Sophisticated preference aggregation

An institution is viewed as an arrangement of the society through which various social states emerge as outcomes from the actions and interactions of individuals belonging to the society. Following an earlier contribution by Pattanaik and Suzumura (Oxford Economic Papers 48:194–212, 1996), we subscribe to the view that the ethical desirability of an institution is based on the goodness of the outcomes emerging from individuals’ actions and interactions via the institution as well as the intrinsic attractiveness of the institution itself. In this paper, we explore the structure of an individual’s ethical evaluations of institutions. For this purpose, we discuss how social choices are made through institutions given profiles of individual preferences over social states, propose several a priori properties of institutions and examine their plausibility, and introduce and discuss a lexicographic maximin rule for evaluating institutions ethically.

We develop an algorithm for the axiomatic justification problem in social choice that is sufficiently efficient to be applicable in decision making scenarios of real practical interest. Given a profile of individual preferences, a suggested election outcome, and a corpus of axioms encoding fundamental normative principles of electoral fairness, solving this justification problem involves computing a minimal set of instances of some of the axioms in the corpus that together rule out any outcome that is different from the one we want to justify. Our approach combines the use of state-of-the-art tools for computing minimally unsatisfiable sets of constraints with a graph-search algorithm. The latter searches the graph induced by the set of all axiom instances in an incremental manner and relies on a number of heuristics to further improve performance.

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

This paper presents a proof of the Gibbard-Satterthwaite theorem. The importance of the theorem itself has been widely recognized, and there already exist several alternative proofs. The present one is offered because it is technically simple, direct, and emphasizes the role of pivotal individuals in the manipulation of voting schemes. Some indirect proofs of the theorem rely on the connections between voting schemes and social welfare functions, and one interesting corollary of such proofs is to provide new arguments in behalf of Arrow's condition of independence of irrelevant alternatives. Yet, a direct proof has the advantage of showing the complete independence of the manipulation phenomena from any requirement of consistency in choice under varying sets of alternatives. Also, our proof emphasizes the role of pivotal individuals in manipulation. A classical approach in social choice theory is to concentrate on the global distribution of power among groups of agenits, i.e., on the ability of coalitions to impose outcomes regardless of the preferences of agents not in the coalition. For example, standard proofs of Arrow's Theorem concentrate on decisive coalitions, to end up proving that there must exist one such coalition containing a single individual, the dictator. Our approach concentrates on the local distribution of power among single agents, i.e., on the ability of each single individual to determine the social outcome, given the preferences of all other members of society.' This approach may be more intuitive for some readers; moreover, it closely parallels the work on incentives in economic environments with public goods and suggests a possible way to unify results which have been obtained from different initial specifications. We do not attempt such a rejoinder here, but let us observe the following. For certain environments with public goods, where transfer payments make perfect sense, nontrivial strategy-proof mechanisms can be obtained by appropriately taxing pivotal agents so that they take into account the costs that their actions impose upon others.2 One explanation for the nonexistence of equivalent mechanisms in our case is that the environment, as specified, does not allow for a corresponding procedure whereby different costs to individuals could be attached to different acts of preference revelation.

Social choice theory without the Pareto Principle

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 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 essay will consider the relation between the theory of committees put forward by Professor Kenneth J Arrow in his Social Choice and Individual Values (1951, 1963) and other writings, and ‘the preceding theory’, as we will call it, of the present writer. My own theory had been set out, when a book on the subject failed to gain publication, in some seven articles1 in the journals of 1948 and 1949, and again in the booklet written in collaboration with Dr R. A. Newing, Committee Decisions with Complementary Valuation (1951), whose MS, towards the end of 1949, had been submitted for publication as an article in a journal.

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.

When choosing a voting rule to make subsequent decisions, the members of a committee may wish this rule to be self-selected when it is the object of a choice among a menu of different possible voting rules. Such concepts have recently been explored in Social Choice theory, and a menu of voting rule is said to be stable if it contains at least one self-selective voting rule at each profile of preferences on voting rules. We consider in this article the menu constituted by the three well-known scoring rules {Borda, Plurality, and Antiplurality}. Under the Impartial Culture assumption, which proposes an a priori model to estimate the likelihood of the profiles, we will derive a probability for the stability of this triplet of voting rules.

In this article we will focus on the definitions of the concepts of Globalisation and Sustainable Development, in order to trace some of their most relevant features and analyse its consequences, aims and evolution over the last decades. Afterwards, we will take an approach to some of the criticisms concerning Sustainable Development, and which must be taken into account, so that they do not become true and, therefore, do not truncate the whole process. We will also provide an analysis of how the Sustainable Development is taking shape, which will be carried both from a global perspective, which related to the change in individual and social values, and from a more technological perspective, which focuses on production efficiency and technical and scientific developments. As we will see, both perspectives are necessary and can be implemented, even though some changes need to be done in the values of the social (political and cultural) system. Such changes do not refer only to personal and social values —these are very important to help us adopt attitudes that are on the line of sustainability—, but also to the way of governing, the way in which decisions are made and, especially, to the distribution of economic power.

Previous articleNext article No AccessCommentComment on “Rotten Kids, Purity, and Perfection”Pierre‐André Chiappori and Iván WerningPierre‐André ChiapporiUniversity of Chicago Search for more articles by this author and Iván WerningUniversity of Chicago and Universidad Torcuato di Tella Search for more articles by this author University of ChicagoUniversity of Chicago and Universidad Torcuato di TellaPDFPDF PLUSFull Text Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by Journal of Political Economy Volume 110, Number 2April 2002 Article DOIhttps://doi.org/10.1086/338745 Views: 95Total views on this site Citations: 10Citations are reported from Crossref © 2002 by The University of Chicago. All rights reserved. PDF download Crossref reports the following articles citing this article:Thomas Demuynck, Tom Potoms Weakening transferable utility: The case of non-intersecting Pareto curves, Journal of Economic Theory 188 (Jul 2020): 105035.https://doi.org/10.1016/j.jet.2020.105035João Ricardo Faria, Emilson Caputo Delfino Silva Leadership delegation in rotten kid families, Journal of Population Economics 33, no.22 (Nov 2019): 441–460.https://doi.org/10.1007/s00148-019-00755-4Helmuth Cremer, Kerstin Roeder Rotten spouses, family transfers, and public goods, Journal of Population Economics 30, no.11 (Aug 2015): 141–161.https://doi.org/10.1007/s00148-015-0564-xEmilson Silva Selective Decentralized Leadership, SSRN Electronic Journal (Jan 2013).https://doi.org/10.2139/ssrn.2343231Richard Cornes, Jun-ichi Itaya, Aiko Tanaka Private provision of public goods between families, Journal of Population Economics 25, no.44 (Oct 2011): 1451–1480.https://doi.org/10.1007/s00148-011-0388-2Arthur J. Caplan, Emilson C. D. Silva Impure public goods, matching grant rates and income redistribution in a federation with decentralized leadership and imperfect labor mobility, International Tax and Public Finance 18, no.33 (Dec 2010): 322–336.https://doi.org/10.1007/s10797-010-9158-4Bouwe R. Dijkstra Samaritan versus rotten kid: Another look, Journal of Economic Behavior & Organization 64, no.11 (Sep 2007): 91–110.https://doi.org/10.1016/j.jebo.2006.06.006Marko Köthenbürger Ex-post redistribution in a federation: Implications for corrective policy, Journal of Public Economics 91, no.3-43-4 (Apr 2007): 481–496.https://doi.org/10.1016/j.jpubeco.2006.08.004Arthur J. Caplan, Emilson C. D. Silva An equitable, efficient and implementable scheme to control global carbon dioxide emissions, International Tax and Public Finance 14, no.33 (Aug 2006): 263–279.https://doi.org/10.1007/s10797-006-9002-zVan Kolpin The modeling and analysis of rotten kids, Social Choice and Welfare 26, no.11 (Oct 2005): 23–30.https://doi.org/10.1007/s00355-005-0025-7

Focus on Authors

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].

Extension of Arrow's theorem to symmetric sets of tournaments