Choice procedures and power structure in social decisions

Colman (1984) has proposed a new justification for studying the weak Borda effect. He argues that it represents the violation by the plurality procedure of the weak dominance axiom. Weak dominance is a condition which some social choice theorists consider that a fair and reasonable collective choice procedure should satisfy. However, there are fundamental difficulties associated with this new position. The criterion defined by Colman as underlying the weak Borda effect differs considerably from the weak dominance axiom. It is also inconsistent with the definition of the weak Borda effect itself. Moreover, it can be argued that the criterion underlying the weak Borda effect is in fact an unreasonably severe standard. It confounds an undesirable requirement (that only tied winners should be permitted when there is a cyclical majority) with a desirable requirement (the Condorcet criterion). Thus, only social choice procedures with a tendency to produce indecisive outcomes can satisfy the criterion. Other problems with the approach are pointed out. It is concluded that the weak Borda effect is of little relevance to social choice theory.

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.

Various voting rules (or social choice procedures) have been proposed to select a winner from the preferences of an entire population: Plurality, veto, Borda, Minimax, Copeland, etc. Although in theory, these rules may yield drastically different outcomes, for real-world datasets, behavioral social choice analyses have found that the rules are often in perfect agreement with each other! This work attempts to give a mathematical explanation of this phenomenon. We quantify the gap between the outcomes of two voting rules by the pairwise margin between their winners. We show that for many common voting rules, the gap between them can be almost as large as 1 when the votes are unrestricted. As a counter, we study the behavior of voting rules when the vote distribution is a uniform mixture of a small number of multinomial logit distributions. This scenario corresponds to a population consisting of a small number of groups, each voting according to a latent preference ranking. We show that for any such voting profile on g groups, at least 1/2g fraction of the population prefers the winner of a Borda election to any other candidate.

Chapter Fifteen - Competitive Market Mechanisms as Social Choice Procedures

This Chapter extends the ideas deal with description of individual opinions and social decisions that were briefly presented in Chapter 1. Section 2.2 investigates various types of binary relations and defines the notion of pair-dominant, or rationalizable by a binary relation, choice. In this Section main types of binary relations used in social choice theory are defined — linear orders, weak orders, strict partial orders, and acyclic relations. Section 2.3 gives another well-known concept of choice, based on the ‘extremization paradigm’ — that of a choice function rationalizable by some numerical (utility) function, studies the classical unicriterial and multicriterial choice models. We study three different types of multicriteral models — Paretian, weak Paretian, and joint-extremal ones. The equivalence of Paretian and weak Paretian models is shown. Section 2.4 lists Expansion-Contraction Axioms (rationality conditions) for choice functions, and studies their mutual relations. The axioms of Heredity, Concordance, Outcast, Arrow’s Choice Axiom in different versions, Choice Monotonicity, Choice Resolutness are studied. Section 2.5 establishes relations between the classes of rationalizable choice functions and the domains in the space of choice functions described in Section 2.4. The classical pair-dominant choice functions are shown to define a small, but important part of the models describing individual opinions and social decisions. Section 2.6 contains concluding remarks and gives a guide to the literature.

The theory of social choice is concerned with the problem of aggregating the preferences of several persons into a single preference order. The problem has the same structure as that of aggregating the preference orders of a single person with regard to several aspects of alternatives into a single preference order on the set of alternatives. For this reason, the theory of social choice comes logically not under the topic of collective action (as one might suppose) but rather under the topic of multi-objective decisions. This is so because the several participants in a situation defined as a problem of social choice do not really select courses of action among several available ones when they present their preference orders on a set of alternatives. Therefore they are not ‘actors’, as actors are defined in the theory of decision. To be sure, there are situations where voters do choose strategies, that is, choose among different preference orders to present, which may or may not represent their true preferences but which they believe will be more likely to lead to a more desirable aggregated order. These situations can be considered as n-person decision problems, and we will examine them in the context of non-cooperative n-person games (see Chapter 14. At this time, however, we will suppose that each voter acts ‘sincerely’, that is, presents his ‘actual’ preference order. The decision is now up to some agency, which must combine all these submitted preference orders into a ‘social’ preference order.KeywordsSocial ChoicePreference OrderPareto OptimalitySocial Welfare FunctionSimple MajorityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

and overview: Social decision making on technological projects.- Social choice theory and practice.- Promoting personal decisions supporting the achievement of risky public goods.- Cognitive dimensions of conflicts over new technology.- Approaches towards conflict resolution in decision processes.- Requisite decision modelling for technological projects.- Value oriented social decision analysis: a communication tool for public decision making on technological projects.- Contributing to social decision methodology: citizen reports on technological projects.- Computer assisted group decision making.- Technological risk, policy theories and public perception in connection with the siting of hazardous facilities.- Planning and procedural aspects of the windfarm project of the Dutch Electricty Generating Board.- Current radioactive waste management policy in the Netherlands.- Nuclear waste: public perception and siting policy.- Designing technological hazard information programs: towards a model of risk-adaptive decision making.- Decision making in technological emergencies.- Social decision making on technological projects: review of key issues and a recommended procedure.- Author index.- Appendix: Authors' Addresses.

Journal Article Algorithms for Social Choice Functions Get access Donald E. Campbell Donald E. Campbell Ontario Economic Council and University of Toronto Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 47, Issue 3, April 1980, Pages 617–627, https://doi.org/10.2307/2297312 Published: 01 April 1980 Article history Received: 01 June 1977 Accepted: 01 April 1979 Published: 01 April 1980

Perhaps the most influential result in social choice theory is Arrow’s impossibility theorem, which states that a seemingly modest set of desiderata cannot be satisfied when aggregating preferences [1]. While Arrow’s theorem might appear rather negative, it can also be interpreted in a positive way by identifying what can be achieved in preference aggregation.In this talk, I present a number of variations of Arrow’s theorem–such as those due to Mas-Colell and Sonnenschein [8] and Blau and Deb [2]–in their choice-theoretic version. The critical condition in all these theorems is the assumption of a rationalizing binary relation or equivalent notions of choice-consistency. The bulk of my presentation contains three escape routes from these results. The first one is to ignore consistency with respect to a variable set of alternatives altogether and require consistency with respect to a variable electorate instead. As Smith [12] and Young [14] have famously shown, this essentially characterizes the class of scoring rules, which contains plurality and Borda’s rule. For the second escape route, we factorize choice-consistency into two parts, contraction-consistency and expansions-consistency [11]. While even the mildest dose of the former has severe consequences on the possibility of choice, varying degrees of the latter characterize a number of appealing social choice functions, namely the top cycle, the uncovered set, and the Banks set [3,9,4]. Finally, I suggest to redefine choice-consistency by making reference to the set of chosen alternatives rather than individual chosen alternatives [6]. It turns out that the resulting condition is a weakening of transitive rationalizability and can be used to characterize the minimal covering set and the bipartisan set. Based on a two decades-old conjecture due to Schwartz [10], the tournament equilibrium set can be characterized by the same condition or, alternatively, by a weak expansion-consistency condition from the second escape route. Whether Schwartz’s conjecture actually holds remains a challenging combinatorial problem as well as one of the enigmatic open problems of social choice theory.Throughout the presentation I will discuss the algorithmic aspects of all considered social choice functions. While some of the mentioned functions can be easily computed, other ones do not admit an efficient algorithm unless P equals NP [13,5,7].

A promising direction in computational social choice is to address research problems using computer-aided proving techniques. In particular with SAT solvers, this approach has been shown to be viab...

Arrow's theorem is really a theorem about the independence condition. In order to show the very crucial role that this condition plays, the theorem is proved in a refined version, where the use of the Pareto condition is almost avoided. A distinction is made between group preference functions and group decision functions, yielding respectively preference relations and optimal subsets as values. Arrow's theorem is about the first kind, but some ambiguities and mistakes in his book are explained if we assume that he was really thinking of decision functions. The trouble then is that it is not clear how to formulate the independence condition for decision functions. Therefore the next step is to analyse Arrow's argument for accepting the independence condition. The most frequent ambiguity depends on an interpretation of A as the set of all conceivable alternatives, while the variable subset B is the set of all feasible or available alternatives. He then argues that preferences between alternatives that are not feasible shall not influence the choice from the set of available alternatives. But even if this principle is accepted, it only forces us to require independence with respect to some specific set B and not to every B simultaneously. Therefore the independence condition cannot be accepted on these grounds. Another argument is about an election where one of the candidates dies. On one interpretation this argument can be taken to support an independence requirement which leads to a contradiction. On another interpretation it is a condition about connexions between choices from different sets. The so-called problem of binary choice is found to be different from the independence problem and it plays no essential role in Arrow's impossibility result. Other impossibility results by Sen, Batra and Pattanaik and by Schwartz are of a different character. In the last section, several weaker independence conditions are presented. Their relations to Arrow's condition are stated and the arguments supporting them are discussed.

A social choice correspondence is self-implementable in strong equilibrium if it is implementable in strong equilibrium by a social choice function selecting from the correspondence itself as a game form. We characterize all social choice correspondences implementable this way by an anonymous social choice function satisfying no veto power, given that the number of agents is large relative to the number of alternatives. It turns out that these are exactly the social choice correspondences resulting from feasible elimination procedures as introduced in Peleg (Econometrica 46:153–161, 1978).

<p>One important issue in mechanism design theory is to model agents’ behaviors under uncertainty. The classical approach assumes that agents hold commonly known probability assessments towards uncertainty, which has been challenged by economists in many fields. My thesis adopts alternative methods to model agents’ behaviors. The new findings contribute to understanding how the mechanism designer can benefit from agents’ uncertainty aversion and how she should respond to the lack of information on agents’ probability assessments.</p> <p>Chapter 1 of this thesis allows the mechanism designer to introduce ambiguity to the mechanism. Instead of informing agents of the precise payment rule that she commits to, the mechanism designer can tell agents multiple payment rules that she may have committed to. The multiple payment rules are called ambiguous transfers. As agents do not know which rule is chosen by the designer, they are assumed to make decisions based on the worst-case scenario. Under this assumption, this chapter characterizes when the mechanism designer can obtain the first-best outcomes by introducing ambiguous transfers. Compared to the standard approach where the payment rule is unambiguous, first-best mechanism design becomes possible under a broader information structure. Hence, there are cases when the mechanism designer can benefit from introducing ambiguity.</p> <p>Chapter 2 assumes that the mechanism designer does not know agents’ probability assessments about others’ private information. The mechanisms designed to implement the social choice function thus should not depend on the probability assessments, which are called robust mechanisms. Different from the existing robust mechanism design literature where agents are always assumed to act non-cooperatively, this chapter allows them to communicate and form coalitions. This chapter provides necessary and almost sufficient conditions for robustly implementing a social choice function as an equilibrium that is immune to all coalitional deviations. As there are social choice functions that are only implementable with coalitional structures, this chapter provides insights on when agents should be allowed to communicate. As an extension, when the mechanism designer has no information on which coalitions can be formed, this chapter also provides conditions for robust implementation under all coalition patterns.</p> <p>Chapter 3 assumes that agents are not probabilistic about others’ private information. Instead, when they hold ambiguous assessments about others’ information, they make decisions based on the worst-case belief. This chapter provides necessary and almost sufficient conditions on when a social choice goal is implementable under such a behavioral assumption. As there are social choice goals that are only implementable under ambiguous assessments, this chapter provides insights on what information structure is desirable to the mechanism designer.</p>

In this conference we celebrate the 50th anniversary of the publication of "Social Choice and Individual Values" by Kenneth Arrow [14]. Fyodor Dostoevski once said that the literature of the second half of the 19th century grew out of Nikolai Gogol's short novel, "An Overcoat." To paraphrase Dostoevski, we can say that the theory of social choice after 1951 grew out of "Social Choice and Individual Values." Although social decisions are universal, very little work was completed in Russia and the Soviet Union on the theoiy of social choice up until recent times. Thus I am first going to discuss briefly the histoiy of social choice in Russia. I restrict myself to the period up to 1 991 , since I believe this was the year in which a new era in Russian history began. The development of social choice after 1991 is a subject for future investigation.

The size and quality of this two-volume special issue in honor of Salvador Barbera speaks to the wide scope of his contributions as a friend, co-author, mentor, and builder. We begin by framing some of Salvador’s important research contributions. The theory of social choice is at the very center of economic analysis. In the late 1960s, following various contributions by William Vickrey, Robin Farquharson, Edward Clarke, Ted Groves, Alan Gibbard and Mark Satterthwaite, the notion of strategy-proofness took form and, together with ideas emerging in game theory, produced an “economics of incentives”. This line of research became among the most fruitful work in all of social science of the last quarter of the twentieth century. Salvador Barbera is among the most influential scholars in this line of research, particularly on the voting models side. He stands among the world leaders. In particular, Salvador Barbera’s work on strategy-proofness has been of fundamental importance and he has made several seminal contributions. These begin with papers that follow from his Ph.D. thesis and are particularly concerned with strategyproofness when one allows some randomization in outcomes. Those papers helped uncover the role of chance or randomization in social decisions, and showed the limited extent to which that can help in mitigating individual incentives for manipulation. That work has recently sparked a series of interesting follow-up papers. Salvador’s other important works on strategy-proofness in such rich domains include insightful proofs based on pivotal voter arguments and extensions to infinite settings (in work with Bezalel Peleg).