Open Access
Instructional design for tutoring on interactive platforms: creating educational interventions overcoming the digital gap
(Springer, 2025-05-27) Rodríguez Rincón, Yeray; Munárriz Iriarte, Ana; Campión Arrastia, María Jesús; Goicoechea López-Vailo, María Isabel; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Research in Business and Economics - INARBE; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
This article proposes an instructional model based on psycho-pedagogical theories to serve as a basic structural unit for the creation of educational reinforcement platforms aimed at strengthening quantitative competences with which students enroll mathematics and statistics subjects (or other subjects that draw on this knowledge) at university. Although there are Intelligent Tutoring Systems (ITS) that are beneficial for students, the difficulty of manipulation and programming, together with their high economic cost when lacking programming skills, have prevented a widespread use of this type of interventions. Following the first steps of the ADDIE model, this article develops an instructional model that can be easily replicated by instructors lacking in programming and digital skills, designed to be applied in free and easy-to-handle interactive tutoring platforms, such as Genially.com or Canva, among others. The main foundations on which the pedagogical guideline is based are extracted through an extensive review of academic literature on psycho-pedagogical theories such as scaffolding, effective learning, metacognition, educational reinforcement, or feedback. Through it, students will be able to strengthen their quantitative conceptual foundations and reflect on their own learning process.
Open Access
Aggregation of individual rankings through fusion functions: criticism and optimality analysis
(IEEE, 2020) Bustince Sola, Humberto; Bedregal, Benjamin; Campión Arrastia, María Jesús; Silva, Ivanoska da; Fernández Fernández, Francisco Javier; Induráin Eraso, Esteban; Raventós Pujol, Armajac; Santiago, Regivan; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas
Throughout this paper, our main idea is to analyze from a theoretical and normative point of view different methods to aggregate individual rankings. To do so, first we introduce the concept of a general mean on an abstract set. This new concept conciliates the social choice where well-known impossibility results as the Arrovian ones are encountered and the decision-making approaches where the necessity of fusing rankings is unavoidable. Moreover it gives rise to a reasonable definition of the concept of a ranking fusion function that does indeed satisfy the axioms of a general mean. Then we will introduce some methods to build ranking fusion functions, paying a special attention to the use of score functions, and pointing out the equivalence between ranking and scoring. To conclude, we prove that any ranking fusion function introduces a partial order on rankings implemented on a finite set of alternatives. Therefore, this allows us to compare rankings and different methods of aggregation, so that in practice one should look for the maximal elements with respect to such orders defined on rankings IEEE.
Open Access
Why using topological and analytical methods in aggregation of fuzzy preferences?
(2020) Campión Arrastia, María Jesús; Induráin Eraso, Esteban; Raventós Pujol, Armajac; Estatistika, Informatika eta Matematika; Institute for Advanced Research in Business and Economics - INARBE; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas
The Arrow’s Impossibility Theorem states that there is no function fusing individual preferences into a social one satisfying certain properties of 'common sense'. On the contrary, in some of the fuzzy extensions of the Arrovian model, possibility arises. We have developed a technique which has been able to prove new impossibility results in the fuzzy approach. In this poster, we will explain the fundaments of this technique and in which models we can apply it. This technique, is based on controlling the aggregation of fuzzy preferences through some aggregation functions of dichotomic preferences. For each fuzzy aggregation function, we get a family of dichotomic aggregation functions. Studying this family, we obtain information about the initial aggregation function. We will discuss why the fuzzy Arrovian models in which we can apply this technique are, in some sense, less fuzzy. Moreover, we will expose why we should use topological and analytical methods in the fuzzy models out of the scope of our technique.
Open Access
What do law and mathematics have in common? The sustainable development goals as a transversal substrate of numbers and laws
(CEUR-WS, 2022) Chicharro Lázaro, Alicia; Campión Arrastia, María Jesús; Derecho; Zuzenbidea; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Research in Business and Economics - INARBE; Institute for Advanced Social Research - ICOMMUNITAS
This paper presents two experiences of innovative teaching at the Public University of Navarra that have as a fundamental common link: the mainstreaming of the Sustainable Development Goals in the curriculum. With this objective in mind, the subjects International Law and Mathematics, that are a priori conceptually different, can be worked on at a competency level with the same common challenge. This challenge consists in promoting the exercise of global citizenship, active, supportive, responsible, and committed to sustainable development. For both experiences, some of the activities carried out with this objective are described, contextualized in the framework of the Sustainable Development Goals (SDGs). The main conclusions drawn from the experience are analyzed, highlighting the fundamental role of universities as a driving force for social transformation from different dimensions.
Open Access
A mathematical approach to law and deal modelling: legislation and agreements
(MDPI, 2021) Benito Ostolaza, Juan Miguel; Campión Arrastia, María Jesús; Estevan Muguerza, Asier; Estatistika, Informatika eta Matematika; Institute for Advanced Research in Business and Economics - INARBE; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas
Social norms are a set of rules to be followed by the people of a community in order to have a better coexistence, to which the behaviors, tasks, and activities of the human being must be adjusted. The set or system of norms, rules, or duties regulates the actions of individuals among themselves. This work presents a new and original approach to the situations of agreement as well as to the constructions of regulations. This is done by giving a mathematical formalization to the set of all possible agreements or regulations, so that, then, the proximity between them is defined by means of a premetric. Thanks to this mathematical structure that tries to capture the problematic of agreements and modifications of regulations, some currently issues related to game theory or law are now reduced to mathematical optimization problems.
Open Access
Decomposition of fuzzy relations: an application to the definition, construction and analysis of fuzzy preferences
(MDPI, 2023) Campión Arrastia, María Jesús; Induráin Eraso, Esteban; Raventós Pujol, Armajac; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Institute for Advanced Research in Business and Economics - INARBE
In this article, we go deeper into the study of some types of decompositions defined by triangular norms and conorms. We work in the spirit of the classical Arrovian models in the fuzzy setting and their possible extensions. This allows us to achieve characterizations of existence and uniqueness for such decompositions. We provide rules to obtain them under some specific conditions. We conclude by applying the results achieved to the study of fuzzy preferences.
Open Access
La ciudadanía global como reto en la enseñanza-aprendizaje de las universidades: las experiencias de innovación educativa de desarrollo y cooperación internacional, derecho Internacional y matemáticas
(Universitat Politècnica de València, 2021) Chicharro Lázaro, Alicia; Campión Arrastia, María Jesús; Zuzenbidea; Estatistika, Informatika eta Matematika; Institute for Advanced Research in Business and Economics - INARBE; Institute for Advanced Social Research - ICOMMUNITAS; Derecho; Estadística, Informática y Matemáticas
Se presentan varias experiencias de innovación educativa en la Universidad Pública de Navarra que tienen como nexo común fundamental la transversalización de los Objetivos de Desarrollo Sostenible en el currículo. Con este objetivo se presenta el curso de extensión universitaria de Desarrollo y Cooperación Internacional, transversal a todas las titulaciones y en el que participan las autoras, así como en las asignaturas que imparten en sus respectivas titulaciones: Derecho Internacional Público y Matemáticas. Se observa cómo dichas asignaturas, a priori dispares a nivel conceptual, pueden ser trabajadas a nivel competencial con un mismo reto común, que es el fomento del ejercicio de una ciudadanía global, activa, solidaria, responsable y comprometida con el desarrollo sostenible. Se describe para cada una de dichas experiencias algunas de las actividades llevadas a cabo con dicho objetivo, contextualizadas en el marco de los ODS. Se analizan las principales conclusiones extraídas de la experiencia, poniendo de relieve el papel fundamental de las universidades como motor de transformación social desde distintas dimensiones.
Open Access
Mathematics in economic and business science: how to reach the top without a pathway
(Universitat Politècnica de València, 2023) Rodríguez Rincón, Yeray; Munárriz Iriarte, Ana; Goicoechea López-Vailo, María Isabel; Campión Arrastia, María Jesús; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
The level of mathematical knowledge with which students enter Economics and Business Administration Degrees varies according to the Baccalaureate pathway taken. The Zone of Real Development of students coming from the Social Sciences Baccalaureate differs from the Necessary Zone of Real Development for the correct acquisition of academic competences, which is close to that developed in the Scientific-Technological pathway. In order to characterise the existing mathematical deficit, a quantitative and perceptive analysis of the mathematical deficiencies of new students in those Degrees coming from the Social Sciences pathway is proposed. The results allow the identification of various areas where training deficiencies exist, which are corroborated by the students' perception. To solve them, the creation of a virtual platform that identifies, in a personalised way, the deficiencies of each student is proposed. Through guided gamification, the complementary course would allow students to reach the Necessary Real Development Zone before starting University.
Open Access
Past-myopic economic agents
(Economics Bulletin, 2025-03-30) Campión Arrastia, María Jesús; Induráin Eraso, Esteban; Munárriz Iriarte, Ana; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Research in Business and Economics - INARBE; Institute for Advanced Materials and Mathematics - INAMAT2
In this paper, the idea of myopic preference and myopic topology provided by Brown and Lewis is further explored. In this sense, new definitions of myopia are introduced for finite spaces. The main contribution of the work is the inclusion of the past in the models. We have defined the notions of past-myopic preference and topology for sequence spaces and n-dimensional spaces. Adding this new dimension makes it possible to work with decision spaces where the economic agent only has information about past events and when she has to choose accordingly to it, which is in line with the reality of certain economic situations, such as voting or finances. This approach generates a wide room for future research lines related to the idea of myopia. Based on this, it would allow to study in forthcoming research past-hyperopic topologies and preferences, and to interconnect different preferences, defined on the past and future models.
Open Access
Sports betting and the Black-Litterman model: a new portfolio-management perspective
(FiT Publishing, 2021) Abinzano Guillén, María Isabel; Campión Arrastia, María Jesús; Muga Caperos, Luis Fernando; Raventós Pujol, Armajac; Institute for Advanced Research in Business and Economics - INARBE
This paper transfers and adapts the Black-Litterman portfolio management model and its subsequent generalizations to the characteristics and specificities of assets quoted on sports betting markets. The results show that these assets are suitable for the application of portfolio management models with possible inclusion of investors' opinions. Information based on the variability of market prices and the attention received by NBA teams in Google Trends is successfully used to simulate the opinions expressed by a hypothetical portfolio manager. Furthermore, this makes these assets suitable for inclusion in portfolios in which managers are seeking returns uncorrelated with other assets.