A new approach on distributed systems: orderings and representability

In the present paper we propose a new approach on `distributed systems': the processes are represented through total orders and the communications are characterized by means of biorders. The resulting distributed systems capture situations met in various fields (such as computer science, economics and decision theory). We investigate questions associated to the numerical representability of order structures, relating concepts of economics and computing to each other. The concept of `quasi-finite partial orders' is introduced as a finite family of chains with a communication between them. The representability of this kind of structure is studied, achieving a construction method for a finite (continuous) Richter-Peleg multi-utility representation

Quasi-metrics for possibility results: intergenerational preferences and continuity

In this paper, we provide the counterparts of a few celebrated impossibility theorems for continuous social intergenerational preferences according to P. Diamond, L.G. Svensson and T. Sakai. In particular, we give a topology that must be refined for continuous preferences to satisfy anonymity and strong monotonicity. Furthermore, we suggest quasi-pseudo-metrics as an appropriate quantitative tool for reconciling topology and social intergenerational preferences. Thus, we develop a metric-type method which is able to guarantee the possibility counterparts of the aforesaid impossibility theorems and, in addition, it is able to give numerical quantifications of the improvement of welfare. Finally, a refinement of the previous method is presented in such a way that metrics are involved

Open questions in utility theory

Throughout this paper, our main idea is to explore different classical questions arising in Utility Theory, with a particular attention to those that lean on numerical representations of preference orderings. We intend to present a survey of open questions in that discipline, also showing the state-of-art of the corresponding literature.This work is partially supported by the research projects ECO2015-65031-R, MTM2015-63608-P (MINECO/ AEI-FEDER, UE), and TIN2016-77356-P (MINECO/ AEI-FEDER, UE)

Continuous Representations of Interval Orders by Means of Two Continuous Functions

In this paper, we provide a characterization of the existence of a representation of an interval order on a topological space in the general case bymeans of a pair of continuous functions, when neither the functions nor the topological space are required to satisfy any particular assumptions. Such a characterization is based on a suitable continuity assumption of the binary relation, called weak continuity. In this way, we generalize all the previous results on the continuous representability of interval orders, and also of total preorders, as particular cases

Approximating SP-orders through total preorders: incomparability and transitivity through permutations

We study finite partial orders and the concept of indistinguishability. In particular, we focus on SP-orders. These orderings can be represented by means of Hasse diagrams and numerical labels. Since these numerical representations can be interpreted by means of permutations, we extend the study to the field of group theory. Through this point of view, we introduce the new concept of total extension and total inclusion of a partial order as the total preorders closest to the initial partial order from below and from above, respectively. Finally, we show a possible study of finite T0 topologies by means of its corresponding partial order.Keywords: SP-orders, indistinguishability, incomparability, transitivity, symmetric group, MOQ

Quasi-Metrics for Possibility Results: Intergenerational Preferences and Continuity

In this paper, we provide the counterparts of a few celebrated impossibility theorems for continuous social intergenerational preferences according to P. Diamond, L.G. Svensson and T. Sakai. In particular, we give a topology that must be refined for continuous preferences to satisfy anonymity and strong monotonicity. Furthermore, we suggest quasi-pseudo-metrics as an appropriate quantitative tool for reconciling topology and social intergenerational preferences. Thus, we develop a metric-type method which is able to guarantee the possibility counterparts of the aforesaid impossibility theorems and, in addition, it is able to give numerical quantifications of the improvement of welfare. Finally, a refinement of the previous method is presented in such a way that metrics are involved