### Perspectives on Social Choice

**2007 (29) Issue 2**

Guest-Editor: Marlies Ahlert

### Editorial

Introduction and Overview

This volume of Analyse & Kritik approaches social choice from different angles. Each of the papers thematically has some relation with the work of Wulf Gaertner. This provides some topical unity to the volume. However, other than in case of a typical Festschrift the refereed papers are in all other regards independent contributions to the field of social choice as very widely understood. Methods reach from axiomatic analyses over experiments to simulations and from the theoretical to the applied.

Contributions to the volume are presented in alphabetical order of the authors. The first one by Marlies Ahlert develops an axiomatic model of sequential negotiations between two parties. The analysis is based on descriptive theories of aspiration adaptation in bargaining. Such descriptive theories were introduced already in the 1960s by Heinz Sauermann and Reinhard Selten. They have been refined through the decades by Reinhard Selten, Reinhard Tietz and others. A series of experiments conducted by Ahlert at the University of Osnabrück in the 1990s laid the basis for the argument in the paper (c.f. Gaertner and Klemisch-Ahlert 1992; Klemisch-Ahlert 1996) The paper characterizes the bounded rationality of decisions in a bargaining process axiomatically. The modifications of proposals as made by the negotiators are modeled as concessions. These derive from adapting own aspirations or by making proposals that fulfill certain aspirations of the opponent. Solution areas of such processes where parties’ behavior fulfils the axioms are uniquely defined. It is proved that the set of solutions that can be achieved in view of the axioms is described by the aspiration balancing principle. The principle which forms an important and well known observation of descriptive bargaining theory can also be interpreted as a principle of distributive justice. The paper adds a new aspect to the discussion on bargaining perspectives on distributive justice of Gaertner and Klemisch-Ahlert (1992) by characterizing boundedly rational sequential interactions in bargaining in a novel axiomatic way.

The paper by Nick Baigent has to be seen as one of several contributions by Nick Baigent, Wulf Gaertner and Yongsheng Xu on the problem of rationalizability of choice if external references or normative constraints are present. The development of this line of publications started with the paper by Nick Baigent and Wulf Gaertner “Never Choose the Uniquely Largest“ (1996). There the authors rationalize choice decisions that follow such a precept of civility. Other types of choices, e.g. choosing the median (Gaertner and Xu 1999), and more general analyses followed. In this paper Nick Baigent considers situations where there are two possible influences on the choice of an agent. First, she may have the interest to maximize the satisfaction of a given preference on the other hand she might want to comply with a certain norm. In cases where a norm is present, can one conclude from her choices whether the choice maker is an optimizer or not? Among the many possibilities to combine a preference and a norm, the author considers lexicographical combinations as a special, however, important case. He shows that no general claims can be made unless restrictions concerning the type of norm apply. The choices und the lexicographical combination of influences can be consistent with maximizing a revealed preference but not necessarily so.

Salvador BarberÃ addresses from a theoretical point of view how domain restrictions on profiles of preferences affect aggregation results in Social Choice Theory (for an excellent overview about domain conditions, existing theorems and own results see Gaertner 2001). The ma jority of findings in the literature concentrate on restrictions when individuals have linear orderings. Salvador BarberÃ inquires whether and how results on domain restrictions that exist under the assumption of linear orderings can be extended to cases where individuals are allowed to express indifferences among alternatives. The author proves and also illustrates by referring to results from the literature that there is no unique general answer to the problem and that the complexity of the problem depends on the class of preferences considered. In doing so BarberÃ starts by investigating two generalizations of single peaked profiles, first indifferences between best alternatives are allowed, second, indifferences between worst alternative are introduced by taking into account an outside option. The first change leads to more complicated, nevertheless positive results that are similar to the case of single peaked profiles with linear orderings. The second change seems to be more fundamental since it destroys the typical results that would hold good without this extension. Turning this on its head the author then construes examples of preference families where indifferences help to prove positive results. There is more than one lesson to be learnt from the paper which should trigger quite some further research. But for sure, the reader will not any longer feel entitled to treat the exclusion of indifferences as an innocuous technical assumption that may be introduced without further ado whenever it is convenient.

Walter Bossert and Kotaro Suzumura consider a type of rationality that diverges from the traditional assumptions of decision as well as social choice theory according to which the decision maker chooses greatest or maximal elements with respect to some preference relation. They analyze a form of rationality such that the decision maker chooses an alternative that is at least as good as some reference alternative. The authors use the example of the status quo in bargaining theory. From the experimental literature on decision behavior it is well known that sub jects often do not maximize but satisfice, a notion which goes back to Herbert Simon (1955). According to his view actors form an aspiration which characterizes the degree to which a goal must be fulfilled to let them rest content while they will search on as long as the aspiration is not met. The views of Bossert und Suzumura are akin to this approach to bounded rationality which is also applied in Ahlert’s analysis of concession making in a bargaining process. In the formal part of the paper the authors characterize this type of individual and social choice on general domains without the assumption of full transitivity. They use different assumptions about the degree of transitivity instead. For many classes of problems Bossert and Suzumura provide complete characterizations, show aspects of comparison to the traditional approach and open up further research perspectives.

Friedrich Breyer and Hartmut Kliemt focus on the shortage of human organ transplants in Germany as a problem of applied social choice. Both authors are members of a group of researchers who have thoroughly investigated different categories of causes and consequences of that problem (Breyer et al. 2006). Among the causes they investigate the role of hospitals and the present extrinsic i.e. financial and intrinsic i.e. motivational incentives for hospitals to participate in the procurement of human organs. The authors also describe and discuss different potential rules for cadaveric organ donation including presumed consent and reciprocity rules. They conclude their investigation by proposing five measures to reform the institutions of organ transplantation: removal of financial obstacles for reporting hospitals, establishment of a nationwide organ donor registry, reorganization of the coordination process, introduction of a presumed consent rule, and willingness to donate as a criterion of organ allocation (the possibility to expand the supply of donated human organs by introducing types of market solutions can be found in Aumann and Gaertner 2004).

The paper by Wolfgang Eichhorn and Manfred Krtscha deals with the theoretical analysis of multidimensional distributions. Empirical social choice theorists use the “classical“ Lorenz curve as a tool to describe, compare, and analyze income distributions. The criterion induces a dominance relation in terms of equality. This results in a partial ordering on income distributions. The Gini-coefficient defines a numerical measure that enlarges the possibilities of ranking (income) distributions in terms of equality. By extending comparisons to cases where the Lorenz dominance fails it implies a complete ordering. The model Eichhorn and Krtscha analyze does not consist of just one attribute of an individual, like personal income. Their approach allows to include other numerically measurable aspects that affect the individual’s welfare, too, like e.g. health status or leisure time. The authors consider generalizations of the Lorenz dominance to the multi-attribute case. These rankings again induce partial orderings. The authors then propose two new heterogeneity measures that can be interpreted as generalizations of the Gini-Index. These measures induce orderings that complete the rankings by the multivariate Lorenz ma jorization. The authors axiomatically characterize and compare the proposed measures.

Marc Fleurbaey contributes to the discussion of how to evaluate, measure or compare capability sets, i.e. opportunity sets consisting of vectors of functionings (c.f. for example Sen 1992). The author starts by describing a proposal by Wulf Gaertner and Yongsheng Xu (2006). The latter introduce a measure of distance from some reference point to the boundary of the capability set. Marc Fleurbaey criticizes that this measure is not strictly increasing with respect to set inclusion. He also emphasizes that it may result in equal values for substantially different opportunity sets, because it allows compensations between different functionings. This leads to a discussion of the pros and cons of requiring equality of capability sets versus equal values of capability sets to assess indifferences between capability sets. This seems crucial when comparing capability sets of individuals or when evaluating the distribution of these sets in a society. Fleurbaey suggests a framework of comparison that enables him to analyze requirements like perfect egalitarianism and perfect equity and to find out the very limited range of the validity and applicability of these axioms. This study, though it may on the first glance seem somewhat frustrating, can nevertheless be used as a springboard for further research on measures of living standards.

Dorothea K. Herreiner and Clemens Puppe present a questionnaire study on distributive decisions and results concerning the tension between different fairness principles and the goal of efficiency. This stands in the same tradition as the widely cited paper “On Dividing Justly“ by Menahem Yaari and Maya Bar-Hillel (1984) published as lead article in the very first volume of the Journal Social Choice and Welfare (for a combination of theories and experiments on distributive justice c.f. also Gaertner and Klemisch-Ahlert 1992). In the experiment by Dorothea K. Herreiner and Clemens Puppe sub jects had to decide without monetary incentives on the allocation of several indivisible goods and a divisible amount of money to some hypothetical recipients. The authors are interested in finding out which fairness criteria are relevant for the chosen allocations. They consider the concepts of envy-freeness, inequality aversion, the utilitarian principle and the Rawlsian maximin solution. The design also allowed the participants to describe their decision making process in written form. The analysis of the written statements is very exciting proving that the method can be an extremely useful tool to understand the decisions making of human sub jects.

Eliora van der Hout, Jack Stecher and Harrie de Swart’s paper uses the axiomatic method to analyze and compare two election systems. After keeping us in suspense for quite a while Eliora van der Hout finally agreed to the publication. We are happy to include it in the volume since the paper is representative of an important line of research in social choice theory, namely axiomatic analyses of voting rules or election systems. Choices of new electoral systems or changes of them are not made very often in states. However, whenever such choices must be made, it is important to understand the formal properties of electoral institutions and to think about the strengths an weaknesses of the existing election rules. The paper looks at the Dutch electoral system which is based on a plurality ranking vis a vis the British one which is a “First-Past-The-Post“-system. The authors compare the theoretical properties of both and characterize each rule by a set of independent properties. In addition they collect arguments for and against the properties that distinguish them. The balancing of arguments does not lead the authors to an unambiguous conclusion in favour of one of the two systems. Given the complexities of voting systems this seems as it should be. Prudent constitutional choices must be made. But with analyses like those of the paper in hand prudence can be enhanced.

The paper by Jochen Jungeilges can be seen as a contribution to the use of rationality concepts in economic theory. The technique of simulations and the framework is analogous to research activities in dynamic systems and chaos theory, Wulf Gaertner started in the late 1980s. That time both authors together had run simulations to understand the dynamics of a market model where the consumption decisions of consumers were related by interdependent utility functions (cf. Gaertner and Jungeilges 1994). In the present paper Jochen Jungeilges analyses the concept of consistent expectation equilbria in the context of a cobweb model. It is asked whether agents in such a model are able to discriminate between the actual law of motion and the perceived law of motion. The tools the agents may use to learn about reality and that they are assumed to be able to apply are the basic methods of statistics. The author shows by numerical simulations that under these assumptions in the considered model the existence of consistent expectation equilibria is only a temporary phenomenon. One can interpret this result as a contribution to the broad field that deals with problems of how to model rationality of agents appropriately in different economic circumstances. It is an important matter to find out, given the economic environment, how strong the rationality assumptions for decision making should be in view of the “bounded“ abilities of agents to collect and process information.

Prasanta K. Pattanaik and Yongsheng Xu contribute to the discussion of the concept of social capital. In the sociological literature this concept is seen to rest on three pillars, trust, norms, and networks. The authors concentrate on the aspect of social networks and develop an approach that enables them to construct measures from two different classes. The first class consists of measures for the personal connectedness between individuals in a given social network. The authors present and discuss a list of axioms concerning measures of that type. They axiomatically characterize two measures that are based on a definition of benign chains of friends linking two individuals. The measures involve the shortest of these chains. Other measures of personal connectedness are characterized from the point of view that networks are a useful, even necessary medium to transmit messages. Here the authors take into account that messages can partly or completely get lost during the transmission. The second class of measures evaluates the extent to which social networks exist in different societies. The authors use the previously characterized measures of personal connectedness to construct measures from this second class. Their approach can be interpreted as the problem of how to aggregate evaluations of personal connections of all individuals in a society to one evaluation for the whole network. The authors solve this problem in a specific way. As a solution they propose the sum of all values of personal connectedness under some fixed measure of all pairs of distinct individuals. They characterize the social network measures of this type derived from different personal connectedness measures under some quite plausible conditions.

Ashley Piggins and Maurice Salles investigate a problem which is often neglected in classical economic theory. When preferences are involved or rational decision making is considered it is most often assumed that the preferences are complete, i.e. it is assumed the decision maker is able to compare and rank-order any two available alternatives or ob jects. Which solutions in instances of indeterminacy of an ordinal preference ranking can be offered or could be appropriate for economic applications is seldom asked. The authors motivate their research question and develop a precise definition what they mean by indeterminacy in this paper. They present an overview over models that map or are able to map the problem of indeterminacy of preferences into a formal framework and they develop their arguments on how philosophy and economics could or should deal with it. Their discussion includes ideas like that of parity or that indeterminacy could be implied by vagueness. With respect to concepts of vagueness the authors thoroughly discuss and compare supervaluation theory and fuzzy set theory and illustrate their reasoning with examples and applications.

The last paper by Yongsheng Xu, like the paper by Nick Baigent in this volume, is again a contribution to the field of decision making when norms are present. In my comments on Nick Baigent’s paper I have already mentioned some norms like never choose the uniquely largest (Baigent and Gaertner 1996) and choose the median (Gaertner and Xu 1999), where these authors succeeded in rationalizing choices that obey these norms. In this paper Yongsheng Xu raises the problem how to construct an approach that is general enough to cover the rationalizations of different types of norm-constrained behaviors. The author proposes a general concept where the individual first applies her internalized norms to exclude alternatives that are unacceptable under these norms and then chooses a best from the remaining alternatives. The author formulates and explains a set of axioms a choice function in this approach might have. He is able to uniquely characterize several different types of norm-constrained choice functions by subsets of these axioms, amongst them behaviour that is governed by some modesty-norm, by the median-norm, or by some protest-based norm.

Bibliography

Aumann, C./W. Gaertner (2004), Die Organknappheit: Ein Plädoyer für eine Marktlösung, in: Ethik in der Medizin 16, 105â€“111

Baigent, N./W. Gaertner (1996), Never Choose the Uniquely Largest: A Characterization, in: Economic Theory 8, 239â€“249

Breyer, F./W. v. d. Daele/M. Engelhard et al. (2006), Organmangel. Ist der Tod auf der Warteliste vermeidbar?, Berlin

Gaertner, W. (2001), Domain Conditions in Social Choice Theory, Cambridge

â€”/J. Jungeilges (1994), A Model of Interdependent Consumer Behavior: Nonlinear Dynamics in R^2 , in: W. Eichhorn (Hrsg.), Models and Measurement of Welfare and Inequality, Berlin-Heidelberg-New York, 941â€“962

â€”/M. Klemisch-Ahlert (1992), Social Choice and Bargaining Perspectives on Distributive Justice, in: Lecture Notes in Economics and Mathematical Systems 387, Berlin-Heidelberg-New York

â€”/ Y. Xu (1999), On Rationalizability of Choice Functions: A Characterization of the Median, in: Social Choice and Welfare 16(4), 629â€“638

â€”/â€” (2006), Capability Sets as a Basis of a New Measure of Human Development, in: Journal of Human Development 7, 311â€“321

Klemisch-Ahlert, M. (1996), Bargaining in Economic and Ethical Environmentsâ€”An Experimental Study and Normative Solution Concepts, in: Lecture Notes in Economics and Mathematical Systems 436, Berlin-Heidelberg-New York

Sen, A. (1992), Inequality Re-examined, Oxford

Simon, H. A. (1955), A Behavioral Model of Rational Choice, in: Quarterly Journal of Economics 69, 99â€“118

Yaari, M./M. Bar-Hillel (1984), On Dividing Justly, in: Social Choice and Welfare 1, 1â€“24

### Table of Contents

**Title: **Aspiration Balancing Agreements: A New Axiomatic Approach to Bounded Rationality in Negotiations**Author: **Marlies Ahlert

**Page: **121-138

Abstract: A wealth of experimental findings on how real actors do in fact bargain exists. However, as long as there is no systematic general account of the several experiments bargaining theory remains dominated by axiomatic approaches based on normative requirements or on assumptions of full rather than bounded rationality. Contrary to that, the new axiomatic account of aspiration level balancing in negotiations of boundedly rational actors presented in this paper incorporates experimental findings systematically into economic bargaining theory. It thereby forms a descriptive theory of bargaining that has normative power as well.

**Title: **Choice, Norms and Revealed Preference**Author: **Nicholas Baigent

**Page: **139-145

Abstract: This paper considers lexical combinations of choice functions where at least one is interpreted as arising from a norm. It is shown that in for all possibilities in which a norm is present, in general final choice may be consistent with preference optimization, but that it need not be so. It is concluded therefore that a fruitful approach to understanding the effect of norms on choice is to consider particular classes of norms rather than norms in general as in the work by Wulf Gaertner among others.

**Title: **Indifferences and Domain Restrictions**Author: **Salvador BarberÃ

**Page: **146-162

Abstract: The purpose of this paper is to discuss the extent to which allowing for individuals to be indifferent among alternatives may alter the qualitative results that are obtained in social choice theory when domain restrictions are defined on profiles of linear orders. The general message is that indifferences require attention and careful treatment, because the translation of results from a world without indifferences to another where agents may be indifferent among some alternatives is not always a straightforward exercise. But the warning is not one-directional: sometimes indifferences complicate the statement of results, but preserve their essential message. Some- times, they help to create domains where some rules work better than in the presence of linear orders. In other cases, however, their presence destroys the positive results that would apply in their absence. I provide examples of these three situations.

**Title: **Non-deteriorating Choice without Full Transitivity**Author: **Walter Bossert / Kotaro Suzumura

**Page: **163-187

Abstract: Although the theory of greatest-element rationalizability and maximal-element rationalizability on general domains and without full transitivity of rationalizing relations is well-developed in the literature, these standard notions of rational choice are often considered to be too demanding. An alternative definition of rationality of choice is that of non-deteriorating choice, which requires that the chosen alternatives must be judged at least as good as a reference alternative. In game theory, this definition is well-known under the name of individual rationality when the reference alternative is construed to be the status quo. This alternative form of rationality of individual and social choice is characterized inthispaperongeneraldomainsandwithout full transitivity of rationalizing relations.

**Title: **The Shortage of Human Organs: Causes, Consequences and Remedies**Author: **Friedrich Breyer / Hartmut Kliemt

**Page: **188-205

Abstract: There is an ever increasing shortage of human organ transplants in Germany. This paper aims at understanding the reasons for that shortage better and then discusses various ways to overcome it. After estimating the potential supply of donor organs it is discussed why actual supply remains far below potential supply. Insufficient reimbursement for hospitals, a lack of incentives to donate, and mistaken donation rules are diagnosed to cause the shortage. Thus, organ shortage is due not to natural constraints but to inappropriate social institutions. Introducing a presumed consent rule, reciprocity in organ allocation, better payments for hospitals and for donors seem potential remedies.

**Title: **Multivariate Lorenz Ma jorization and Heterogeneity Measures: An Axiomatic Approach**Author: **Wolfgang Eichhorn / Manfred Krtscha

**Page: **206-225

Abstract: This work introduces two new curves that are multivariate generalizations of the ’classical’ Lorenz curve. All data of d-variate distributions can be visualized by drawing these curves in the plane, whereas Koshevoy’s and Mosler’s generalization by a lift zonoid in R^(d+1) can only be drawn for d = 2. The generalizations of the Lorenz curve induce partial orderings of d-variate distributions. Furthermore, two inequality or heterogeneity measures that are consistent with the induced rankings are proposed. They can be considered as new generalizations of the univariate Gini coefficient. For deciding which of the two measures is more appropriate for measuring a sort of convergence concerning different countries of an union or of regions of a country, we establish systems of axioms. Although these systems are reflecting natural properties, several of the axioms are new. Moreover, by means of these axioms well-known inequality measures are tested, too.

**Title: **Living Standards and Capabilities: Equal Values or Equal Sets?**Author: **Marc Fleurbaey

**Page: **226-234

Abstract: Inspired by Gaertner and Xu (2006), this paper examines the possibility to construct a social ordering over distributions of capability sets, and a measure of the value of individual capability sets, such that perfect equality of sets, across individuals, is preferable to a simple equality of the value of sets. It is shown that this is a rather demanding requirement.

**Title: **Distributing Indivisible Goods Fairly: Evidence from a Questionnaire Study**Author: **Dorothea Herreiner / Clemens Puppe

**Page: **235-258

Abstract: We report the results of a questionnaire study on the fair distribution of indivisible goods. We collected data from three different sub ject pools, first- and second- year students ma joring in economics, law students, and advanced economics students with some background knowledge of fairness theories. The purpose of this study is to assess the empirical relevance of various fairness criteria such as inequality aversion, the utilitarian principle of maximizing the sum of individual payoffs, the Rawlsian ’maximin’ principle of maximizing the payoff of the worst-off individual, and the criterion of envy-freeness (in the sense of Foley 1967).

**Title: **A Critical Discussion of the Characteristic Properties of List PR and FPTP Systems**Author: **Eliora van der Hout / Jack Stecher / Harrie de Swart

**Page: **259-268

Abstract: This paper discusses the characteristic properties of List PR systems and FPTP systems, as given in Hout 2005 and Hout et al. 2006. While many of the properties we consider are common to both systems, it turns out (see Hout 2005) that the British system distinguishes itself by satisfying the district cancel lation property, while the Dutch system distinguishes itself by satisfying consistency and anonymity. For scoring rules, topsonlyness is equivalent to being party fragmentation-proof (see Hout 2005; Hout et al. 2006). One might present this as an argument in favour of requiring topsonlyness. However, we will also give counter-arguments against insisting upon the property of being party fragmentation-proof.

**Title: **On Chaotic Consistent Expectations Equilibria**Author: **Jochen Jungeilges

**Page: **269-289

Abstract: The notion of consistent expectations equilibria (CEE) as propagated by Hommes/Sorger (1998) is reviewed. Focusing on their example of a chaotic CEE constructed in the context of a cobweb model, it is argued that such an equilibrium is a temporary one. Assuming that an agent modeled as an individual, versatile in applying the basic tools of linear time-series econometrics has learned the CEE, I analyze the duration of the time period over which the agent maintains her/his beliefs concerning the perceived law of motion (AR(1)). The analysis based on numerical simulations indicates that the use of techniques rooted in the linear paradigm is sufficient to generate convincing evidence against the underlying perceived law of motion.

**Title: **On Measuring Personal Connections and the Extent of Social Networks**Author: **Prasanta K. Pattanaik / Yongsheng Xu

**Page: **290-310

Abstract: The notions of personal connection and social networks are key ingredients of the increasingly important concept of social capital in social sciences in general and in economics in particular. This paper discusses the problem of measuring personal connection and the extent of social networks that may exist in a society. For this purpose we develop several conceptual and analytical frameworks. In the process, we axiomatically characterize several measures of personal connection and social networks.

**Title: **Instances of Indeterminacy**Author: **Ashley Piggins / Maurice Salles

**Page: **311-328

Abstract: This paper is a survey of how economists and philosophers approach the issue of comparisons. More precisely, it is about what formal representation is appropriate whenever our ability to compare things breaks down. We restrict our attention to failures that arise with ordinal comparisons. We consider a number of formal approaches to this problem including one based on the idea of parity. We also consider the claim that the failure to compare things is a consequence of vagueness. We contrast two theories of vagueness; fuzzy set theory and supervaluation theory. Some applications of these theories are described.

**Title: **Norm-Constrained Choices**Author: **Yongsheng Xu

**Page: **329-339

Abstract: This paper develops a general and unified framework to discuss individual choice behaviors that are constrained by the individual’s internalized norms. We propose a new notion of rationalizablity of a choice function that incorporates such constraints, and axiomatically study several norm-constrained choice behaviors.