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)

Knowledge spaces and learning spaces

How to design automated procedures which (i) accurately assess the knowledge of a student, and (ii) efficiently provide advices for further study? To produce well-founded answers, Knowledge Space Theory relies on a combinatorial viewpoint on the assessment of knowledge, and thus departs from common, numerical evaluation. Its assessment procedures fundamentally differ from other current ones (such as those of S.A.T. and A.C.T.). They are adaptative (taking into account the possible correctness of previous answers from the student) and they produce an outcome which is far more informative than a crude numerical mark. This chapter recapitulates the main concepts underlying Knowledge Space Theory and its special case, Learning Space Theory. We begin by describing the combinatorial core of the theory, in the form of two basic axioms and the main ensuing results (most of which we give without proofs). In practical applications, learning spaces are huge combinatorial structures which may be difficult to manage. We outline methods providing efficient and comprehensive summaries of such large structures. We then describe the probabilistic part of the theory, especially the Markovian type processes which are instrumental in uncovering the knowledge states of individuals. In the guise of the ALEKS system, which includes a teaching component, these methods have been used by millions of students in schools and colleges, and by home schooled students. We summarize some of the results of these applications

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

{P, Q, I, J} - preference structures

info:eu-repo/semantics/publishe

Recursive decomposition tree of a Moore co-family and closure algorithm

International audienceA collection of sets on a ground set U n (U n = {1, 2, ..., n}) closed under intersection and containing U n is known as a Moore family. The set of Moore families for a fixed n is in bijection with the set of Moore co-families (union-closed families containing the empty set) denoted M n. This paper follows the work initiated in [9] in which we have given an inductive definition of the lattice of Moore co-families. In the present paper we use this definition to define a recursive decomposition tree of any Moore co-family and we design an original algorithm to compute the closure under union of any family. Then we compare performance of this algorithm to performance of Ganter's algorithm and Norris' algorithm

Some implications of a mandatory gender quota for firms implementing at different points in time

This master’s thesis examines some of the implications of the Norwegian gender quota for firms implementing it at different points in time. It is found that firms lose between 14% and 22% of their general board experience dependent on when they implement the quota. Firms implementing earlier lose on average less experience than firms adapting later. However, the earliest implementers nominate women, and the later adapters men with more previous board experience in the same sector of the economy, in the mandatory transition period. The later a firm adapts is also found to be casually related to the probability of the firm changing its board size in order to meet the quota. Further, firms implementing later has higher board turnover among both female and male members in the years prior to and after the quota became mandatory. The compensation offered the CEO increases sharply for the earliest adapters when they implement the quota. This could be consistent with either a stronger governance structure and better incentives, or weaker governance where the CEO utilizes a relatively enhanced bargaining position.nhhma