Does majoritarian approval matter in selecting a social choice rule? An exploratory panel study

This study is an attempt to empirically detect the public opinion concerning majoritarian approval axiom. A social choice rule respects majoritarian approval iff it chooses only those alternatives which are regarded by a majority of “voters” to be among the “better half” of the candidates available. We focus on three social choice rules, the Majoritarian Compromise, Borda’s Rule and Condorcet’s Method, among which the Majoritarian Compromise is the only social choice rule always respecting majoritarian approval. We confronted each of our 288 subjects with four hypothetical preference profiles of a hypothetical electorate over some abstract set of four alternatives. At each hypothetical preference profile, two representing the preferences of five and two other of seven voters, the subject was asked to indicate, from an impartial viewpoint, which of the four alternatives should be chosen whose preference profile was presented, which if that is unavailable, then which if both of the above are unavailable, and finally which alternative should be avoided especially. In each of these profiles there is a Majoritarian Compromise-winner, a Borda-winner and a Condorcet-winner, and the Majoritarian Compromise-winner is always distinct from both the Borda-winner and the Condorcet-winner, while the Borda- and Condorcet-winners sometimes coincide. If the Borda- and Condorcet-winners coincide then there are two dummy candidates, otherwise only one, and dummies coincide with neither of the Majoritarian Compromise-, Borda- or Condorcet-winner. We presented our subjects with various types of hypothetical preference profiles, some where Borda respecting majoritarian approval, some where it failed to do so, then again for Condorcet, some profiles it respected majoritarian approval and some where it did not. The main thing we wanted to see was whether subjects’ support for Borda and Condorcet was higher when this social choice rule respected majoritarian approval than it did not. Our unambiguous overall empirical finding is that our subjects’ support for Borda and Condorcet was significantly stronger as they respect majoritarian approval.     

Dictatorial domains in preference aggregation

We call a domain of preference orderings “dictatorial” if there exists no Arrovian (Pareto optimal, IIA and non-dictatorial) social welfare function defined over that domain. In a finite world of alternatives where indifferences are ruled out, we identify a condition which implies the dictatoriality of a domain. This condition, to which we refer as “being essentially saturated”, is fairly weak. In fact, independent of the number of alternatives, there exists an essentially saturated (hence dictatorial) domain which consists of precisely six orderings. Moreover, this domain exhibits the superdictatoriality property, i.e., every superdomain of it is also dictatorial. Thus, given m alternatives, the ratio of the size of a superdictatorial domain to the size of the full domain may be as small as 6/m!, converging to zero as m increases.     

Money-egalitarian-equivalent and gain-maximin allocations of indivisible items with monetary compensation

Suppose that a certain quantity M of money and a finite number of indivisible items are to be distributed among n people, all of whom have equal claims on the whole. Different allocations are presented using various criteria of fairness in the special case where each player's utility function is additively separable. An allocation is “money-egalitarian-equivalent” (MEE) if each player's monetary valuation of his or her bundle is a fixed constant. We show that there is an essentially unique allocation that is MEE and Pareto-optimal; it is also envy-free. Alternatively, the “gain” of a player may be defined as the difference between how the player evaluates his bundle and an exact nth part of the whole according to his numerical evaluation of the whole. A “gain-maximin” criterion would maximize the minimum gain obtained by any player. We show that Knaster's procedure finds an allocation which is optimal under the gain-maximin criterion. That allocation is not necessarily envy-free, so we also find the envy-free allocation that is optimal under the gain-maximin criterion among all envy-free allocations. It turns out that, even though there exist allocations that are simultaneously envy-free and Pareto-optimal, this optimal allocation may fail to be Pareto-optimal, and it may also violate monotonicity criteria. Received: 30 September 1996/Accepted: 6 March 2002 The author would like to thank Professor William Thomson for a discussion on this subject; and he would like to thank the anonymous referees, who made many substantive suggestions for improving this paper – shortening it, streamlining the arguments, improving the terminology, making further ties with the literature, and improving the exposition.     

Top-Pair and Top-Triple Monotonicity

We say that a social choice function (SCF) satisfies Top-k Monotonicity if the following holds. Suppose the outcome of the SCF at a preference profile is one of the top k-ranked alternatives for voter i. Let the set of these k alternatives be denoted by B. Suppose that i’s preference ordering changes in such a way that the set of first k-ranked alternatives remains the set B. Then the outcome at the new profile must belong to B. This definition of monotonicity arises naturally from considerations of set “improvements” and is weaker than the axioms of strong positive association and Maskin Monotonicity. Our main results are that if there are two voters then a SCF satisfies unanimity and Top-2 or Top-pair Monotonicity if and only if it is dictatorial. If there are more than two voters, then Top-pair Monotonicity must be replaced by Top-3 Monotonicity (or Top-triple Monotonicity) for the analogous result. Our results demonstrate that connection between dictatorship and “improvement” axioms is stronger than that suggested by the Muller–Satterthwaite result (Muller and Satterthwaite in J Econ Theory 14:412–418, 1977) and the Gibbard–Sattherthwaite theorem.     

On strategy-proof social choice under categorization

I consider social choice problems such that (i) the set of alternatives can be partitioned into categories based on a prominent and objective feature and (ii) agents have strict preferences over the alternatives. Main results are characterizations of the structure of the strategy-proof social choice functions. I prove that each social choice function is strategy-proof if and only if it is decomposable into “small” strategy-proof social choice functions; one of them chooses one category and each of the others chooses one alternative from a category.     

Characterizations of two power indices for voting games with r alternatives

In the first three sections of this paper we present a set of axioms which provide a characterization of an extension of the Banzhaf index to voting games with r alternatives, such as the United Nations Security Council where a nation can vote “yes”, “no”, or “abstain”. The fourth section presents a set of axioms which characterizes a power index based on winning sets instead of pivot sets. Received: 4 April 2000/Accepted: 30 April 2001     

A simple procedure for finding equitable allocations of indivisible goods

The paper investigates how far a particular procedure, called the “descending demand procedure,” can take us in finding equitable allocations of indivisible goods. Both interpersonal and intrapersonal criteria of equitability are considered. It is shown that the procedure generally fares well on an interpersonal criterion of “balancedness”; specifically, the resulting allocations are Pareto-optimal and maximize the well-being of the worst-off individual. As a criterion of intrapersonal equitability, the property of envy-freeness is considered. To accommodate envy-freeness, a modification of the basic procedure is suggested. With two individuals, the modified procedure is shown to select the envy-free allocations that are balanced, i.e. the allocations that maximize the well-being of the worse-off individual among all envy-free allocations. Received: 3 March 2000/Accepted: 27 November 2000     

Mental Health of Non-gamblers Versus “Normal” Gamblers Among American Indian Veterans: A Community Survey

Goal This analysis was undertaken to assess the demographic and mental health characteristics of “normal” or non-problem gamblers versus non-gamblers in a representative community sample. Sample Study participants consisted of 557 North Central American Indian veterans. Data collection included a demographic and trauma questionnaire, a computer-based Diagnostic Interview Schedule for DSM-III-R, and a treatment history algorithm. Findings Univariate analyses revealed that gamblers had greater social competence (i.e., higher education, living with a spouse) and higher lifetime psychiatric morbidity. Binary regression analysis revealed that, compared to non-gamblers, gamblers were older, more highly educated, and more apt to be married. More gamblers showed evidence for lifetime risk-taking as evidenced by Antisocial Personality Disorder and Tobacco Dependence. Conclusions Social achievement and disposable income function as prerequisites for “normal” gambling in this population, although “externalizing” or “risk-taking” disorders also serve as independent contributors to at least some gambling. The increased rate of “internalizing” or emotional disorders are only indirectly related to gambling, perhaps through increasing age or through the “externalizing” disorders.     

Negatively interdependent preferences

We develop a theory of representation of interdependent preferences that reflect the widely acknowledged phenomenon of keeping up with the Joneses (i.e. of those preferences which maintain that well-being depend on “relative standing” in the society as well as on material consumption). The principal ingredient of our analysis is the assumption that individuals desire to occupy a (subjectively) better position than their peers. This is quite a primitive starting point in that it does not give any reference to what is actually regarded as “status” in the society. We call this basic postulate negative interdependence, and study its implications. In particular, combining this assumption with some other basic postulates that are widely used in a number of other branches of the theory of individual choice, we axiomatize the relative income hypothesis, and obtain an operational representation of interdependent preferences. Received: 7 December 1998/Accepted: 24 August 1999     

A new monotonic, clone-independent, reversal symmetric, and condorcet-consistent single-winner election method

In recent years, the Pirate Party of Sweden, the Wikimedia Foundation, the Debian project, the “Software in the Public Interest” project, the Gentoo project, and many other private organizations adopted a new single-winner election method for internal elections and referendums. In this article, we will introduce this method, demonstrate that it satisfies, e.g., resolvability, Condorcet, Pareto, reversal symmetry, monotonicity, and independence of clones and present an O(C^3) algorithm to calculate the winner, where C is the number of alternatives.     

Keywords and Cultural Change: Frame Analysis of <Emphasis Type="Italic">Business Model</Emphasis> Public Talk, 1975–2000

Keywords chronicle and capture cultural change by creating common categories of meaning against diverse local usages. We call this the global-local tension. To test competing theories of this tension, we employ frame analysis of more than 500 journal abstracts over a 25-year period, tracking the spread of business model as an economic keyword generated during unsettled economic times. Analyses reveal the simultaneous adoption of “global” and “local”frames without one supplanting or co-opting the other. The global-local tension is conciliated by providing primacy across communities of discourse to a small collection of frames (i.e., the global presence) while maintaining a plurality of local use within communities (i.e., the local alternative).     

Disciplinary knowledge revisited: The social construction of sociology

In Making Science (1992) I make the distinction between two types of knowledge: research frontier knowledge and core knowledge. Core knowledge is the small body of knowledge for which the entire scientific community treats as indisputable facts. The research frontier is all new knowledge which makes claim to being facts but in practice there is no consensus on this knowledge. The two types of knowledge are linked together by the evaluation process. Most frontier knowledge turns out to be insignificant and is ignored. A small part of frontier knowledge is taken as candidates for the core and evaluated. Most of this knowledge turns out to be “wrong.” Thus the important data of Jacobs ( 1989) loses a good deal of its impact because he forces it into a theory which he calls “social control”: a theory for which there is no evidence. Stephen Cole is professor of sociology at the State University of New York at Stony Brook. He is the author of Making Science: Between Nature and Society and, with Jonathan R. Cole, Social Stratification in Science. Stephen Cole is professor of sociology at the State University of New York at Stony Brook. He is the author of Making Science: Between Nature and Society and, with Jonathan R. Cole, Social Stratification in Science.     

Acyclic sets of linear orders

 A set of linear orders on {1,2, ℕ, n} is acyclic if no three of its orders have an embedded permutation 3-cycle {abc, cab, bca}. Let f (n) be the maximum cardinality of an acyclic set of linear orders on {1,2, ℕ, n}. The problem of determining f (n) has interested social choice theorists for many years because it is the greatest number of linear orders on a set of n alternatives that guarantees transitivity of majority preferences when every voter in an arbitrary finite set has any one of those orders as his or her preference order. This paper gives improved lower and upper bounds for f (n). We note that f (5)=20 and that all maximum acyclic sets at n=4, 5 are generated by an “alternating scheme.” This procedure becomes suboptimal at least by n=16, where a “replacement scheme” overtakes it. The presently-best large-n lower bound is approximately f (n)≥(2.1708) ⁿ . Received: 5 April 1995/Accepted: 10 November 1995     

What is a problem?

Among others, the term “problem” plays a major role in the various attempts to characterize interdisciplinarity or transdisciplinarity, as used synonymously in this paper. Interdisciplinarity (ID) is regarded as “problem solving among science, technology and society” and as “problem orientation beyond disciplinary constraints” (cf. Frodeman et al.: The Oxford Handbook of Interdisciplinarity. Oxford University Press, Oxford, 2010). The point of departure of this paper is that the discourse and practice of ID have problems with the “problem”. The objective here is to shed some light on the vague notion of “problem” in order to advocate a specific type of interdisciplinarity: problem-oriented interdisciplinarity. The outline is as follows: Taking an ex negativo approach, I will show what problem-oriented ID does not mean. Using references to well-established distinctions in philosophy of science, I will show three other types of ID that should not be placed under the umbrella term “problem-oriented ID”: object-oriented ID (“ontology”), theory-oriented ID (epistemology), and method-oriented ID (methodology). Different philosophical thought traditions can be related to these distinguishable meanings. I will then clarify the notion of “problem” by looking at three systematic elements: an undesired (initial) state, a desired (goal) state, and the barriers in getting from the one to the other. These three elements include three related kinds of knowledge: systems, target, and transformation knowledge. This paper elaborates further methodological and epistemological elements of problem-oriented ID. It concludes by stressing that problem-oriented ID is the most needed as well as the most challenging type of ID.     

Aggregation of smooth preferences

Suppose p is a smooth preference profile (for a society, N) belonging to a domain P ^N . Let σ be a voting rule, and σ(p)(x) be the set of alternatives in the space, W, which is preferred to x. The equilibrium E(σ(p)) is the set {x∈W:σ(p)(x) is empty}. A sufficient condition for existence of E(σ(p)) when p is convex is that a “dual”, or generalized gradient, dσ(p)(x), is non-empty at all x. Under certain conditions the dual “field”, dσ(p), admits a “social gradient field”Γ(p). Γ is called an “aggregator” on the domain P ^N if Γ is continuous for all p in P ^N . It is shown here that the “minmax” voting rule, σ, admits an aggregator when P ^N is the set of smooth, convex preference profiles (on a compact, convex topological vector space, W) and P ^N is endowed with a C ¹-topology. An aggregator can also be constructed on a domain of smooth, non-convex preferences when W is the compact interval. The construction of an aggregator for a general political economy is also discussed. Some remarks are addressed to the relationship between these results and the Chichilnisky-Heal theorem on the non-existence of a preference aggregator when P ^N is not contractible. Received: 4 July 1995 / Accepted: 26 August 1996     

The Application of Co-modality in Greece: a Critical Appraisal of Progress in the Development of Co-modal Freight Centres and Logistics Services

This paper discusses the situation in Greece as regards the introduction of co-modal transport services. It starts with basic definitions of “co-modality” and what it means for Greece. It then presents the results of a demand data collection and analysis exercise which resulted in the first ever estimates of the “potential” for road/rail co-modal transport in Greece today and in 2015. Based on these forecasts it seems that at least for two thickly populated areas of the country (i.e. Athens and Thessaloniki) this demand can be as high as 40% of the total freight flows. The paper then goes on to examine the means by which the responsible authorities can “induce” co-modal services in the country. It does this by examining the policies necessary, the infrastructure (both hard and “soft”), the necessary actions and incentives for the development of a “co-modal” market, and the necessary training––education actions for human resource development. The overall conclusion is that unless specific actions are taken on behalf of the government (such as those mentioned in the paper) the “land” based co-modal transport has no future in Greece.

Studying social capital in situ: A qualitative approach

In recent years, the concept of social capital – broadly defined as co-operative networks based on regular, personal contact and trust – has been widely applied within cross-disciplinary human science research, primarily by economists, political scientists and sociologists. In this article, I argue why and how fieldwork anthropologists should fill a gap in the social capital literature by highlighting how social capital is being built in situ. I suggest that the recent inventions of “bridging” and “bonding” social capital, e.g., inclusive and exclusive types of social capital, are fruitful concepts to apply in an anthropological fieldwork setting. Thus, my case study on the relationship between local people and newcomers in the rural Danish marginal municipality of Ravnsborg seeks to reveal processes of bridging/bonding social capital building. Such a case study at the micro level has general policy implications for a cultural clash between two different groups by demonstrating the complexity of a social capital mix where bonding social capital strongly prevails. This ultimately leads to a “social trap” (Rothstein 2005), implying widespread distrust and serious social and economic costs for a whole population. Gunnar Lind Haase Svendsen is Senior Researcher, at the Institute of Rural Research and Development, Southern University of Denmark. He is the co-author, with G. T. Svendsen, of The Creation and Destruction of Social Capital: Entrepreneurship, Co-operative Movements and Institutions (Edward Elgar, Cheltenham, UK, 2004, Paperback edition, October 2005); and author of Samarbejde og konfrontation. Opbygning og nedbrydning af social kapital i de danske landdistrikter 1864–2003 [Cooperation and Confrontation. The Creation and Destruction of Social Capital in Rural Denmark 1864–2003], Ph.D. dissertation, University of Sourthern Denmark, Esbjerg, 2004: http://www.humaniora.sdu.dk/phd/dokumenter/filer/Afhandlinger-30.pdfg. Gunnar Svendsen's scholarly interests include Bourdieusian Economics (new socioeconomics), capital theory, social capital, rural civic movements, and rural discourses. He has recently finished a research project for the Danish Ministry of the Interior about the role of intangible assets (culture, networks, and historical traditions) for differences in economic performance (DEP) among four Danish local communities.     

On the multi-preference approach to evaluating opportunities

The purpose of the paper is to provide a general framework for analyzing “preference for opportunities.” Based on two simple axioms a fundamental result due to Kreps is used in order to represent rankings of opportunity sets in terms of multiple preferences. The paper provides several refinements of the basic representation theorem. In particular, a condition of “closedness under compromise” is suggested in order to distinguish the flexibility interpretation of the model from normative interpretations which play a crucial role in justifying the intrinsic value of opportunities. Moreover, the paper clarifies the link between the multiple preference approach and the “choice function” approach to evaluating opportunities. In particular, it is shown how the well-known Aizerman/Malishevski result on rationalizability of choice functions can be obtained as a corollary from the more general multiple preference representation of a ranking of opportunity sets. Received: 3 September 1996 / Accepted: 18 August 1997