Consistent Relations

Consistency, a natural weakening of transitivity introduced in a seminal contribution by Suzumura (1976b), has turned out to be an interesting and promising concept in a variety of areas within economic theory. This paper summarizes its recent applications and provides some new observations in welfarist social choice and in population ethics. In particular, it is shown that the conclusion of the welfarism theorem remains true if transitivity is replaced by consistency and that an impossibility result in variable-population social-choice theory turns into a possibility if transitivity is weakened to consistency.

The Possibility of Ordering Infinite Utility Streams

This paper revisits Diamond’s classical impossibility result regarding the ordering of infinite utility streams. We show that if no representability condition is imposed, there do exist strongly Paretian and finitely anonymous orderings of intertemporal utility streams with attractive additional properties. We extend a possibility theorem due to Svensson to a characterization theorem and we provide characterizations of all strongly Paretian and finitely anonymous rankings satisfying the strict transfer principle. In addition, infinite horizon extensions of leximin and of utilitarianism are characterized by adding an equity preference axiom and finite translation-scale measurability, respectively, to strong Pareto and finite anonymity.

Upper Semicontinuous Extensions of Binary Relations.

Suzumura shows that a binary relation has a weak order extension if and only if it is consistent. However, consistency is demonstrably not sufficient to extend an upper semi-continuous binary relation to an upper semicontinuous weak order. Jaffray proves that any asymmetric (or reflexive), transitive and upper semicontinuous binary relation has an upper semicontinuous strict (or weak) order extension. We provide sufficient conditions for existence of upper semicontinuous extensions of consistence rather than transitive relations. For asymmetric relations, consistency and upper semicontinuity suffice. For more general relations, we prove one theorem using a further consistency property and another with an additional continuity requirement.

Harsanyi’s Social Aggregation Theorem : A Multi-Profile Approach with Variable-Population Extensions

This paper provides new versions of Harsanyi’s social aggregation theorem that are formulated in terms of prospects rather than lotteries. Strengthening an earlier result, fixed-population ex-ante utilitarianism is characterized in a multi-profile setting with fixed probabilities. In addition, we extend the social aggregation theorem to social-evaluation problems under uncertainty with a variable population and generalize our approach to uncertain alternatives, which consist of compound vectors of probability distributions and prospects.

An axiomatic characterization of the MVSHN group fitness ordering

In order to analyze a unicellular-multicellular evolutionary transition, a multicellular organism is identified with the vector of viabilities and fecundities of its constituent cells. The Michod–Viossat–Solari–Hurand–Nedelcu index of group fitness for a multicellular organism is a function of these cell viabilities and fecundities. The MVSHN index has been used to analyze the germ-soma specialization and the fitness decoupling between the cell and organism levels that takes place during the transition to multicellularity. In this article, social choice theory is used to provide an axiomatic characterization of the group fitness ordering of vectors of cell viabilities and fecundities underlying the MVSHN index.

Dénombrement dans les empilements apolloniens généralisés et distribution angulaire dans les extensions quadratiques imaginaires.

Cette thèse traite de deux thèmes principaux. Le premier concerne l'étude des empilements apolloniens généralisés de cercles et de sphères. Généralisations des classiques empilements apolloniens, dont l'étude remonte à la Grèce antique, ces objets s'imposent comme particulièrement attractifs en théorie des nombres. Dans cette thèse sera étudié l'ensemble des courbures (les inverses des rayons) des cercles ou sphères de tels empilements. Sous de bonnes conditions, ces courbures s'avèrent être toutes entières. Nous montrerons qu'elles vérifient un principe local-global partiel, nous compterons le nombre de cercles de courbures plus petites qu'une quantité donnée et nous nous intéresserons également à l'étude des courbures premières. Le second thème a trait à la distribution angulaire des idéaux (ou plutôt ici des nombres idéaux) des corps de nombres quadratiques imaginaires (que l'on peut voir comme la distribution des points à coordonnées entières sur des ellipses). Nous montrerons que la discrépance de l'ensemble des angles des nombres idéaux entiers de norme donnée est faible et nous nous intéresserons également au problème des écarts bornés entre les premiers d'extensions quadratiques imaginaires dans des secteurs.

Sharing a River

A group of agents located along a river have quasi-linear preferences over water and money. We ask how the water should be allocated and what money transfers should be performed. We are interested in efficiency, stability (in the sense of the core), and fairness (in a sense to be defined). We first show that the cooperative game associated with our problem is convex : its core is therefore large and easily described. Next, we propose the following fairness requirement : no group of agents should enjoy a welfare higher than what it could achieve in the absence of the remaining agents. We prove that only one welfare vector in the core satisfies this condition : it is the marginal contribution vector corresponding to the ordering of the agents along the river. We discuss how it could be decentralized or implemented.

Non-Deteriorating Choice

We analyze an alternative to the standard rationalizability requirement for observed choices by considering non-deteriorating selections. A selection function is a generalization of a choice function where selected alternatives may depend on a reference (or status quo) alternative in addition to the set of feasible options. A selection function is non-deteriorating if there exists an ordering over the universal set of alternatives such that the selected alternatives are at least as good as the reference option. We characterize non-deteriorating selection functions in an abstract framework and in an economic environment.

Simulation-Based Finite-Sample Tests for Heteroskedasticity and ARCH Effects.

A wide range of tests for heteroskedasticity have been proposed in the econometric and statistics literature. Although a few exact homoskedasticity tests are available, the commonly employed procedures are quite generally based on asymptotic approximations which may not provide good size control in finite samples. There has been a number of recent studies that seek to improve the reliability of common heteroskedasticity tests using Edgeworth, Bartlett, jackknife and bootstrap methods. Yet the latter remain approximate. In this paper, we describe a solution to the problem of controlling the size of homoskedasticity tests in linear regression contexts. We study procedures based on the standard test statistics [e.g., the Goldfeld-Quandt, Glejser, Bartlett, Cochran, Hartley, Breusch-Pagan-Godfrey, White and Szroeter criteria] as well as tests for autoregressive conditional heteroskedasticity (ARCH-type models). We also suggest several extensions of the existing procedures (sup-type of combined test statistics) to allow for unknown breakpoints in the error variance. We exploit the technique of Monte Carlo tests to obtain provably exact p-values, for both the standard and the new tests suggested. We show that the MC test procedure conveniently solves the intractable null distribution problem, in particular those raised by the sup-type and combined test statistics as well as (when relevant) unidentified nuisance parameter problems under the null hypothesis. The method proposed works in exactly the same way with both Gaussian and non-Gaussian disturbance distributions [such as heavy-tailed or stable distributions]. The performance of the procedures is examined by simulation. The Monte Carlo experiments conducted focus on : (1) ARCH, GARCH, and ARCH-in-mean alternatives; (2) the case where the variance increases monotonically with : (i) one exogenous variable, and (ii) the mean of the dependent variable; (3) grouped heteroskedasticity; (4) breaks in variance at unknown points. We find that the proposed tests achieve perfect size control and have good power.

The Measurement of Diversity

The notion of diversity is an issue that is of relevance in several contexts. For example, the biodiversity of a given ecological environment and the diversity of the options available to a decision maker have attracted some attention in recent research. This paper provides an axiomatic approach to the measurement of diversity. We characterize two nested classes of ordinal measures of diversity and an important member of these classes. We prove that the latter special case is equivalent to a diversity ordering proposed by Weitzman.

Fair Production and Allocation of an Excludable Nonrival Good

We study fairness in economies with one private good and one partially excludable nonrival good. A social ordering function determines for each profile of preferences an ordering of all conceivable allocations. We propose the following Free Lunch Aversion condition: if the private good contributions of two agents consuming the same quantity of the nonrival good have opposite signs, reducing that gap improves social welfare. This condition, combined with the more standard requirements of Unanimous Indifference and Responsiveness, delivers a form of welfare egalitarianism in which an agent's welfare at an allocation is measured by the quantity of the nonrival good that, consumed at no cost, would leave her indifferent to the bundle she is assigned.

Consistent Rationalizability

Consistency of a binary relation requires any preference cycle to involve indifference only. As shown by Suzumura (1976b), consistency is necessary and sufficient for the existence of an ordering extension of a relation. Because of this important role of consistency, it is of interest to examine the rationalizability of choice functions by means of consistent relations. We describe the logical relationships between the different notions of rationalizability obtained if reflexivity or completeness are added to consistency, both for greatest-element rationalizability and for maximal-element rationalizability. All but one notion of consistent rationalizability are characterized for general domains, and all of them are characterized for domains that contain all two-element subsets of the universal set.

Explaining the Persistence of Commodity Prices

This paper extends the Competitive Storage Model by incorporating prominent features of the production process and financial markets. A major limitation of this basic model is that it cannot successfully explain the degree of serial correlation observed in actual data. The proposed extensions build on the observation that in order to generate a high degree of price persistence, a model must incorporate features such that agents are willing to hold stocks more often than predicted by the basic model. We therefore allow unique characteristics of the production and trading mechanisms to provide the required incentives. Specifically, the proposed models introduce (i) gestation lags in production with heteroskedastic supply shocks, (ii) multiperiod forward contracts, and (iii) a convenience return to inventory holding. The rational expectations solutions for twelve commodities are numerically solved. Simulations are then employed to assess the effects of the above extensions on the time series properties of commodity prices. Results indicate that each of the features above partially account for the persistence and occasional spikes observed in actual data. Evidence is presented that the precautionary demand for stocks might play a substantial role in the dynamics of commodity prices.

Consistent House Allocation

In practice we often face the problem of assigning indivisible objects (e.g., schools, housing, jobs, offices) to agents (e.g., students, homeless, workers, professors) when monetary compensations are not possible. We show that a rule that satisfies consistency, strategy-proofness, and efficiency must be an efficient generalized priority rule; i.e. it must adapt to an acyclic priority structure, except -maybe- for up to three agents in each object's priority ordering.

Sharing the Cost of a Public Good without Subsidies

We study the construction of a social ordering function for the case of a public good financed by contributions from the population, and we extend the analysis of Maniquet and Sprumont (2004) to the case when contributions cannot be negative, i.e. agents cannot receive subsidies from others.