Liberal approaches to ranking infinite utility streams: when can we avoid interference?

In this work we analyse social welfare relations on sets of finite and infinite utility streams that satisfy various types of liberal non-interference principles. Earlier contributions have established that (finitely) anonymous and strongly Paretian quasiorderings exist that verify non-interference axioms together with weak preference continuity and further consistency. Nevertheless Mariotti and Veneziani (2011) prove that a fully liberal non-interfering view of a finite society leads to dictatorship if the weak Pareto principle is imposed. We first prove that this impossibility result vanishes when we extend the horizon to infinity. Then we investigate a related problem: namely, the possibility of combining “standard” semicontinuity with efficiency in the presence of non-interference. We provide several impossibility results that prove that there is a generalised incompatibility between relaxed forms of continuity and non-interference principles, both under ordinal and cardinal views of the problem.     

The Libertarian paradox: some further observations

It is shown that the weak Pareto principle consists of two parts: Pareto Neutrality and Weak Pareto Unanimity. It is the Pareto Neutrality which is responsible for the Paradox of the Paretian Libertarian. The libertarianism condition can also be factorized into two parts: the Libertarian Invariance and the Libertarian Non-Imposition. It is the Libertarian Invariance which is responsible or the Paradox of the Paretian Libertarian. Under conditions of Unrestricted Domain, Pareto Neutrality and Libertarian Invariance, if we require a social preference to be acyclic, then(1) neither can individuals' personal rights be respected, nor can they be reversed;(2) neither can unanimous group rights be respected, nor can they be reversed. Consequently, the Paradox of the Paretian Libertarian is due to the inconsistent use of information contained in the weak Pareto principle and the libertarianism condition.I would like to thank Nick Baigent, Prasanta Pattanaik, John Riley, Amartya Sen and Kotaro Suzumura for their comments. I would also like to thank two anonymous referees for their suggestions and comments on earlier drafts of the paper which led to a great improvement of the present version.     

Covering relations,closest orderings and hamiltonian bypaths in tournaments

We show that the Slater's set of a tournament, i.e. the set of the top elements of the closest orderings, is a subset of the top cycle of the uncovered set of the tournament. We also show that the covering relation is related to the hamiltonian bypaths of a strong tournament in that if x covers y, then there exists an hamiltonian bypath from x to y.We thank B. Monjardet and an anonymous editor for helpful suggestions.     

Topological aggregation, the case of an infinite population

 The literature on infinite Chichilnisky rules considers two forms of anonymity: a weak and a strong. This note introduces a third form: bounded anonymity. It allows us to prove an infinite analogue of the “Chichilnisky– Heal-resolution” close to the original theorem: a compact parafinite CW-complex X admits a bounded anonymous infinite rule if and only if X is contractible. Furthermore, bounded anonymity is shown to be compatible with the finite and the [0, 1]-continuum version of anonymity and allows the construction of convex means in infinite populations. With X=[0, 1], the set of linear bounded anonymous rules coincides with the set of medial limits. Received: 30 October 1993/Accepted: 22 April 1996     

On continuity of Arrovian social welfare functions

We study continuity properties of Arrovian social welfare functions in the infinite population framework. We show that continuous welfare functions satisfying unanimity and independence of irrelevant alternatives are dictatorial. Weak anonymity is shown to be incompatible with continuity and unanimity: every continuous weakly anonymous social welfare function must be a constant function.     

A complete and strongly anonymous leximin relation on infinite streams

Various extensions of the leximin order to the infinite dimensional setting have been suggested. They relax completeness and strong anonymity. Instead, by removing sensitivity to generations at infinite rank this paper defines a complete and strongly anonymous leximin relation on infinite streams. The order is axiomatized, and it is shown to be the limit of extended rank-discounted utilitarianism for any utility function, as the discount factor approaches zero.     

STEROIDS AND HOME RUNS

There has been no change in Major League Baseball home run hitting for 45 yr, in spite of the new records. Players hit with no more power now than before. Records are the result of chance variations in at bats, home runs per hit, and other factors. The clustering of records is implied by the intermittency of the law of home runs. Home runs follow a stable Paretian distribution with infinite variance. The shape and scale of the distribution have not changed over the years. The greatest home run hitters are as rare as great scientists, artists, or composers. (JEL A10, C02, C16, C52, L51)     

Some issues related to the topological aggregation of preferences

This paper deals with the topological approach to social choice theory initiated by Chichilnisky. We study several issues concerning the existence and uniqueness of Chichilnisky rules defined on preference spaces. We show that on topological vector spaces the only additive, anonymous, and unanimous aggregation n-rule is the convex mean. We study the case of infinite agents and show that an infinite Chichilnisky rule might be considered as the limit of rules for finitely many agents. Finally, we show that under some restrictions on the preference space, the existence of a Chichilnisky rule for every finite case implies the existence of a weak Chichilnisky rule for the infinite case.     

Continuity and egalitarianism in the evaluation of infinite utility streams

There exists a utilitarian tradition à la Sidgwick of treating equal generations equally. Diamond showed that there exists no social evaluation ordering over infinite utility streams in the presence of the Pareto principle, the Sidgwick principle, and continuity. Instead of requiring the Sidgwick principle of procedural fairness, we focus on two principles of distributional egalitarianism along the line of the Pigou–Dalton transfer principle and the Lorenz domination principle, and show that there exists no social evaluation relation satisfying one of these egalitarian principles and the weakened continuity and rationality axioms even in the absence of the Pareto principle. This paper is a substantially revised version of our foregoing paper, “On the Possibility of Continuous, Paretian and Egalitarian Evaluation of Infinite Utility Streams,” which was based on our joint research conducted as a part of the Project on Intergenerational Equity under the auspices of the Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology of Japan. Thanks are due to Geir Asheim, Kaushik Basu, Walter Bossert, Hajime Hori, Tomoki Inoue, Mitsunori Noguchi and Koichi Tadenuma with whom we had several discussions on this and related issues. We are also grateful to the anonymous referees and the Associate Editor in charge of our earlier paper for their helpful comments and suggestions. Needless to say, no one other than ourselves should be held responsible for any remaining defect of this paper.     

The C1 topology on the space of smooth preference profiles

This paper defines a fine C ¹-topology for smooth preferences on a “policy space”, W, and shows that the set of convex preference profiles contains open sets in this topology.  It follows that if the dimension(W)≤v(?)−2 (where v(?) is the Nakamura number of the voting rule, ?), then the core of ? cannot be generically empty. For higher dimensions, an “extension” of the voting core, called the heart of ?, is proposed. The heart is a generalization of the “uncovered set”. It is shown to be non-empty and closed in general. On the C ¹-space of convex preference profiles, the heart is Paretian. Moreover, the heart correspondence is lower hemi-continuous and admits a continuous selection. Thus the heart converges to the core when the latter exists. Using this, an aggregator, compatible with ?, can be defined and shown to be continuous on the C ¹-space of smooth convex preference profiles. Received: 3 April 1995/Accepted: 8 April 1998     

The Lorenz zonotope and multivariate majorizations

 The distribution of d commodities among n individuals is described by an n×d row stochastic matrix. We present a geometric approach to order such matrices. For a row stochastic matrix the Lorenz zonotope is investigated, which is a higher dimensional generalization of the Lorenz curve. The Lorenz zonotope is a convex polytope. The inclusion of Lorenz zonotopes defines an ordering between row stochastic matrices, which is a multivariate majorization. For a cone in nonnegative d-space, a cone extension of the Lorenz zonotope and the respective inclusion ordering are introduced. We study this class of orderings and establish equivalence with known majorizations. It is provided a finite set of inequalities to which the ordering is equivalent. Received: 16 February 1994/Accepted: 22 May 1996     

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.     

The Bordes-LeBreton exceptional case

Bordes and LeBreton have found a set D of weak orderings of X that includes all linear (strong) orderings of X but where there exists a social welfare function f on D ^N satisfying all of Arrow's (non-domain) conditions. In this paper we characterize all such D and f possibilities.     

The Moulin–Shenker rule

The Moulin–Shenker rule is a non-linear solution concept for solving heterogeneous cost sharing problems. It is the unique continuous rule with the properties scale invariance, bounds on cost shares and self-consistency. I am indebted to several anonymous referees and especially to Hervé Moulin for many useful suggestions.     

On the leximin and utilitarian overtaking criteria with extended anonymity

We present an extension of the overtaking criterion, called fixed-step overtaking social welfare relation (SWR), and its leximin counterpart, called fixed-step W-leximin SWR, for the evaluation of infinite utility streams. Our SWRs satisfy Fixed-step Anonymity. First, we characterize them by using the consistency, called Weak Fixed-step Indifference Consistency, which links indifference for infinite utility streams to indifference for their truncated vectors that are taken periodically. Second, we characterize another utilitarian extension, called S{\mathcal{S}}-overtaking SWR, by replacing the consistency with Fixed-step Anonymity. The S{\mathcal{S}}-overtaking SWR is a subrelation of the fixed-step overtaking SWR. Meanwhile, the leximin counterpart of the S{\mathcal{S}}-overtaking SWR coincides with the fixed-step W-leximin SWR, and we obtain its alternative characterization using Fixed-step Anonymity. Finally, we generalize the impossibility of combining Fixed-step Anonymity with the catching-up SWR by showing the Pareto and strong consistency axioms satisfied by the catching-up SWR come in conflict with Fixed-step Anonymity.     

Finite decentralization in a Tiebout economy with crowding types

We study a model with local public goods in which agents' crowding effects are formally distinguished from their taste types. It has been shown that the core of such an economy can be decentralized with anonymous admission prices (which are closely related to cost share prices). Unfortunately, such a price system allows for an arbitrary relationship between the public goods level in a given jurisdiction and the cost to an agent for joining. Formally, this means that admission prices are infinite dimensional. Attempts to decentralize the core with finite price systems such as Lindahl prices suggest that this is possible only under fairly restrictive conditions. In this paper, we introduce a new type of price system called finite cost shares. This system has strictly larger dimension than Lindahl prices but, in contrast to general cost share prices, is finite. We show that this allows for decentralization of the core under more general conditions than are possible with Lindahl prices. Received: 18 January 2000/Accepted: 21 January 2002 The authors would like to thank two anonymous referees for their helpful comments.     

An axiomatic approach to intergenerational equity

We present a set of axioms in order to capture the concept of equity among an infinite number of generations. There are two ethical considerations: one is to treat every generation equally and the other is to respect distributive fairness among generations. We find two opposite results. In Theorem 1, we show that there exists a preference ordering satisfying anonymity, strong distributive fairness semiconvexity, and strong monotonicity. However, in Theorem 2, we show that there exists no binary relation satisfying anonymity, distributive fairness semiconvexity, and sup norm continuity. We also clarify logical relations between these axioms and non-dictatorship axioms. Received: 30 August 2000/Accepted: 18 March 2002 This paper is based on Chapt. 4 of my Masters Thesis [15] submitted to Kobe University, and won the Kanematsu Fellowship from the Research Institute for Economics and Business Administration of Kobe University in May 2001. I am grateful to Jun Iritani for helpful discussions and encouragement, two anonymous referees of this journal, three anonymous referees of the Kanematsu Fellowship, Eiichi Miyagawa, Noritsugu Nakanishi, Nguyen Huu Phuc, Hiroo Sasaki, Koji Shimomura, William Thomson, and Toyoaki Washida for detailed comments. I also thank participants at the spring meeting of Japanese Economic Association at Yokohama City University in May 2000, at the annual meeting of the Society for Environmental Economics and Policy Studies in Tsukuba in September 2000, and at the Kanematsu Fellowship Seminar at Kobe University in May 2001 for valuable comments.     

Taking empirical studies seriously: the principle of concentration and the measurement of welfare and inequality

The paper investigates the implications of empirical studies by Amiel and Cowell (J Public Econ 47:3–26, 1992) of the public’s attitude towards inequality. It demonstrates that the value judgments concerning the redistribution of income which have been revealed in these studies can be represented by the principle of concentration. A concentration is a redistribution of income which reduces the distance between each income and the average income in the same proportion. Imposing this principle and some other basic properties the paper characterizes several families of social welfare orderings which imply generalized Atkinson inequality measures. They do not necessarily satisfy the principle of progressive transfers. I thank two anonymous referees for helpful comments.     

Measurement of inequality: An attempt at unification and generalization

This paper reviews and extends the theory of ethical inequality indices. It presents a novel axiom (strict separability of social welfare orderings in rank-ordered subspaces). This axiom allows to provide joint characterizations of the most important inequality measures (Atkinson family, Kolm-Pollak family and Generalized Ginis) and of some new more general classes of indices. The whole derivation is based on weak assumptions. In an ordinal framework only continuity of the underlying ordering is required and no cardinal properties are employed.I thank two anonymous referees for helpful comments and suggestions.     

Paretian efficiency,rawlsian justice and the Nozick theory of rights

In this paper the circumstances under which a Nozickian libertarian claim can produce self-consistent results are studied. These circumstances are shown to consist of technological separability of social alternatives and partial separability of individual preferences. Under these conditions some restricted versions of the Pareto principle and of the Rawlsian maximin can be reformulated consistently with the Nozickian libertarian claim. Also, in absence of external utility, Paretian efficiency, Rawlsian distributive justice and the Nozickian libertarian claim are consistent and can be together satisfied by a choice procedure. Moreover, the Nozick libertarian claim is shown to be satisfied by a perfectly competitive economy. A parallelism between a general equilibrium market system and a Nozickian rights system is pointed out.For helpful comments on an earlier version I am very grateful to C.J. Bliss, G. De Fraja, A. Sen, and an anonymous referee