and mathematics that analyzes abstract objects called preference aggregation functions, social welfare functions, and social choice functions. But more broadly, social choice theory identifies, analyzes, and evaluates rules that may be used to make collective decisions. So understood, social choice is a subfield of the social sciences that examines what may be called “voting rules” of various sorts. While social choice theory typically assumes a finite set of alternatives over which voter preferences are unrestricted, the spatial model of social choice assumes that policy alternatives can be represented by points in a space of one or more dimensions, and that voters have preferences that are plausibly shaped by this spatial structure.Social choice theory has considerable relevance for the study of legislative (as well as electoral) institutions. The concepts and tools of social choice theory make possible formal descriptions of legislative institutions such as bicameralism, parliamentary voting procedures, effects of decision rules (e.g., supramajority vs. simple majority rule and executive veto rules), sincere vs. strategic voting by legislators, agenda control, and other parliamentary maneuvers. Spatial models of social choice further enrich this analysis and raise additional questions regarding policy stability and change. Spatial models are used increasingly to guide empirical research on legislative institutions and processes.

Lost in Translation: Social Choice Theory is Misapplied Against Legislative Intent

This essay presents a sequential choice theory of legislative organization as an alternative to social choice theories. Because of the sequential process of proposal making and voting, sequential choice theory yields equilibrium predictions for both particularistic goods programs and unidimensional and multidimensional collective goods programs. The theory thus does not require legislative organization and procedures to yield stability. Although this study does not present a formal theory of the choice of legislative organization, sequential choice theory allows an assessment of collective and individualistic incentives for the choice of legislative organization and procedures. For example, the legislature has collective incentives to control individualistic incentives and can exercise control by allowing amendments to committee proposals. Sequential choice theory also addresses the durability issue that arises because current legislatures cannot bind future legislatures. In the theory, legislators position programs strategically to limit future changes. As Shepsle and Weingast indicate in their contribution to this volume, theories of legislative organization are based on an underlying body of social choice theory. The principal objective of this study is to offer an alternative theory-a sequential choice theory-as a basis for reasoning about collective choice and legislative organization. In the terminology of Shepsle and Weingast, sequential choice theory is a substitute for social choice theory in that it is not built on the results of that theory, and therefore the central issues it addresses are somewhat different. For example, sequential choice theory does not share with social choice theory the notion that institutions, other than a minimal legislative process, are necessary to capture the gains from cooperation nor that an exchange of rights is central to that capture. Instead, the theory is based on a sequential process of proposal making and voting that yields equilibrium behavior and outcomes and provides an alternative perspective on legislative organization. There are analogies between the approaches, however. The legislative implications of social choice theory are drawn from equilibria

This article discusses the role played by interpersonal comparisons (of utility or goodness) in matters of justice and equity. The role of such interpersonal comparisons has initially been made explicit in the context of social choice theory through the concept of extended preferences. Social choice theorists have generally claimed that extended preferences should be taken as being uniform across a population. Three related claims are made within this perspective. First, though it is sometimes opposed to social choice theory, the social contract approach may also consider the possibility of interpersonal comparisons. This is due to the fact that justice principles may be partially justified on a teleological basis. Second, searching for the uniformity of interpersonal comparisons is both hopeless and useless. In particular, moral disagreement does not originate in the absence of such uniformity. Third, interpersonal comparisons should be accounted for both in social choice and social contract theories in terms of sympathetic identification based on reciprocal respect and tolerance, where each person’s conception of the good partially takes care of others’ good. From the moral point of view, any person’s conception of the good should thus be ‘extended’ to others’ personal conceptions. This extension is, however, limited due to the inherent limitations in sympathetic identification and is a long way from guaranteeing the uniformity assumed by social choice theorists.

It is a research hotspot to study the social choice theory from the perspective of logic in recent years. The judgment aggregation model based on logic supports a new way for the research of social choice theory. We attempt to analyze judgment aggregation dilemmas based on the judgment aggregation model, explore different aggregation problem solutions. KEYWORD: Logic; Judgment aggregation; Escape routs International Conference on Social Science, Education Management and Sports Education (SSEMSE 2015) © 2015. The authors Published by Atlantis Press 917 ΦA. We sometimes call a member of A an agenda item. (2) consistent: A set A⊆L (L) is consistent unless A⊦LΦΦ for some ΦL(L). (3) complete: A set A⊆L (L) is complete if either ΦA or ΦA for every ΦA which does not start with negation. (4) judgment set: A judgment set is a complete and consistent subset A⊆A. (5) judgment profile: An judgment profile is an ntuple (A1,...,An) , where Ai(1≤i≤n) is the individual judgment set of agent i. J(A,L) denotes the set of all individual (complete and L-consistent) judgment sets over A. When J(A,L) n , we use i to denote the ith element of , i.e., agent i's individual judgment set in judgment profile . (6) judgment aggregation rule: A judgment aggregation rule is a function f: J(A,L) n J(A,L). The judgment aggregation rule should usually meet the following conditions: (1) Independence: The group’s judgment on any agenda item in an agenda only depends on individuals’ judgment on this agenda item and has nothing to do with other factors. (2) Unanimity: If all individuals agree with certain agenda item in the agenda, then the group holds the same view. (3) Non-dictatorship: We should not ignore others’ different judgment and make a fixed individual’s judgment always be the group’s. Discursive Dilemma: If there are at least three subjects need to make a judgment on at least two different formulas p, q, and pq, then we may find out an inconsistent group judgment if we adopt majority vote aggregation rule. Similar to Arrow’s Theorem and many other impossibility theorems, there are also several impossibility theorems in judgment aggregation. Because of the advantages of judgment aggregation which preference aggregation does not have, the social choice theory researchers gradually focus on judgment aggregation. Judgment aggregation model based on logic explores a new road for researchers on social choice theory and also provides new ideas to solve problems in social choice theory. 3 ESCAPE ROUTES FROM THE PROBLEMS OF JUDGMENT AGGREGATION The impossibility theorems in judgment aggregation not only prove that there is no perfect rule for aggregation, but also make us realize that we should relax these requirements to find an aggregation rule which can be accepted. 3.1 Restricting the domain The impossibility theorems in judgment aggregation take the aggregation rule to be defined on the domain of all judgment profiles which consist of any consistent and complete individual judgment sets and place no restriction. Dietrich and List propose that whether there is admissible restriction of domain to make sure that majority judgment of agenda items is consistent.[10] Some restrictions, which are discussed, are similar to some classic domain restrictions in preference aggregation(such as single-peakedness). The method of unidimensionally aligned is based on the idea to restrict the domain. A judgment profile is unidimensionally aligned if the individuals in N can be ordered from left to right such that the individuals who agree p for every proposition p in the agenda. Consider the following example, the agenda contains the following propositions and their negations: p: Carbon emissions are above a given threshold; pq: If Carbon emissions are above a given threshold, there will be a critical temperature increase; q: There will be a critical temperature increase. As is shown in Table 2: the result is unidimensionally aligned. Any proposition in the agenda is agreed by majority if and only if it is agreed by the median individual on the given leftright order. Here the majority judgments(group judgments) are those of individual 3. For any given judgment set of all individuals consistent, thus the majority judgment set is consistent. The method of unidimensionally aligned is strong domain-restriction condition in judgment aggregation. Only if the number of individuals is odd number, this method may be effective and must be invalid when the number of individuals is even number. Table 2 A unidimensionally aligned judgment profile Ind.1 Ind.2 Ind.3 Ind.4 Ind.5

Social choice theory, belief merging, and strategy-proofness

The subject of social choice includes within its capacious frame various problems with the common feature of relating social judgments and group decisions to the views and interests of the individuals who make up the society or the group. Some challenges and foundational problems faced by social choice theory as a discipline are discussed. Social choice theory is a subject in which formal and mathematical techniques have been very extensively used. Voting-based procedures are entirely natural for some kinds of social choice problems, such as elections, referendums, or committee decisions. They are, however, altogether unsuitable for many other problems of social choice. Impossibility results in social choice theory - led by the pioneering work of Arrow (1951) - have often been interpreted as being thoroughly destructive of the possibility of reasoned and democratic social choice, including welfare economics. That view is argued against.

The subject of social choice includes within its capacious frame various problems with the common feature of relating social judgments and group decisions to the views and interests of the individuals who make up the society or the group. Some challenges and foundational problems faced by social choice theory as a discipline are discussed. Social choice theory is a subject in which formal and mathematical techniques have been very extensively used. Voting-based procedures are entirely natural for some kinds of social choice problems, such as elections, referendums, or committee decisions. They are, however, altogether unsuitable for many other problems of social choice. Impossibility results in social choice theory - led by the pioneering work of Arrow (1951) - have often been interpreted as being thoroughly destructive of the possibility of reasoned and democratic social choice, including welfare economics. That view is argued against.

Chapter 6 - Social choice and game theory: Recent results with a topological approach

Chichilnisky attempts a unified treatment of existence problems in general equilibrium and social choice theory. More specifically, she presents results showing that a single condition on the set of agents' preferences — limited arbitrage — is necessary and sufficient for existence in the three areas of general equilibrium, social choice and game theory. What is most interesting is not so much the individual existence results,1 but the fact that a framework (an exchange economy) is presented within which it is shown that the same condition 'does the job' in all three areas.

Over the past few years there has been a lively exchange of ideas between computer science, in particular theoretical computer science and artificial intelligence, on the one hand and economics, in particular game theory and social choice, on the other. This exchange goes in both directions and has produced active research areas such as algorithmic game theory and computational social choice. Social choice theory concerns the formal analysis and design of methods for aggregating possibly conflicting preferences such as in voting, assignment, or matching problems. Much of the work in classic social choice theory has focused on results concerning the formal possibility and impossibility of aggregation functions that combine desirable properties. This tutorial provided an overview of central results in social choice theory with a special focus on axiomatic characterizations as well as computational aspects. While some aggregation functions can be easily computed, others have been shown to be computationally intractable (e.g., NP-hard or #P-hard). Topics that were covered in this tutorial included (i) rational choice theory, (ii) Arrow's impossibility theorem, (iii) tournament solutions (such as the top cycle, the uncovered set, the Banks set, or the tournament equilibrium set), and (iv) randomized social choice functions. The overarching theme were escape routes from negative results such as Arrow's impossibility theorem.

About forty colleagues from France and abroad were pleased to come to Caen from 10th to 12th June 2009 to thank and honor Maurice for the outstanding work he accomplished in the field. The meeting, entitled New Developments in Social Choice and Welfare Theories--Conferences in Honor of Maurice Salles was the annual conference of the ADRES (Association pour le Developpement de la Recherche en Economie et Statistiques). Preliminary versions of most of the papers in this special issue of Social Choice and Welfare were presented at the conference. The organizers were pleased to host Amartya Sen as a plenary speaker, and thank him for letting them publish his speech. The other nineteen articles collected here examine five aspects of modern social choice theory: Preferences and Aggregation, Voting Rules and Ranking Rules, Applications of Cooperative Game Theory, Implementing Fairness in Economic Environments, and Inequality, Poverty and Opportunities.