Rational budgeters in the theory of social choice

The purpose of this paper is to explore duality in the theory of social choice. As application Arrow's Impossibility Theorem and another impossibility theorem using the notion of positive responsiveness are chosen. It will be seen that we can establish notions and theorems which are symmetric to the original ones. However, if we establish impossibility theorems when rational behaviour is described by budget correspondences and not by choice correspondences, we need not assume that every subset of X (a family of alternatives) with cardinality 2 is a budget set. Therefore the dual theorems also may hold for families of competitive budget sets. It will also be shown that although the underlying preferences on X need not be acyclic, local decisiveness on budget sets may lead to global decisiveness on these sets.     

Generalizing the Gibbard–Satterthwaite theorem: partial preferences,the degree of manipulation,and multi-valuedness

The Gibbard–Satterthwaite (GS) theorem is generalized in three ways: First, it is proved that the theorem is still valid when individual preferences belong to a convenient class of partial preferences; second, it is shown that every non-dictatorial surjective social choice function (SCF) is not only manipulable, but it can be manipulated in such a way that some individual obtains either his best or second best alternative; third, we prove a variant of the theorem where the outcomes of the SCF are subsets of the set of alternatives of an a priori fixed size. In addition, all results are proved not only for finite, but also for countably infinite sets of alternatives.     

On the manipulation of social choice correspondences

Duggan and Schwartz (Soc Choice and Welfare 17: 85–93, 2000) have proposed a generalization of the Gibbard–Satterthwaite Theorem to multivalued social choice rules. They show that only dictatorial rules are strategy-proof and satisfy citizens sovereignty and residual resoluteness. Citizens sovereignty requires that each alternative is chosen at some preference profile. Residual resoluteness compels the election to be single-valued when the preferences of the voters are “similar”. We propose an alternative proof to the Duggan and Schwartz’s Theorem. Our proof highlights the crucial role of residual resoluteness. In addition, we prove that every strategy-proof and onto social choice correspondence concentrates the social decision power in the hands of an arbitrary group of voters. Finally, we show that this result still holds in a more general framework in which voters report their preferences over sets of alternatives.     

Strategy-proof allocation of multiple public goods

This paper characterizes strategy-proof social choice functions (SCFs), the outcome of which are multiple public goods. Feasible alternatives belong to subsets of a product set . The SCFs are not necessarily “onto”, but the weaker requirement, that every element in each category of public goods A _k is attained at some preference profile, is imposed instead. Admissible preferences are arbitrary rankings of the goods in the various categories, while a separability restriction concerning preferences among the various categories is assumed. It is found that the range of the SCF is uniquely decomposed into a product set in general coarser than the original product set, and that the SCF must be dictatorial on each component B _l . If the range cannot be decomposed, a form of the Gibbard–Satterthwaite theorem with a restricted preference domain is obtained.     

A characterization of the single-crossing domain

We characterize single-crossing preference profiles in terms of two forbidden substructures, one of which contains three voters and six (not necessarily distinct) alternatives, and one of which contains four voters and four (not necessarily distinct) alternatives. We also provide an efficient way to decide whether a preference profile is single-crossing.     

Opportunity sets and individual well-being

 An opportunity set ranking rule assigns an ordering of opportunity sets to each individual utility function (defined on the universal set of alternatives) within the domain of this rule. Using an axiomatic approach, this paper characterizes a general class of opportunity set ranking rules which are based on the utilities associated with the elements of an opportunity set. It is argued that the addition of an alternative to a given opportunity set is not necessarily desirable in terms of overall well-being, and this position is reflected in replacing a commonly used monotonicity axiom with an alternative condition. Received: 15 May 1995/Accepted: 14 December 1995     

AN EXPERIMENTAL STUDY OF ALTERNATIVE CAMPAIGN FINANCE SYSTEMS: TRANSPARENCY,DONATIONS, AND POLICY CHOICES

We experimentally study the transparency effect of alternative campaign finance systems on donations, election outcomes, policy choices, and welfare. Three alternatives are considered: one where donors' preferences and donations are unobserved by the candidate and public; one where they are observed by the candidate but not the public; and one where they are observed by all. We label them full anonymity (FA), partial anonymity (PA), and no anonymity (NA), respectively. We find that in NA and PA candidates consistently respond to donations by choosing policies favoring the donors. FA, in contrast, is the most successful in limiting the influence of donations on policy choices. Donors benefit greatly from the possibility of donations whereas social welfare may be harmed in some treatments. To our knowledge, this article is the first to investigate the effect of different campaign finance systems distinguished by their transparency level. (JEL D72)     

On the likelihood of Condorcet's profiles

Consider a group of individuals who have to collectively choose an outcome from a finite set of feasible alternatives. A scoring or positional rule is an aggregation procedure where each voter awards a given number of points, w _j, to the alternative she ranks in j ^th position in her preference ordering; The outcome chosen is then the alternative that receives the highest number of points. A Condorcet or majority winner is a candidate who obtains more votes than her opponents in any pairwise comparison. Condorcet [4] showed that all positional rules fail to satisfy the majority criterion. Furthermore, he supplied a famous example where all the positional rules select simultaneously the same winner while the majority rule picks another one. Let P ^* be the probability of such events in three-candidate elections. We apply the techniques of Merlin et al. [17] to evaluate P ^* for a large population under the Impartial Culture condition. With these assumptions, such a paradox occurs in 1.808% of the cases. Received: 30 April 1999/Accepted: 14 September 2000     

Agreement, separability, and other axioms for quasi-linear social choice problems

A quasi-linear social choice problem is concerned with choosing one among a finite set of public projects and determining side payments among agents to cover the cost of the project, assuming each agent has quasi-linear preferences. We first investigate the logical relations between various axioms in this context. They are: agreement, separability, population solidarity, consistency, converse consistency, and population-and-cost solidarity. Also, on the basis of these axioms, we present alternative characterizations of egalitarian solutions; each solution assigns to each agent an equal share of the surplus derived from the public project over some reference utility level, but uses a different method to compute the reference utility level. Received: 18 May 1998/Accepted: 1 July 1999     

Distribution of coalitional power in randomized multi-valued social choice

This paper considers the distribution of coalitional influence under probabilistic social choice functions which are randomized social choice rules that allow social indifference by mapping each combination of a preference profile and a feasible set to a social choice lottery over all possible choice sets from the feasible set. When there are at least four alternatives in the universal set and ex-post Pareto optimality, independence of irrelevant alternatives and regularity are imposed, we show that: (i) there is a system of additive coalitional weights such that the weight of each coalition is its power to be decisive in every two-alternative feasble set; and (ii) for each combination of a feasible proper subset of the universal set and a preference profile, the society can be partioned in such a way that for each coalition in this partition, the probability of society's choice set being contained in the union of the best sets of its members is equal to the coalition's power or weight. It is further shown that, for feasible proper subsets of the universal set, the probability of society's choice set containing a pair of alternatives that are not jointly present in anyone's best set is zero. Our results remain valid even when the universal set itself becomes feasible provided some additional conditions hold. Received: 10 May 1999/Accepted: 18 June 2000 I would like to thank Professor Prasanta Pattanaik for suggesting to me the line of investigation carried out in this paper. I am solely responsible for any remaining errors and omissions.     

On asymptotic strategy-proofness of the plurality and the run-off rules

In this paper we prove that the plurality rule and the run-off procedure are asymptotically strategy-proof for any number of alternatives and that the proportion of profiles, at which a successful attempt to manipulate might take place, is in both cases bounded from above by , where n is the number of participating agents and K does not depend on n. We also prove that for the plurality rule the proportion of manipulable profiles is asymptotically bounded from below by , where k also does not depend on n. Received: 10 February 2000/Accepted: 19 October 2000     

An axiomatization of the Kalai-Smorodinsky solution when the feasible sets can be finite

We axiomatize the Kalai-Smorodinsky solution (1975) in the Nash bargaining problems if the feasible sets can be finite. We show that the Kalai-Smorodinsky solution is the unique solution satisfying Continuity (in the Hausdorff topology endowed with payoffs space), Independence (which is weaker than Nash's one and essentially equivalent to Roth (1977)'s one), Symmetry, Invariance (both of which are the same as in Kalai and Smorodinsky), and Monotonicity (which reduces to a little bit weaker version of the original if the feasible sets are convex). Received: 4 November 1999/Accepted: 6 June 2001     

Metabolism, energy, and entropy in Marx's critique of political economy: Beyond the Podolinsky myth

Until recently, most commentators, including ecological Marxists, have assumed that Marx's historical materialism was only marginally ecologically sensitive at best, or even that it was explicitly anti-ecological. However, research over the last decade has demonstrated not only that Marx deemed ecological materialism essential to the critique of political economy and to investigations into socialism, but also that his treatment of the coevolution of nature and society was in many ways the most sophisticated to be put forth by any social theorist prior to the late twentieth century. Still, criticisms continue to be leveled at Marx and Engels for their understanding of thermodynamics and the extent to which their work is said to conflict with the core tenets of ecological economics. In this respect, the rejection by Marx and Engels of the pioneering contributions of the Ukrainian socialist Sergei Podolinsky, one of the founders of energetics, has been frequently offered as the chief ecological case against them. Building on an earlier analysis of Marx's and Engels's response to Podolinsky, this article shows that they relied on an open-system, metabolic-energetic model that adhered to all of the main strictures of ecological economics – but one that also (unlike ecological economics) rooted the violation of solar and other environmental-sustainability conditions in the class relations of capitalist society. The result is to generate a deeper understanding of classical historical materialism's ecological approach to economy and society – providing an ecological-materialist critique that can help uncover the systemic roots of today's “treadmill of production” and global environmental crisis. Paul Burkett is Professor of Economics at Indiana State University, Terre Haute. He is the author of Marx and Nature: A Red and Green Perspective (1999), and the co-author, with Martin Hart-Landsberg, of China and Socialism: Market Reforms and Class Struggle (2005). John Bellamy Foster is Professor of Sociology at the University of Oregon in Eugene, Oregon, and co-editor of Monthly Review (New York). He is the author of The Vulnerable Planet (1994, 1999); “Marx's Theory of Metabolic Rift: Classical Foundations for Environmental Sociology,” American Journal of Sociology (September 1999); Marx's Ecology (2000); Ecology Against Capitalism (2002); and Naked Imperialism (2005).     

Is a continuous rational social aggregation impossible on continuum spaces?

This paper provides a global topological setting for the social choice theory on continuum spaces of alternatives, in contrast to the local differentiable setting of Chichilnisky. Chichilnisky proved that a rational continuous social choice must be discontinuous in her setting. Our paper revisits her theorem to trace the source of this discontinuity. We find that the discontinuity is irrelevant to social aggregation, per se. The main theorem states that there exist a number of continuous social utility maps which are anonymous and satisfy the Pareto condition. As a corollary, we show that there exist corresponding continuous social welfare functions, if singularity is not separated from regular preferences in social preference topology. This extends the possibility result of Jonnes-Zhang-Simpson on linear preferences, to the general ones. The notion of singularity of preferences, relative to the given mathematical structure of an alternative space, is carefully studied.     

Coalitionally strategyproof functions depend only on the most-preferred alternatives

In a framework allowing infinitely many individuals, I prove that coalitionally strategyproof social choice functions satisfy “tops only.” That is, they depend only on which alternative each individual prefers the most, not on which alternative she prefers the second most, the third,…, or the least. The functions are defined on the domain of profiles measurable with respect to a Boolean algebra of coalitions. The unrestricted domain of profiles is an example of such a domain. I also prove an extension theorem. Received: 10 August 1998/Accepted: 3 May 1999     

Interpretation of electoral mixed strategies

In this paper is remarked that “mixed” strategies in games of electoral competition do not need to be interpreted as random moves. There are two a priori symmetric parties, and a finite (non spatial) set of alternatives. Parties are allowed to take unclear positions, by campaining on a “platform” that is a mix of several alternatives. Each individual nevertheless identifies a party with a single alternative, the number of individuals who identify a party with a given alternative being proportional to the importance of that alternative in the party’s platform. Received: 24 March 1998/Accepted: 3 March 1999     

Core concepts for share vectors

A value mapping for cooperative games with transferable utilities is a mapping that assigns to every game a set of vectors each representing a distribution of the payoffs. A value mapping is efficient if to every game it assigns a set of vectors which components all sum up to the worth that can be obtained by all players cooperating together.? An approach to efficiently allocate the worth of the ‘grand coalition’ is using share mappings which assign to every game a set of share vectors being vectors which components sum up to one. Every component of a share vector is the corresponding players' share in the total payoff that is to be distributed among the players. In this paper we discuss a class of share mappings containing the (Shapley) share-core, the Banzhaf share-core and the Large Banzhaf share-core, and provide characterizations of this class of share mappings. Received: 9 August 1999/Accepted: 25 April 2000     

Identification of domain restrictions over which acyclic, continuous-valued, and positive responsive social choice rules operate

We consider a social choice problem in various economic environments consisting of n individuals, 4≤n<+∞, each of which is supposed to have classical preferences. A social choice rule is a function associating with each profile of individual preferences a social preference that is assumed to be complete, continuous and acyclic over the alternatives set. The class of social choice rules we deal with is supposed to satisfy the two conditions; binary independence and positive responsiveness. A new domain restriction for the social choice rules is proposed and called the classical domain that is weaker than the free triple domain and holds for almost all economic environments such as economies with private and/or public goods. In this paper we explore what type of classical domain that admits at least one social choice rule satisfying the mentioned conditions to well operate over the domain. The results we obtained are very negative: For any classical domain admitting at least one social choice rule to well operate, the domain consists only of just one profile.     

Global Studies: Have Catechism,Will Travel

This second response to comments on my article ‘What is Global studies?’ (Globalizations 10, 4, 2013) notes that the comments feature research agendas. These provide scaffolding for global studies but not of course a complete building. Among themes that need further attention are political economy and finance, the dimension of time and history, and the dynamics of twenty-first century globalization and the role of emerging economies.