Reallocation of an infinetely divisible good

We consider the problem of reallocating the total initial endowments of an infinitely divisible commodity among agents with single-peaked preferences. With the uniform reallocation rule we propose a solution which satisfies many appealing properties, describing the effect of population and endowment variations on the outcome. The central properties which are studied in this context are population monotonicity, bilateral consistency, (endowment) monotonicity and (endowment) strategy-proofness. Furthermore, the uniform reallocation rule is Pareto optimal and satisfies several equity conditions, e.g., equal-treatment and envy-freeness. We study the trade-off between properties concerning variation and properties concerning equity. Furthermore, we provide several characterizations of the uniform reallocation rule based on these properties.mathematical economics and econometrics ;

Maximal Domains for Strategy-Proof or Maskin Monotonic Choice Rules

Domains of individual preferences for which the well-known impossibility Theorems of Gibbard-Satterthwaite and Muller-Satterthwaite do not hold are studied. First, we introduce necessary and sufficient conditions for a domain to admit non-dictatorial, Pareto efficient and either strategy-proof or Maskin monotonic social choice rules. Next, to comprehend the limitations the two Theorems imply for social choice rules, we search for the largest domains that are possible. Put differently, we look for the minimal restrictions that have to be imposed on the unrestricted domain to recover possibility results. It turns out that, for such domains, the conditions of inseparable pair and of inseparable set yield the only maximal domains on which there exist non-dictatorial, Pareto efficient and strategy-proof social choice rules. Next, we characterize the maximal domains which allow for Maskin monotonic, non-dictatorial and Pareto-optimal social choice rules

Collective choice rules on restricted domains based on a priori information

We consider restricted domains where each individual has a domain of preferences containing some partial order. This partial order might differ for different individuals. Necessary and sucient conditions are formulated under which these restricted domains admit unanimous, strategy-proof and, non-dictatorial choice rules

Towards an axiomatization of orderings

A set of six axioms for sets of relations is introduced. All well-known sets of specific orderings, such as linear and weak orderings, satisfy these axioms. These axioms impose criteria of closedness with respect to several operations, such as concatenation, substitution and restriction. For operational reasons and in order to link our results with the literature, it is shown that specific generalizations of the transitivity condition give rise to sets of relations which satisfy these axioms. Next we study minimal extensions of a given set of relations which satisfy the axioms. By this study we come to the fundamentals of orderings: They appear to be special arrangements of several types of disorder. Finally we notice that in this framework many new sets of relations have to be regarded as a set of orderings and that it is not evident how to minimize the number of these new sets of orderings