Axiomatic analysis of aggregation methods for collective annotation

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].

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.

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.

The extraordinary technological progress we have witnessed in recent years has made it possible to generate and exchange multimedia content at an unprecedented rate. As a consequence, massive collections of multimedia objects are now widely available to a large population of users. As the task of browsing such large collections could be daunting, Recommender Systems are being developed to assist users in finding items that match their needs and preferences. In this article, we present a novel approach to recommendation in multimedia browsing systems, based on modeling recommendation as a social choice problem. In social choice theory, a set of voters is called to rank a set of alternatives, and individual rankings are aggregated into a global ranking. In our formulation, the set of voters and the set of alternatives both coincide with the set of objects in the data collection. We first define what constitutes a choice in the browsing domain and then define a mechanism to aggregate individual choices into a global ranking. The result is a framework for computing customized recommendations by originally combining intrinsic features of multimedia objects, past behavior of individual users, and overall behavior of the entire community of users. Recommendations are ranked using an importance ranking algorithm that resembles the well-known PageRank strategy. Experiments conducted on a prototype of the proposed system confirm the effectiveness and efficiency of our approach.

Book Review: An Anatomy of Values: Problems of Personal and Social Choice

AINYONE CONCERNED to think clearly and well has to make at least two principle decisions. The first, and often most neglected, involves separating the from the trivial: making distinctions between things that we need to know now, from those that we might want to know at a later, less perilous time, from those that we really can do without now and forever. This is not necessarily easy as the advocates of pure science often remind us. Still, I suspect that the choice is not as difficult as it may seem, especially in a world of widening extremes between the winners and the losers, that is busily engaged in pulling the ecological rug out from under its own feet while developing more clever and more probable ways to incinerate itself. The second decision involves making distinctions within the category of important between the true, the less true, and the false, knowing all the while that reality is more complex than our ability to think about it. Moreover, the characteristics of relativity, randomness, indeterminacy, and incompleteness found in the physical/mathematical universe doubtless have analogs in the social world, which are compounded by problems of irony, values, ethics, and social choice. Moreover, disciplinary paradigms, research methods, and the institutional context of research and thought can seriously distort what we think to be true. The two decisions, of course, are related. The choice of what is depends to some extent on what is thought to be true and vice versa. In both decisions a healthy concern for good thought en-

The problem of social choice when individual orderings are lexicographic is discussed in this paper. In addition to assuming that individual orderings over the social alternatives are lexicographic, the assumptions are made that the set of criteria which constitute the basis of each individual's ordering are identical for all individuals and also that the ranking of these criteria, in terms of priority, is the same for all individuals. Given these assumptions, the author establishes conditions for the existence of a socially best alternative under binary, decisive, neutral and nonnegatively responsive group decision rules, which constitute a very wide class of group decision rules. The result established turns out to be more general than the results proved earlier by Encarnación (1969) and Taylor (1970).

The assignment problem, a well-known variant of which is the problem of optimal staff distribution, has formerly been treated as a problem of linear optimization starting with numerical evaluations of the assignments. In this paper the assignment problem is regarded as a problem of social choice, where preference orders are used as the sole initial information. A formal definition of an assignment function is given and various conditions for such functions are suggested. Some conditions are found to be incompatible. Several reasonable assignment functions are examined with respect to which conditions they fulfil. Finally, some problems, related to the assignment problem, are informally discussed.

We consider collective choice with agents possessing strictly monotone, strictly convex and continuous preferences over a compact and convex constraint set contained in +k . If it is non-empty the core will lie on the efficient boundary of the constraint set and any policy not in the core is beaten by some policy on the efficient boundary. It is possible to translate the collective choice problem on this efficient boundary to another social choice problem on a compact and convex subset of +c (c<k) with strictly convex and continuous preferences. In this setting the dimensionality results in Banks (1995) and Saari (1997) apply to the dimensionality of the boundary of the constraint set (which is lower than the dimensionality of the choice space by at least one). If the constraint set is not convex then the translated lower dimensional problem does not necessarily involve strict convexity of preferences but the dimensionality of the problem is still lower. Broadly, the results show that the homogeneity afforded by strict monotonicity of preferences and a compact constraint set makes generic core emptyness slightly less common. One example of the results is that if preferences are strictly monotone and convex on 2 then choice on a compact and convex constraint exhibits a version of the median voter theorem.

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,