Individually Rational Strategy-Proof Social Choice with Exogenous Indifference Sets

Social choice problems with fixed sets of alternatives

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.

The class of Groves mechanisms has been attracting much attention in called social welfare maximization) and dominant strategy incentive compatibility. However, when strategic agents can create multiple fake identities and reveal more than one preference under them, a refined characteristic called false-name-proofness is required. Utilitarian efficiency and false-name-proofness are incompatible in combinatorial auctions, if we also have individual rationality as a desired condition. However, although individual rationality is strongly desirable, if participation is mandatory due to social norms or reputations, a mechanism without individual rationality can be sustained.In this paper we investigate the relationship between utilitarian efficiency and false-name-proofness in a social choice environment with monetary transfers. We show that in our modelization no mechanism simultaneously satisfies utilitarian efficiency, false-name-proofness, and individual rationality. Considering this fact, we ignore individual rationality and design various mechanisms that simultaneously satisfy the other two properties. We also compare our different mechanisms in terms of the distance to individual rationality. Finally we illustrate our mechanisms on a facility location problem.

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].

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.

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,

Truthful mechanism for task allocation with lowest revenue limit in spatial crowdsourcing

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.

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

Sybil attacks, in which fake or duplicate identities (a.k.a., Sybils) infiltrate an online community, pose a serious threat to such communities, as they might tilt community-wide decisions in their favor. While the extensive research on sybil identification may help keep the fraction of sybils in such communities low, it cannot however ensure their complete eradication. Thus, our goal here is to enhance social choice theory with effective group decision mechanisms for communities with bounded sybil penetration. Inspired by Reality-Aware Social Choice, we use the status quo as the anchor of Sybil Resilience, characterized by Sybil Safety -- the inability of sybils to change the status quo against the will of the genuine agents, and Sybil Liveness -- the ability of the genuine agents to change the status quo against the will of the sybils. We consider the social choice settings of deciding on a single proposal, on multiple proposals, and on updating a parameter. For each, we present social choice rules that are sybil-safe and, under certain conditions, satisfy sybil-liveness.

<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>

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.

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...

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.