A Multimedia Recommender System

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.

In this paper, we provide axiomatic foundations for social choice rules on a domain of convex and comprehensive social choice problems when agents have cardinal utility functions. We translate the axioms of three well known approaches in bargaining theory (Nash 1950; Kalai and Smorodinsky 1975; Kalai 1977) to the domain of social choice problems and provide an impossibility result for each. We then introduce the concept of a reference function which, for each social choice set, selects a point from which relative gains are measured. By restricting the invariance and comparison axioms so that they only apply to sets with the same reference point, we obtain characterizations of social choice rules that are natural analogues of the bargaining theory solutions.

Collective decision making is the process of mapping the individual views of several individual agents into a joint decision. The need for collective decision making mechanisms is abundant, not just in the realm of politics, but also for a wide range of scientific and technological applications. These include, for instance, logistics, grid computing, and recommender systems. The alternatives to be decided upon often have a combinatorial structure: an alternative is characterised by a tuple of variables, each ranging over a finite domain. Classical approaches to collective decision making, developed in social choice theory, do not take the computational limitations induced by the combinatorial nature of the problem into account. For instance, if we are asked to elect a committee consisting of k representatives, choosing from a pool of n candidates, then we are in fact faced with a social choice problem with $(^n_k)$ alternatives. Asking each voter for their full preferences over these $(^n_k)$ alternatives may not be feasible in practice. Similarly, if we have to choose between accepting or rejecting each of n different propositions, then we are dealing with a social choice problem with 2 n possible outcomes. In this talk I will report on a number of recent developments in the area of collective decision making in combinatorial domains. This includes the study of languages for the compact representation of preferences [2,4], the design of voting rules for multi-issue elections [1], and the analysis of the computational complexity of decision problems arising in judgment aggregation [3].

Social choice problems with fixed sets of alternatives

We consider a social choice problem where individual rationality is required. The status quo belongs to the outcome space, and the selected alternative must be weakly better than the status quo for everybody. If the mechanism designer has no knowledge of the alternatives, we obtain a negative result: any individually rational (IR) and strategy-proof (SP) mechanism can choose at most one alternative (besides the status quo), regardless of the preferences. To overcome this negative result, we consider a domain where the alternatives have a known structure, i.e., an agent is indifferent between the status quo and a subset of the outcomes. This set is exogenously given and public information. This assumption is natural if the social choice involves the participation of agents. For example, consider a group of people organizing a trip where participation is voluntary. We can assume each agent is indifferent between the trip plans in which she does not participate and the status quo (i.e., no trip). In this setting, we obtain more positive results: we develop a class of mechanisms called Approve and Choose mechanisms, which are IR and SP, and can choose multiple alternatives as well as the status quo.

Crowdsourcing is an important tool, e.g., in computational linguistics and computer vision, to efficiently label large amounts of data using nonexpert annotators. The individual annotations collected need to be aggregated into a single collective annotation. The hope is that the quality of this collective annotation will be comparable to that of a traditionally sourced expert annotation. In practice, most scientists working with crowdsourcing methods use simple majority voting to aggregate their data, although some have also used probabilistic models and treated aggregation as a problem of maximum likelihood estimation. The observation that the aggregation step in a collective annotation exercise may be considered a problem of social choice has only been made very recently. Following up on this observation, we show that the axiomatic method, as practiced in social choice theory, can make a contribution to this important domain and we develop an axiomatic framework for collective annotation, focusing amongst other things on the notion of an annotator's bias. We complement our theoretical study with a discussion of a crowdsourcing experiment using data from dialogue modelling in computational linguistics.

We approach the social choice problem as one of optimal statistical infer- ence. If individual voters or judges observe the true order on a set of alternatives with error, then it is possible to use the set of individual rankings to make probability state- ments about the correct social order. Given the posterior distribution for orders and a suitably chosen loss function, an optimal order is one that minimises expected poster- ior loss. The paper develops a statistical model describing the behaviour of judges, and discusses Markov chain Monte Carlo estimation. We also discuss criteria for choos- ing the appropriate loss functions. We apply our methods to a well-known problem: determining the correct ranking for figure skaters competing at the Olympic Games.

We present a method for using standard techniques from satisfiability checking to automatically verify and discover theorems in an area of economic theory known as ranking sets of objects. The key question in this area, which has important applications in social choice theory and decision making under uncertainty, is how to extend an agent's preferences over a number of objects to a preference relation over nonempty sets of such objects. Certain combinations of seemingly natural principles for this kind of preference extension can result in logical inconsistencies, which has led to a number of important impossibility theorems. We first prove a general result that shows that for a wide range of such principles, characterised by their syntactic form when expressed in a many-sorted first-order logic, any impossibility exhibited at a fixed (small) domain size will necessarily extend to the general case. We then show how to formulate candidates for impossibility theorems at a fixed domain size in propositional logic, which in turn enables us to automatically search for (general) impossibility theorems using a SAT solver. When applied to a space of 20 principles for preference extension familiar from the literature, this method yields a total of 84 impossibility theorems, including both known and nontrivial new results.

Previous articleNext article No AccessArrow's Theorem, Indeterminacy, and Multiplicity Reconsidered*Mathias RisseMathias Risse Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by Ethics Volume 111, Number 4July 2001 Article DOIhttps://doi.org/10.1086/233570 Views: 53Total views on this site Citations: 18Citations are reported from Crossref © 2001 by The University of Chicago. All rights reserved.PDF download Crossref reports the following articles citing this article:Henrik D. Kugelberg Social choice problems with public reason proceduralism, Economics and Philosophy 38, no.11 (Feb 2021): 51–70.https://doi.org/10.1017/S0266267120000498Wesley H. Holliday, Eric Pacuit Axioms for defeat in democratic elections, Journal of Theoretical Politics 33, no.44 (Nov 2021): 475–524.https://doi.org/10.1177/09516298211043236Hannu Nurmi The Incidence of Some Voting Paradoxes Under Domain Restrictions, Group Decision and Negotiation 29, no.66 (Aug 2020): 1107–1120.https://doi.org/10.1007/s10726-020-09697-9Adiel Teixeira de Almeida, Danielle Costa Morais, Hannu Nurmi More Than Two Alternatives, (Oct 2019): 21–30.https://doi.org/10.1007/978-3-030-30955-8_4Eerik Lagerspetz Interpretations, (Jan 2016): 247–340.https://doi.org/10.1007/978-3-319-23261-4_5MARK A. BURGMAN, HELEN M. REGAN, LYNN A. MAGUIRE, MARK COLYVAN, JAMES JUSTUS, TARA G. MARTIN, KRIS ROTHLEY Voting Systems for Environmental Decisions, Conservation Biology 28, no.22 (Jan 2014): 322–332.https://doi.org/10.1111/cobi.12209Rosa Camps, Xavier Mora, Laia Saumell A continuous rating method for preferential voting. The incomplete case, Social Choice and Welfare 40, no.44 (Apr 2012): 1111–1142.https://doi.org/10.1007/s00355-012-0663-5Aki Lehtinen A welfarist critique of social choice theory, Journal of Theoretical Politics 23, no.33 (Jul 2011): 359–381.https://doi.org/10.1177/0951629811411753Mathias Risse On the Philosophy of Group Decision Methods I: The Nonobviousness of Majority Rule, Philosophy Compass 4, no.55 (Sep 2009): 793–802.https://doi.org/10.1111/j.1747-9991.2009.00224.xMathias Risse On the Philosophy of Group Decision Methods II: Alternatives to Majority Rule, Philosophy Compass 4, no.55 (Sep 2009): 803–812.https://doi.org/10.1111/j.1747-9991.2009.00225.xArnold Shepperson An economy of impossibility: a preliminary study for an ordinal approach to research methods in cultural studies, Critical Arts 22, no.22 (Nov 2008): 333–357.https://doi.org/10.1080/02560040802472492Joel Parker Peter Emerson, ed., Designing an All-Inclusive Democracy: Consensual Voting Procedures For Use in Parliaments, Councils and Committees, Public Choice 135, no.3-43-4 (Nov 2007): 493–496.https://doi.org/10.1007/s11127-007-9261-yMathias Risse On the Philosophy of Group Decision Methods I: The Non-Obviousness of Majority Rule, SSRN Electronic Journal (Jan 2008).https://doi.org/10.2139/ssrn.1296638MARC FLEURBAEY SOCIAL CHOICE AND JUST INSTITUTIONS: NEW PERSPECTIVES, Economics and Philosophy 23, no.11 (Mar 2007): 15–43.https://doi.org/10.1017/S0266267107001204Donald G. Saari Which is better: the Condorcet or Borda winner?, Social Choice and Welfare 26, no.11 (Jan 2006): 107–129.https://doi.org/10.1007/s00355-005-0046-2Mathias Risse Why the count de Borda cannot beat the Marquis de Condorcet, Social Choice and Welfare 25, no.11 (Nov 2005): 95–113.https://doi.org/10.1007/s00355-005-0045-3Gerry Mackie Democracy Defended, 20 (Sep 2009).https://doi.org/10.1017/CBO9780511490293 by Donald G. Saari Capturing the “Will of the People” Saari, Ethics 113, no.22 (Jul 2015): 333–349.https://doi.org/10.1086/342857

Computational social choice is a new interdisciplinary research area at the intersection of social choice theory and computer science that studies computational aspects of social choice mechanisms as well as applications of social choice ideas in the design and analysis of computing systems. Research on computational social choice now encompasses a variety of topics, including the algorithmic aspects of voting rules, computational barriers to strategic behaviour, collective decision-making in multi-agent systems, preference elicitation and communication issues in voting, fair division, computational aspects of weighted voting games, collective decision-making in combinatorial domains, logic-based formalisms for social choice problems, belief and judgement aggregation, and social software. The aim of this special issue is to build on the spectacular success of two workshops on computational social choice (COMSOC’06, Amsterdam and COMSOC’08, Liverpool), and provide a forum for reseachers in the area to present their ideas on a variety of topics. This special issue is composed of nine research articles and a short note that span a fairly wide range of issues, including voting, mechanism design, judgment aggregation, and fairness, and a similarly wide range of techniques, such as logic, experiments, and computational complexity. The paper by Agotnes, van der Hoek and Wooldridge defines a new modal logic for representing and reasoning about preference and judgment aggregation. The authors show that their logic can be used to express a variety of concepts and results from the social choice domain, including majority voting, the discursive paradox, Arrow’s theorem and Condorcet’s paradox. Baharad, Goldberger, Koppel and Nitzan propose a maximum likelihood estimation-based approach for aggregating voters’ opinions over several issues. They argue that their method is vastly superior to simple majority voting, and use both analytical and empirical evaluation to support their argument. Balan, Richards and Luke deal with the problem of selecting a sequence of actions when the actions have multiple beneficiaries. Their goal is to select the actions according to a lexicographic fairness criterion. The explore the complexity of this problem for both finite and infinite sequences of actions and present both algorithms and intractability results for this problem. The paper by Caminada and Pigozzi applies argumentation theory to judgment aggregation, and proposes aggregation operators satisfying not only the usual property of collective rationality, but another highly desirable property,

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.

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

One of the most exciting areas in economic theory is the study of incentives. Within this rubric a broad range of problems are currently being addressed. They range from the problems of social choice, to the economics of planning, to the character of labor contracts. The central theme of the research agenda concerns how the incentive structure affects the quality of information agents are willing to communicate. The principal question concerns how truthful revelation of information can be induced.1 Such questions are important whenever agents can profit from distorting information. The problem thus arises in all sorts of guises in economics. The purpose of this essay is to illustrate this point by focusing on three distinct areas, social choice, public finance, and economic planning.

There are alternative ways of decomposing a given fuzzy weak preference relation into its antisymmetric and symmetric components. In this paper I have provided support to one among these alternative specifications. It is shown that on this specification the fuzzy analogue of the General Possibility Theorem is valid even when the transitivity restrictions on the individual and the social preference relations are relatively weak. In the special case where the individual preference relations are exact but the social preference relation is permitted to be fuzzy it is possible to distinguish between different degrees of power of the dictator. This power increases with the strength of the transitivity requirement.

This paper establishes a clear connection between equilibrium theory, game theory and social choice theory by showing that, for a well defined social choice problem, a condition which is necessary and sufficient to solve this problem — limited arbitrage — is the same as the condition which is necessary and sufficient to establish the existence of an equilibrium and the core. The connection is strengthened by establishing that a market allocation, which is in the core, can always be realized as a social allocation, i.e. an allocation which is optimal according to an ordering chosen by a social choice rule. Limited arbitrage characterizes those economies without Condorcet triples, and those for which Arrow’s paradox can be resolved on choices of large utility values.KeywordsSocial ChoiceSocial PreferenceCompetitive EquilibriumPareto FrontierSocial Choice RuleThese 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.