Asking infinite voters ‘Who is a J?’: Group Identification Problems in N

We analyze the problem of classifing individuals in a group N taking into account their opinions about which of them should belong to a specific subgroup N0 ⊆ N, in the case that |N| > ∞. We show that this problem is relevant in cases in which the group changes in time and/or is subject to uncertainty. The approach followed here to find the ensuing classification is by means of a Collective Identity Function (CIF) that maps the set of opinions into a subset of N. Kasher and Rubinstein (1997) characterized different CIFs axiomatically when |N| < ∞, in particular the Liberal and Oligarchic aggregators. We show that in the infinite setting the liberal result is still valid but the result no longer holds for the oligarchic case and give a characterization of all the aggregators satisfying the same axioms as the Oligarchic CIF. In our motivating examples, the solution obtained according to the alternative CIF is most cogent.Fil: Fioravanti, Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Tohmé, Fernando Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaVIII Congreso Nacional de Estudiantes de Postgrado en EconomíaArgentinaUniversidad Nacional del Sur. Departamento de EconomíaInstituto de Investigaciones Económicas y Sociales del Su

Visitors Out! The Absence of Away Team Supporters as a Source of Home Advantage in Football

We seek to gain more insight into the effect of the crowds on the Home Advantage by analyzing the particular case of Argentinean football (also known as soccer), where for more than ten years, the visiting team fans were not allowed to attend the games. Additionally, during the COVID-19 lockdown, a significant number of games were played without both away and home team fans. The analysis of more than 20 years of matches of the Argentinean tournament indicates that the absence of the away team crowds was beneficial for the Top 5 teams during the first two years after their attendance was forbidden. An additional intriguing finding is that the lack of both crowds affects significantly all the teams, to the point of turning the home advantage into home `disadvantage' for most of the teams

Modelos Matemáticos en Social Choice: Identificación de Grupos, Inferencia y Competencia

Este trabajo consta de tres partes, que en principio parecen ser bastante diferentes, pero tienen como hilo conductor la toma de decisiones que debe realizar una persona, un grupo de personas, un equipo, etc. Cada una de las partes de este trabajo es autocontenida. La primera parte trata sobre tres diferentes enfoques del Problema de Identificación de Grupos. Este problema surge cuando un grupo de individuos debe identificar a un subgrupo del mismo como poseedor de alguna propiedad en particular. En el primer caso, sea N un conjunto finito de agentes cada uno teniendo una opinión sobre cuál de ellos debe pertenecer a un grupo específico, que llamaremos J. Llamamos Funci´on de Identidad Colectiva (FIC) al agregador que mapea del conjunto de opiniones a un subconjunto de N. Kasher & Rubinstein (1997) caracterizan diferentes FICs de una forma axiomática. Consideramos versiones alternativas del axioma liberal que Kasher & Rubinstein incluyen en su trabajo, que son más naturales en ciertas situaciones. Esto nos permite caracterizar tres agregadores diferentes y probar que estas FICs son las únicas que verifican las correspondientes versiones del axioma. Más aún, hallamos un resultado de imposibilidad para una versión extrema del axioma liberal. Luego, analizamos el mismo problema cuando el grupo de agentes es infinito. Este caso es relevante en casos en los cuales el grupo cambia en el tiempo y/o es sujeto a la incertidumbre. Trabajamos particularmente con las FICs Liberal y Oligárquica, caracterizadas por Kasher & Rubinstein. Mostramos que en el marco infinito el resultado liberal sigue siendo válido, pero el resultado no se mantiene para el caso oligárquico, dando una caracterización de todos los agregadores que verifican los mismo axiomas que la FIC Oligárquica. Por último, volvemos a trabajar con un número finito de agentes, pero ahora las opiniones de los votantes son difusas. Cada agente i tiene una opinión sobre el resto de los miembros de la sociedad, que consiste en una función pi : N ! [0; 1], que indica el grado de membresía de un agente al grupo J. Consideramos el problema de agregar esas funciones, satisfaciendo distintos conjuntos de axiomas y caracterizando nuevos agregadores. Mientras algunos resultados son análogos al caso binario, la versión difusa nos permite dejar de lado ciertas imposibilidades probadas por Kasher & Rubinstein. La segunda parte del trabajo, presenta un proceso diferente al habitual en teoría de Social Choice. El procedimiento usual consiste en postular una serie de propiedades que se desean que un proceso de agregación verifique, y encontrar a partir de allí las características de la correspondiente función de elección social y los resultados que pueden surgir de cada posible perfil de preferencias. Nosotros invertimos esta línea de razonamiento y a partir de lo que llamamos situaciones sociales (cada una de ellas consistiendo en un perfil de opiniones y el orden social asociado), obtenemos el criterio verificado por el proceso de agregación implícito. Este proceso de inferencia, que extrae información intensional de la extensional, puede ser visto como un ejercicio en estadística cualitativa. La última parte de este trabajo, puede ser considerada dentro del área de Matemática del Deporte. Usando simples herramientas de teoría de juegos, comparamos el nivel de "ofensividad" que los equipos de rugby tienen bajo distintos sistemas de puntuación usualmente usados en algunos de los torneos más importantes del mundo. Comparamos tres sistemas de puntuación distintos. Un sistema otorga cuatro puntos al equipo ganador, dos a ambos equipos en caso de empate y ningún punto al equipo perdedor. El segundo sistema, además de otorgar los mismos puntos que el primero, da un punto extra al equipo que anota cuatro o más tries, y al equipo perdedor si es que pierde por menos de un try. El último sistema, da un punto extra si el equipo ganador anota tres tries más que el oponente, y al equipo perdedor si es que pierde por menos un try. Usando un modelo estático, mostramos que los equipos se vuelven más ofensivos cuando el punto extra se otorga por anotar cuatro o más tries. También mostramos que no otorgar punto extra hace a los equipos más ofensivos que darlo por anotar tres tries más que el rival. Finalmente, usando un modelo dinámico en un ejemplo y ciertos resultados de Masso - Neme (1996), comparamos los conjuntos de pagos factibles y de equilibrio. Obtenemos ahora que el sistema que otorga un punto extra por anotar cuatro o más tries tiene una mayor y mejor región de pagos factibles y de equilibrio que los otros dos sistemas. A diferencia del modelo estático, en este caso es preferible el sistema que otorga un punto extra por anotar tres tries más que el rival al sistema que no otorga ningún punto extra.This work has three parts, that at first sight seems to be different, but have as a background the decisions that an agent, a group of people, a team, etc, should take in many ocasions. Each part is self contained. The first part deals with three different approaches of Group Identification Problems. These problems arise when a group of people have to identify a subgroup of themselves with some particular property. On the first approach, let N be a finite set of agents each one having an opinion of which of them should belong to a specific group, that we will call J. We call Choice Identity Function (CIF) the aggregator that maps from the set of opinions to a subset of N. Kasher & Rubinstein (1997) characterize three different CIFs in an axiomatic way. We consider alternative versions of the liberal axiom that Kasher & Rubinstein include in their work, that seem to be more natural in certain situations. This allow us to characterize new aggregators and prove that these CIFs are the only ones that verify the correspondent versions of these axioms. Moreover, we find an impossibility result for an extreme version of the liberal axiom. Then, we analize the same problem when the number of agents is infinite. This case is relevant when the group change in time or is under uncertainty. We work with the Liberal and Oligarchic CIF, characterized by Kasher & Rubinstein. We show that in the infinite setting the liberal result remains valid, but this does not happen for the oligarchic case, finding a new characterization for this setting. Finally, we work again with a finite number of agents, but this time the opinions are fuzzy. Each agent i has an opinion about every other agent, that is a function pi : N - [0; 1], that indicates the grade of membership of an agent to the group of J. We consider the problem of aggregate these functions, satisfying different sets of axioms and characterizing new aggregators. While some results are similar to the crisp setting, the fuzzy version of this problem allow us to leave aside some impossibility results found by Kasher & Rubinstein. The second part of the work presents a process different to the usual in Social Choice. Usual procedure consists in postulating a set of properties that a social planner wish to verify in an aggregation process, and from there find the characteristics of the correspondent social choice function and the results that may arise from every possible preference profile. We invert this line of reasoning and from what we call social situations (each one consisting in a profile of opinions and an associated social order), we obtain the criteria verified for the implicit aggregation procedure. This inference process, that extract intensional information from the extensional, can be seen as an exerxcise of cualitative statistics. The last part of this work, can be considered within the field of Mathematics of Sport. Using simple tools of game theory, we compare the level of "offensiveness" that rugby teams have under some score systems usually used in the most importants tournaments around the world. We compare three different score systems. One system gives four points to the winner, two to each team for a tie and no points for losing. The second system, besides giving the same points as the first one, gives an extra point for the team that scores four or more tries, and to the losing team if it loses for just one try. The last system gives an extra point if the winning team scores three or more tries than the other team, and an extra point for the losing team if it loses for just one try. Using an static model we show that teams become more offensive if an extra point is awarded for scoring four or more tries. We also show that no giving an extra point makes the team more offensive than giving it for scoring three or more tries than the losing team. Finally, using a dynamic model in an example and some results from Masso - Neme (1996), we compare the sets of feasible and equilibrium payoffs. We now obtain that the system that gives an extra point for scoring four or more tries has a better set of feasible and equilibrium payoffs. Unlike the static model, in this model is preferable awarding an extra point for scoring three more tries than the losing team rather that not giving an extra point.Fil: Fioravanti, Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentin

The impact of birth order on behavior in contact team sports: Evidence of rugby teams

Several studies have shown that birth order and the sex of siblings may have an influence on individual behavioral traits. In particular, it has been found that second brothers (of older male siblings) tend to have more disciplinary problems. If this is the case, this should also be shown in contact sports. To assess this hypothesis, we use a data set from the South Rugby Union from the region of Bahía Blanca, Argentina, and information obtained by surveying more than 400 players of that league. We find a statistically significant positive relation between being a second-born male rugby player with an older male brother and the number of yellow cards received.Fil: Delbianco, Fernando Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Fioravanti, Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Tohmé, Fernando Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentin

Inductive Reasoning in Social Choice Theory

The usual procedure in the theory of social choice consists in postulating some desirable properties which an aggregation procedure should verify and derive from them the features of a corresponding social choice function and the outcomes that arise at each possible profile of preferences. In this paper we invert this line of reasoning and try to infer, up from what we call social situations (each one consisting of a profile and the associated social ordering) the criteria verified in the implicit aggregation procedure. This inference process, which extracts intensional from extensional information can be seen as an exercise in “qualitative statistics”.Fil: Tohmé, Fernando Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Fioravanti, Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Auday, Marcelo. Universidad Nacional del Sur; Argentin

Characterization of SERS platforms designed by electrophoretic deposition on CVD graphene and ITO/glass

Here, we perform electrophoretic deposition (EPD) to control the assembly of citrate-coated Au nanoparticles (NPs) on ITO/glass and graphene. Monolayer graphene is obtained by CVD and transferred to ITO/glass free of polymer. A quick surface-enhanced Raman scattering (SERS) test determined that the optimal platform consists of drop-casting methylene blue (MB) onto as-deposited Au NPs (600 s at 1.0 V) to achieve 150× signal enhancement. Therefore, we proceeded in the same manner and deposited Au NPs under identical EPD conditions on graphene/ITO/glass. Then, we tested both platforms by immersing into 0.3 mM MB solution and found similar SERS intensity on the graphene- and ITO-containing platforms after 10 min and 66 h, respectively, which clearly demonstrates the importance of the substrate. To characterize the platforms, linear scan voltammetry (LSV) and SEM were used for assigning the NPs? oxidation peaks to their corresponding areas on the image. We found good agreement with respect to the number of NPs per μm2 as measured by LSV and SEM. We observed that EPD on graphene leads to six-fold larger coverage than on ITO/glass. These Au NPs were mostly assembled in the form of agglomerates located on the defects of graphene. If those agglomerates are dissolved by anodic stripping, no SERS signal was found from the MB analyte. This also demonstrates that the platform can be reused for further deposition and SERS analysis. This work provides a simple and controllable method for the design of advanced SERS platforms.Fil: Fioravanti, Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Investigaciones en Físico-química de Córdoba. Universidad Nacional de Córdoba. Facultad de Ciencias Químicas. Instituto de Investigaciones en Físico-química de Córdoba; ArgentinaFil: Muñetón Arboleda, David. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; ArgentinaFil: Lacconi, Gabriela Ines. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Investigaciones en Físico-química de Córdoba. Universidad Nacional de Córdoba. Facultad de Ciencias Químicas. Instituto de Investigaciones en Físico-química de Córdoba; ArgentinaFil: Ibañez, Francisco Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; Argentin

Efficient generation of highly crystalline carbon quantum dots via electrooxidation of ethanol for rapid photodegradation of organic dyes

Achieving versatile routes to generate crystalline carbon-based nanostructures has become a fervent pursuit in photocatalysis-related fields. We demonstrate that the direct electrooxidation of ethanol, performed on Ni foam, yields ultra-small and highly crystalline graphene-like structures named carbon quantum dots (CQDs). We perform simulations of various sp2 and sp3 domains in order to understand the optical properties of CQDs by accounting their contribution as absorbance/luminescent centers in the overall optical response. Experiments and simulations reveal that absorbance bands for as-synthesized CQDs are dominated by small sp2 domains comprised of r7 aromatic-rings. After 48 h synthesis, the dispersion transition from yellow to red, exhibiting new and red shifted absorbance bands. Furthermore, fluorescence emission is governed by medium-sized sp 2 domains (with aromatic ring counts r12) and oxygen-containing groups. These oxygen-rich groups within the CQDs, confirmed by FT-IR and XPS, are responsible for the fast photodegradation of organic dyes, with B90% of methylene blue (MB) being degraded within the first 5 min of light exposure. Our work provides crucial insights about the electrochemical synthesis and overall optical properties of carbon nanostructures, while being effective and reliable toward the degradation of contaminants in water